Ph.D. Dissertation

Spin-related Phenomena in
BiSb Topological Insulator – Ferromagnet Bilayers
Nguyen Huynh Duy Khang

Dissertation supervisor
Associate Professor Pham Nam Hai

Department of Electrical and Electronic Engineering
Tokyo Institute of Technology

July, 2019

Thesis Defense Committee:
Associate Professor Pham Nam Hai (Chair)
Professor Shigeki Nakagawa
Professor Takaaki Manaka
Professor Akira Yamada
Professor Masaaki Tanaka
Associate Professor Shinsuke Miyajima

Copyright 2019 by Nguyen Huynh Duy Khang

Contents
Chapter 1: Introduction ................................................................................................. 1
1.1.

Spintronics.......................................................................................................... 1

1.2.

Spintronic memory devices ................................................................................ 5

1.2.1.

Magnetic read heads for hard disk drive (HDD) ........................................ 5

1.2.2.

Magnetic random access memory (MRAM) and Spin-transfer torque(STT) – MRAM ........................................................................................................ 6
1.2.3.

Spin-orbit torque (SOT)-MRAM ................................................................ 9

1.2.4.

Racetrack memory .................................................................................... 11

1.3.

Recent evolution of spintronics: Spin-orbitronics............................................ 13

1.4.

Topological insulator ....................................................................................... 15

1.5.

Motivation ........................................................................................................ 19

1.6.

Thesis outline ................................................................................................... 19

1.7.

Summary .......................................................................................................... 20

Chapter 2: Fundamental Physics of Spin-Orbit Interaction .................................... 26
2.1.

Spin-orbit interaction (SOI) ............................................................................. 26

2.2.

Spin-orbit torque (SOT) ................................................................................... 27

2.2.1.

Spin current ............................................................................................... 27

2.2.2.

The Rashba-Edelstein effect ..................................................................... 29

2.2.3.

The spin Hall effect (SHE) ....................................................................... 31

2.2.4.

Spin orbit torque (SOT) ............................................................................ 33

2.3.

The Dzyaloshinskii-Moriya interaction (DMI) ................................................ 34

2.3.1.

The Dzyaloshinskii-Moriya interaction (DMI)......................................... 34

2.3.2.

Skyrmion ................................................................................................... 36

2.3.3.

Topological Hall effect (THE) .................................................................. 38

2.4.

The unidirectional magnetoresistance (UMR) ................................................. 39

2.4.1.

Magnetoresistance .................................................................................... 39

2.4.2.

The spin Hall magnetoresistance (SMR) .................................................. 40

2.4.3.

The unidirectional magnetoresistance (UMR) .......................................... 41

2.5.

Summary .......................................................................................................... 43

Chapter 3: Sample Preparation and Characterization Techniques ........................ 47
3.1.

Sample preparation........................................................................................... 47

3.1.1.

Molecular beam epitaxy (MBE) ............................................................... 47

3.1.2.

Hall bar device fabrication ........................................................................ 51

3.2.

Characterization techniques ............................................................................. 52

3.2.1.

X-ray diffraction (XRD) measurement ..................................................... 52

3.2.2.

Magnetotransport measurements .............................................................. 53

3.2.3.

Magneto-optical measurement .................................................................. 56

3.2.4.

Magnetization measurement ..................................................................... 57

3.2.5.

Atomic force microscopy (AFM) measurement ....................................... 57

3.3.

Summary .......................................................................................................... 59

Chapter 4: MnGa Thin Films with Perpendicular Magnetic Anisotropy Grown on
BiSb Topological Insulator .......................................................................................... 61

4.1.

Growth of BiSb - MnxGa1-x bilayers by MBE .................................................. 62

4.2.

Crystal structure analysis ................................................................................. 65

4.2.1.

MnxGa1-x crystal orientation on BiSb thin films ....................................... 65

4.2.2.

In-plane crystallographic relationships ..................................................... 65

4.3.

Magnetic properties .......................................................................................... 68

4.3.1.

Magneto-optical properties ....................................................................... 68

4.3.2.

Magnetization properties .......................................................................... 71

4.3.3.

Discussion ................................................................................................. 73

4.4.

Summary .......................................................................................................... 74

Chapter 5: Spin Hall Effect in BiSb Topological Insulator ...................................... 78
5.1.

Thin film growth and crystal structure characterizations ................................. 79

5.2.

Magnetic properties and SOT effect in Bi0.9Sb0.1 - Mn0.6Ga0.4 bilayers ........... 81

5.2.1.

Magnetic properties .................................................................................. 81

5.2.2.

SOT effect ................................................................................................. 81

5.3. Magnetic properties and SOT effect in Bi0.9Sb0.1 - Mn0.45Ga0.55 bilayers ................
84
5.3.1.

Magnetic properties .................................................................................. 84

5.3.2.

Magnetic anisotropy of the tilting magnetic domains in Mn0.45Ga0.55 ...... 87

5.3.3.

SOT effect in Bi0.9Sb0.1 - Mn0.45Ga0.55 bilayers under a titling external

magnetic field ......................................................................................................... 91
5.3.4.

SOT effect in Bi0.9Sb0.1 - Mn0.45Ga0.55 bilayers under an in-plane external

magnetic field ......................................................................................................... 945.3.5.

Spin Hall angle evaluation ........................................................................ 96

5.4.

Magnetization switching by ultra-low current density..................................... 97

5.5.

Comparisons with other spin Hall materials .................................................... 99

5.6.

Summary ........................................................................................................ 101

Chapter 6: Topological Hall Effect and Skyrmions in BiSb - MnGa Bilayers ..... 105
6.1.

Sample preparation......................................................................................... 107

6.2.

Topological Hall effect (THE) ....................................................................... 108

6.3.

Condition of DMI constant Dc and anisotropy constant Ku for generation ofskyrmions .................................................................................................................. 120
6.4.

Summary ........................................................................................................ 121

Chapter 7: Unidirectional Magnetoresistance in GaMnAs - BiSb Bilayers .......... 124
7.1.

Background .................................................................................................... 125

7.2.

Preparation of GaMnAs - BiSb bilayers ........................................................ 129

7.3.

UMR of sample A and its origin .................................................................... 132

7.4.

UMR of sample B and its origin .................................................................... 141

7.5.

Discussion ...................................................................................................... 145

7.6.

Summary ........................................................................................................ 146

Chapter 8: Conclusions and Future Perspectives .................................................... 150
8.1.

Conclusions .................................................................................................... 150

8.2.

Future Perspectives ........................................................................................ 153

Appendix A: Hso obtained by fitting data in Figs. 5.8(a)-5.8(b) in the high in-plane
field range (H > 4 kOe) ............................................................................................... 157

Appendix B: MuMax3 script for micro magnetic simulation................................. 161
Acknowledgments ....................................................................................................... 164
Related publications and presentations .................................................................... 166

1|Page

Chapter 1

Chapter 1

Introduction
This chapter gives a brief overview on the concept of spintronics with its key
technology’s features. Typical spintronic memory devices and their working principles
will be explained, with emphasis on recent developments on spins-orbitronic devices.
Next, topological insulators and BiSb in particular will be presented as one of solutions
for ultralow power spintronic memory devices from the material view point. From thesebackgrounds, the motivation and thesis outline will be presented.

1.1. Spintronics
Just two decades ago, “desktop computer” was still a very strange term inelectronics. Nowadays it has been become very popular but nearly replaced by mobile
devices like smartphones or laptops thank to the dazzling speed of technology
development. In order to make these devices more powerful, shrinking the size with
denser storage capacity and high speed operation have become the main topic ofelectronic industry and academic researchers. The early progress of computing
technology that leads to the Digital Revolution can be traced back to the introduction of
the transistor invented in 1947 by J. Barden, W. Shockley and W. Brattain [1]. Becauseof its huge impact in development of the semiconductor industry, they received the Nobel
Prize in Physics in 1956. Since then, the number of transistors that would be able to fit on
a dense integrated circuit has doubled every 18 months, and it is known as the Moore’s
law [2, 3]. However, continuous progress that pushed the electrical circuits to the nanoscale regime has resulted in huge electric energy leakage. The concept of electron’stransportation has begun to pose serious problems and simply packing additional features

2|Page

Chapter 1

into the same area to improve performance of circuits has become more and more difficult.
To further decrease the size of the devices and continuously enhance their performance
while suppressing the energy leakage problem, spintronics comes into play [4].
The spintronics or spin electronics can be known as combination between electriccharge and its intrinsic form of angular momentum called spin. In Figure 1.1, the conceptof spintronics is described as overlap between electronic engineering (electric charge) andmagnetic engineering (spin). Instead of using the “existence’ or “absence” of the electriccharge, the bit “0” and “1” of the binary data can be expressed by up-spin () or downspin (). Because of the unchanged state of spin under the loss of supplied power andadditional functionality that can be controlled by external magnetic field, spintronics
exhibit unique advantages expected for low power consumption, non-volatility and highspeed’s applications [5, 6].

Figure 1.1: The concept of spintronics.

The pioneering work in spintronics can be considered starting from understandingof spin-polarized transport at low temperature in ferromagnetic metals investigated by
Nevill Francis Mott [7, 8]. They observed an unusual behavior of resistance due to theun-mixing scattering process of the majority and minority spin, which was further
explained as two different spin projections in the two-current model proposed by I. A.

3|Page

Chapter 1

Campbell and A. Fert [9]. Then, the giant magnetoresistance (GMR) effect from theelectrical transport measurements of Fe/Cr multilayers system was discovered by P.
Grunberg and A. Fert [10]. In multilayers consisting of two or more ferromagnetic (FM)layers separated by a non-magnetic (NM) layer, the GMR arises from spin-dependent
scattering of conduction electrons at the interface of FM/NM multilayers and in the bulkof FM that results in the difference between low and high resistance, when the FM layer
magnetization’s direction of the two FM layers are parallel and antiparallel to each other,respectively. Shortly after, it was realized that GMR can be enhanced by driving thecurrent perpendicular to the film plane, as shown in Fig. 1.2.

Figure 1.2: Schematic illustrates of (a) Parallel state (P) and (b) Anti-parallel state in
GMR effect.

The GMR effect has not only highlighted the critical role of electron spins inelectrical transport but also impressively boosted the sensitivity of GMR based magnetic
field sensors. Thanks to its high performance in magnetic field’s detection, P. Grunberg
and A. Fert were honored with a Nobel Prize in Physics in 2007, and there has been ahuge effort to deeply understand the GMR effect in order to further enhance its magnitude[11, 12, 13, 14].

4|Page

Chapter 1

Figure 1.3: Schematic illustrates of (a) Parallel state (P) and (b) Anti-parallel state in
TMR effect. Reproduced with permission [15].

In 1975, Julliere experimentally discovered the tunneling magnetoresistance(TMR) effect in a three-layer structure where an insulator layer is used for separating two
ferromagnetic layers instead of a NM layer as in the case of GMR. This structure is called
magnetic tunnel junction (MTJ), and the TMR effect is the result of a spin polarized
current tunneling through the insulator layer, as shown in Fig. 1.3. The electron spins in
one electrode can only tunnel to the electronic states with same spin orientation in the
opposite electrode. Depending on the magnetization configuration (parallel state or antiparallel state), the MTJ resistance can be changed as the consequence of spin polarizedtunneling. However, because of its small magnitude at the time when spintronics is
immature, TMR effect needs over 15 year to get attention and finally matures withrealization of a giant TMR ratio over 400% at room temperature in Co/MgO/Co multiple
layers in 2006 [15].
Because of the great potential and impact of GMR and TMR, over three decades,huge efforts have been spent to apply them to memory applications [16-28].,

17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28].

5|Page

Chapter 1

1.2. Spintronic memory devices
1.2.1.

Magnetic read heads for hard disk drive (HDD)

Since 2006, the TMR effect has played a major role in implementation of the spin
degree of freedom to spintronic devices, and the read head of hard disk drives is an
example of great success. Figure 1.4 illustrates the MTJ read head in an HDD. The readhead structure includes a pinned layer, whose magnetic direction is constrained by anexchange bias field arising from the interface with an antiferromagnetic layer. By
choosing a particular metallic interlayer of adequate thickness, the magnetic moment of
the free layer is always antiferromagnetically coupled with that of the pinned layer. Underinfluence of magnetic fields associated with the magnetic domains in the recording media,
the free layer of the MTJ can change its magnetization and results in the change of thedevice resistance due to the TMR effect.
Since the magnetic domain of a single bit in HDD can become very small, at present
the density of surface recording is reaching 1 Tbit/inch2 for the area per bit of 2525nm2[29]. On the other hand, because of extremely small magnetic flux leaking from a small
domain in high density HDD, magnetic read heads with higher sensitivity need to be
developed, when HDD with a surface recording density exceeding 1 Tbit/cm 2 isconsidered. There have been a lot of investigations in material engineering with high spinpolarization ferromagnets such as Fe, Co and CoFeB in order to increase the sensitivity
when influenced by a small magnetic flux [15]. However, TMR poses the problem with
its too high resistivity which increases Johnson and shot noise as well as limits the data
rate [15]. Recently, MgO-based MTJ as shown in Fig. 1.4(b) has become a great solutionfor HDD read head, because it can achieve very high TMR ratio comparing with otherkind of barrier layers, while device resistance can be controlled by optimizing the barrier
thickness.

6|Page

Chapter 1

Figure 1.4: (a) MTJ read head in an HDD. The free layer of MTJ can freely rotate its
magnetization to response to the stray fields associated with magnetic domains in therecording media. (b) Reported room-temperature TMR ratios over the past decade for AlOxbased MTJ and MgO-based MTJ. Reproduced with permission [15].

1.2.2.

Magnetic random access memory (MRAM) and Spin-transfer

torque (STT) – MRAM
Magnetic random access memory (MRAM), a type of memory with non-volatility,
high speed and high durability is another well-known application of the TMR effect.
Comparing with volatile memories, such as the static random access memory (SRAM)
and dynamic random access memory (DRAM), MRAM inherits the unique characteristicof non-volatile memories that they do not need the power to maintain the data bits. Figure
1.4(a) visualizes the mechanism of MRAM. Instead of using magnetic domains to store
the information like HDD, MRAM uses the free layer to record each data bit with twostates (parallel or anti-parallel) depending on the relative direction between its
magnetization and that of the reference layer. The reading process is achieved bymeasuring the device resistance. In the first generation of MRAM (toggle MRAM), thewriting process utilizes the Oersted field generated by a nearby current. However, thiswriting method requires a large current that does not scale with the MTJ size, limiting the
bit density of toggle MRAM.

7|Page

Chapter 1

In 1996, Slonczewski and Berger independently predicted that a spin polarized
current can induce a torque on the magnetization of the ferromagnetic layer of MTJ [20,21] that can be used for magnetization switching. This phenomena is named as the spintransfer torque (STT) with very promising implications. Three years after the theoreticalprediction, STT effect has been experimentally demonstrated by Tsoi et al., Myers et al.
and Wegrowe et al for the first time [30, 31, 32]. With this discovery, MRAM was pushed
to the next generation where the magnetization of the recording layer can be manipulated
by a spin polarized current, instead of an Oersted field. As illustrated in Fig. 1.4(b), whena charge current is passed through the MTJ, it will be polarized by the fixed layer tobecome the spin-polarized current and injected into the free layer to switch themagnetization of the free layer. STT-MRAM has evolved as the second generation
MRAM.

Figure 1.4: Schematic illustrates of (a) toggle magnetoresistive random access memory(MRAM) and (b) spin transfer torque (STT) – MRAM.

Although STT-MRAM shows the big advantage in higher bit density which canreach gigabits per chip storage capacity with lower writing power than that of toggle
MRAM, the writing current and writing energy of MRAM is still worse than conventional

8|Page

Chapter 1

volatile memory like SRAM or DRAM by one order of magnitude, as shown in Table 1.1.
The large current in the writing process can lead to the breakdown of the tunnel barrieroxide. The read disturbance or accident switching of the magnetic states can also happen
as the result of the read and write current path’s coupling. In addition, high writing current
requires large driving transistors, which makes it difficult to further increase the bit
density of MRAM [23].
Table 1.1: Read latency (ns), write latency (ns), write energy (nJ) and device size (mm2)of STT-MRAM, SRAM and DRAM.
STT-MRAM

SRAM

DRAM

Read latency (ns)

3.1

4.5

4.3

Write latency (ns)

11.2

4.5

4.3

Write Energy (nJ)

20.3

2.2

1.8

Size (mm2)

16.4

80.4

37.4

The reason of the high writing current in STT-MRAM is due to the limitation of thespin-polarization P of the reference layer. As illustrated in Fig. 1.5(a), the spin current
generated by the injected charge current IC is given by

I S  ( / 2e) PI C ,
where

(1.1)

is the reduced Plank constant, and e is the elementary charge.

The fact that P  1 limits the amount of spin current IS generated by a given IC andmakes it difficult to reduce the writing current. For the next generation of magnetic
memory that can compete with commercial DRAM, MRAM must operate with shorter
write latency, lower power consumption and higher bit density.

9|Page

1.2.3.

Chapter 1

Spin-orbit torque (SOT)-MRAM

Recently, spin-orbit torque (SOT)-MRAM has emerged as an alternative magnetic
memory which can overcome the big disadvantages of STT-MRAM. In SOT-MRAM, aspin Hall layer is in contact with the free magnetic layer. As illustrated in Fig. 1.5 (b), a
charge current flowing in the spin Hall layer can generate a pure spin current
perpendicular to the interface by the spin Hall effect. This pure spin current can exerts aspin torque (so called spin-orbit torque) on the free layer and switch its magnetization(this effect will be explained further in the chapter 2). The spin current generated by thisway is given by

I S  ( / 2e)( L / t )SH I C(1.2)

where L is the MTJ size, t the thickness of the spin source layer, and  SH is the spin Hall
angle.
Since L/t is about 10 in realistic MTJs, SOT switching may be more effective than
STT switching if SH > 0.1.

Figure 1.5: Schematic illustrates switching mechanism in writing process of (a) STTMRAM and (b) SOT-MRAM.

The spin dynamics in STT-MRAM as well as SOT-MRAM is described by the Landau-

10 | P a g e

Chapter 1

Liftshitz-Gilbert equation [33]mm  m  H eff   m   (m (  m))
t
t

(1.3)

where m is free layer’s magnetization vector, Heff is the sum of the anisotropy field, thedemagnetizing field and the external field,  is the damping constant,  is the spin torquecoefficient and  is the spin polarization.
In the right hand side, the first term presents for precession of m under Heff, thesecond term stand for the damping torque, the final term is the spin torque. In the case of
STT-MRAM, the spin current injected into the free layer has the spin polarization in thesame direction with the free layer’s magnetization ( || m). As the results, at the beginning
the spin torque is nearly zero, and the write speed is slow (~ 10 ns at acceptable current
densities). In contrast, in the case of SOT-MRAM, the spin polarization of the pure spincurrent injected into the free layer is perpendicular to the magnetization. Thus, the spin
torque gets maximum value, and the writing speed of SOT-RAM is at least 20 time larger
than that of STT-MRAM (200-500 ps). Inheriting both the low write current and highspeed, SOT-MRAM can significantly decrease the writing energy.
Moreover, SOT-MRAM has separated reading path and writing path as shown in
Fig. 1.6. The writing current does not flow through the MTJ in the writing process, andthis scheme can drastically enhance the MTJ’s reliability. Moreover, because of the
reduced charge current in the writing process, SOT-MRAM requires much smaller
driving transistor and can increase the bit density. With these advantages, SOT-MRAM
has become very attractive as the promising candidate for the third generation MRAM
with fast writing, low writing energy and high bit density.

11 | P a g e

Chapter 1

Figure 1.6: Schematic describing the read and write path in (a) STT-MRAM and (b)SOT-MRAM. Reproduced with permission [23].

1.2.4.

Racetrack memory

In 2008, Parkin et al. proposed a new design of magnetic memory where
information can be stored in magnetic domains of U-shaped nanowires, as shown in Fig.
1.7. This memory is called racetrack memory. The position of magnetic domains inracetrack memory is controlled by a pulse current injected from one terminal of the Ushaped nanowire. These magnetic domains can be read out by a MTJ device, while thewriting process can be achieved by using STT or SOT in a similar way to STT-MRAM
or SOT-MRAM, respectively. Its write and read latency can be less than a nano-second.
Comparing with HDD, racetrack memory shows higher performance and greater
reliability, since it does not rely on the mechanical mechanism.
One unique characteristic of racetrack memory is its 3D structure. A racetrack
memory can use hundreds of millions of U-shaped nanowires arranged vertically like aforest in a very small area size [27]. This characteristic allows racetrack memory to store
a vast amounts of data, and makes racetrack memory become a very attractive memory.
As for today, intensive research studies are being carry out to further improve the device’s
operating speed.

12 | P a g e

Chapter 1

Figure 1.7: Schematic of racetrack memory in an array of U-shaped magnetic
nanowires. Reproduced with permission [28].

13 | P a g e

Chapter 1

1.3. Recent evolution of spintronics: Spin-orbitronics
Figure 1.8 summarizes the major achievements in thin film magnetism andspintronics researches in the last decades. Once can see that spintronics is not restricted
to the GMR or TMR’s concept discovered by previous pioneers, but this field has beensteadily evolving in a new road thank to innovation in spin-orbit interaction (SOI) related
phenomena. These phenomena can change direction of spintronics to a new line called
spin-orbitronics. Instead of using the exchange interaction between conduction electron
spin and local spin in magnetic material to create spin polarization, the spin-orbitronics
exploits SOI in paramagnetic materials to generate or even detect the spin-polarized
current. This idea has expanded spintronics to much broader spectra where spin devices
employ not only magnetic materials but also nonmagnetic materials with strong SOI.
The Rashba effect, the spin Hall effect (SHE) or the helical surface states in
topological insulators (TIs) is typical examples of SOI. In 1960, the Rashba effect was
discovered in materials with broken inversion symmetry and uncompensated electricfields at the interface between two different materials. This leaded to new ideas of spincurrent generation by Edelstein [34] (thus called Rashba-Edelstein effect or REE forshort) and experimentally confirmed in GaMnAs [35] by observing a field-like torque.
Similarly, an antidamping-like torque in Pt/Co thin films [36] was reported as an evidenceof a pure spin current generated by SHE. Comparing with P < 1 as the limitation of STT,
both REE and SHE can generate spin currents more efficiently and can be directly applied
to SOT-MRAM [36]. Because of these advantages, intense efforts from different groups
have been carried out to understand SOI-related phenomena in various materials.
Historically, SHE was first observed in 2004 by Y. K. Kato in a GaAs semiconductor
layer [37]. Since then, numerous researches on SHE and related phenomena have been

14 | P a g e

Chapter 1

published for different kind of materials, such as heavy metal (Pt [36], Ta [38] or W [39]),anti-ferromagnet (PtMn [40] or IrMn [41]) and even oxidized material like W(O) [42].
SOT generated by REE or SHE can also play a central role in domain wall motion
in racetrack memory by combining the magnetic layer with another material showing
strong SOI. This can enhance the operating speed and further reduce the driving current
density of the racetrack memory. There have been many experiments demonstrating thisplausible structure in different kind of bilayers [43, 44, 45].
The chiral domain walls from Dzyaloshinskii-Moriya interaction (DMI) or themagnetic skyrmions [46] is another example of SOI. Because skyrmions (whose concept
will be presented in more details in the chapter 2) have small size and ultra-low driven
current density, they have become extremely popular recently for the next generation of
racetrack memory [47].

15 | P a g e

Chapter 1

Figure 1.8: Summary of major achievements in the evolution of the thin film
magnetism and spintronics research in the last decades. Reproduced with permission[48].

1.4. Topological insulator
Recently, topological insulator (TIs) have emerged as exotic materials possessing
huge SOI. TIs are quantum materials with a band gap just like normal insulators but with
topological protected conducting surface/edge states. Because their electrons in thevalence band and conducting band are under a strong SOI, the conduction band bottom
may become lower than the valence band top. This is called invert band structure.
Although the inside of TI materials is similar to normal insulators, states related to the16 | P a g e

Chapter 1

invert band structure are formed on the edges/surfaces for 2D/3D TIs. These states permit
the emergence of a pair of electrical currents flowing with reverse direction and spin. Thisis called helicity and can be imaged as two-way highway where each spin flows in one
direction and back scattering is prohibited, as illustrated in Fig. 1.9(b) and Fig. 1.9(c).
The helical spin polarization of topological surface states on the surface Brillouin zone of
3D TIs with the electron spin orthogonal to direction of their motion is called spinmomentum locking, as shown in Fig. 1.9(d).

Figure 1.9: (a) Energy dispersion of the spin non-degenerate edge state of a 2D TI
forming a 1D Dirac cone. (b) Schematic real-space picture of the 1D helical edge sateof a 2D TI. (c) Schematic real-space picture of the 2D helical surface state of 3D TI.
(d) 2D Dirac cone. Reproduced with permission [49].

In 2007, the spin polarized topological edge states in 2D TIs was first observed in
HgTe-based quantum wells by M. König [50]. 2D surface states of 3D TI were then17 | P a g e

Chapter 1

observed directly using angle resolve photoemission spectroscopy (ARPES). Importantly,
3D TIs feature very large SHE. Giant spin Hall angle in TIs was observed in Bi2Se3 [51]and (Bi0.5Sb0.5)2Te3 [52]. Their spin Hall angle is at least one order of magnitude larger
than that of heavy metals, anti-ferromagnets or oxidized materials. That means TIs canprovide much higher charge-to-spin conversion efficient than regular spin source
materials due to their strong SOI. Figure 1.10(a) compares the power consumption of
SOT switching by using TI and heavy metal as the spin source. SOT switching based on
TIs can reduce the power consumption down to less than 25%. These results make TI
become a very hot topic for spintronic applications.
Unfortunately, in spintronics application, TIs have a problem relating to theirinsulating nature. Because of their large band-gap and low carrier mobility, theconductivity σ of those TIs is limited to ~ 104 Ω-1m-1, which is much lower than that oftypical metallic ferromagnets (~ 6×105 Ω-1m-1) used in MRAM. This causes a serious
problem for TIs as spin Hall materials. As illustrated in Figure 1.10(b), when attached toa metallic ferromagnet, most of the charge current is shunted through the recoding layerand does not contribute to generation of pure spin current in the spin Hall layer. Exploring
new TI materials with both high conductivity and large spin Hall angle has been required.

Figure 1.10: Normalized power consumption (with Ta set to be unity) for SOT
switching using (BiSb)2Te3, Bi2Se3, Pt and Ta. Reproduced with permission [53]. (b)The shunting effect due to low electrical conductivity of TIs.

18 | P a g e

Chapter 1

BiSb, a conductive TI
Bi1-xSbx (0.07  x  0.22) is a very narrow-gap TI [54]. Thanks to its high carrier
mobility (~104 cmV-1s-1), its bulk conductivity is as high as 4×105~6.4×105 Ω-1m-1,
compatible to other metallic materials used in realistic MRAM, as shown in Fig. 1.11(a).
Recently, I and co-workers have developed epitaxial growth technique for high quality
BiSb thin films using molecular beam epitaxy (MBE) [55] and obtained 4×105~6×105
Ω-1m-1for BiSb thin films thicker than 80 nm, and =1×105~4×105 Ω-1m-1(average2.5×105 Ω-1m-1) for BiSb thin films thinner than 25 nm in the TI region (0.07 x  0.22).
On the other hand, BiSb shows strong SOI with topologically protected surface
states as confirmed by ARPES [56, 57, 58] and shown in Fig. 1.11(b). These surface
states were also confirmed by magneto-transport measurements [59, 60]. This promises
the high charge-to-spin conversion efficient. From these reasons, BiSb emerges as thevery promising candidate for spintronic applications.

Figure 1.11: (a) Electrical conductivity at 270 K of various Bi1-xSbx samples withdifferent Sb concentration and thickness. (b) Spin-integrated ARPES intensity map of
the surface state of Bi0.91Sb0.09 at EF. Arrows point in the measured direction of the spin.
Reproduced with permission [55, 56].

19 | P a g e

Chapter 1

1.5. Motivation
Because of the great interest of SOI-related effects in BiSb, it is my motivation to
study various spin-related phenomena, including the SHE, the DMI and the unidirectional
magnetoresistance (UMR), in BiSb-ferromagnet bilayers, as shown in Fig. 1. 12. These
researches will not only provide useful information to deeply understand SOI-related
effects in TIs but also open the pathway to improve the efficiency of spintronic memoryand devices.

Figure 1.12: Spin-related phenomena in BiSb-ferromagnet bilayers and theirapplications to mainstream spintronic devices.

1.6. Thesis outline
My thesis is divided to 8 chapters.

20 | P a g e

Chapter 1

Chapter 1 introduces the thesis background on spintronics in general, spintronic
memory devices, recent evolution in spin-orbitronics, and topological insulators withemphasis on BiSb in particular. Based on these backgrounds, the motivation and thesis
outline are described.
Chapter 2 presents the fundamental physics behind SOI-related phenomena, which
are the main topic in this study.
Chapter 3 describes in details the experimental techniques used for sample
preparation and characterization.
Chapter 4 focuses on the growth and characterization of MnGa thin films withperpendicular magnetic anisotropy on BiSb.
Chapter 5 describes the experiment results of the SHE in BiSb/MnGa bilayers.
Chapter 6 focuses on field-free ground-state skyrmions in BiSb/MnGa bilayers atroom temperature revealed by the topological Hall effect (THE).
Chapter 7 presents the large UMR and its mechanism in GaMnAs/BiSb bilayers.
Chapter 8 summarizes the main results of this thesis and outlooks for future
spintronic applications.

1.7. Summary
As the results of recent rapid developments in spintronics memory devices, spinorbitronics appears as a novel concept that utilizes the SOI in spintronic memory devices.
This makes spintronics not be restricted to conventional concepts of GMR, TMR or STT,
and expand spintronics to much broader spectra where spin devices employ not only
magnetic materials but also nonmagnetic materials with large SOI. Thus, efficient
generation of pure spin current can be easily achieved by employing suitable spin source
materials. As a consequence, spintronics researches have been shifted toward exploring21 | P a g e

Chapter 1

the new materials with strong SOI and understanding their SOI-related effects. TIs and
BiSb in particular appear as one of promising candidates for high efficient pure spincurrent source. Toward novel spintronic applications, further understanding of spinrelated phenomena in bilayers of BiSb/ ferromagnetic material is the main purpose of thisstudy.

22 | P a g e

Chapter 1

References
1. J. Bardeen, and W. H. Brattain, Phys. Rev. 74, 230 (1948).
2. G. E. Moore, Proc. IEEE 86, 82 (1998).
3. G. E. Moore, IEEE S. S. Cir. Soc. News. 20, 11 (2006).
4. S. A. Wolf, D. D. Awschalom, R. A. Buhrman, J. M. Daughton, S. von Molnár, M. L.
Roukes, A. Y. Chtchelkanova, and D. M. Treger, Science 294, 1488 (2001).
5. Akinaga, and H. Ohno, IEEE Trans. Nanotech. 1, 19 (2002).
6. I. Žutić, J. Fabian, and S. D. Sarma, Rev. Mod. Phys. 76, 323 (2004).
7. N. F. Mott, and H. H. Wills. Proc. R. Soc. A Math. Phys. Eng. Sci. 153, 699 (1936).
8. N. F. Mott. Proc. R. Soc. A Math. Phys. Eng. Sci. 156, 368 (1936).
9. I. A. Campbell, A. Fert, and A. R. Pomeroy, Philos. Mag. 15, 977 (1967).
10. M. N. Baibich, J. M. Broto, A. Fert, F. Nguyen Van Dau, F. Petroff, P. Etienne, G.
Creuzet, A. Friederich, and J. Chazelas, Phys. Rev. Lett. 61, 2472 (1988).
11. Robert, E. Camley, and J. Barna´s, Phys. Rev. Lett. 63, 664 (1989).
12. T. Valet, and A. Fert, Phys. Rev. B 48, 7099 (1993).
13. B. Dieny, J. Magn. Magn. Mater. 136, 335 (1994).
14. Randolph, Q. Hood, and L. M. Falicov, Phys. Rev. B 46, 8287 (1992).
15. J. G. Zhu, and C. Park, Materialstoday 9, 36 (2006).
16. K. Ono, N. Ohshima, K. Goto, H. Yamamoto, T. Morita, K. Kinoshita, T. Ishijima,and H. Toyoda, Jpn. J. Appl. Phys. 44, L1442 (2005).
17. K. Tsunekawa, D.D. Djayaprawira, S. Yuasa, M. Nagai, H. Maehara, S. Yamagata,
E. Okada, N. Watanabe, Y. Suzuki, K. Ando, IEEE Trans. Magn. 42, 103 (2006).
18. B.N. Engel, N.D. Rizzo, J. Janesky, J.M. Slaughter, R. Dave, M. DeHerrera, M.
Durlam, S. Tehrani, IEEE Trans. Nano. 1, 32 (2002).
19. S. Tehrani, J.M. Slaughter, M. Deherrera, B.N. Engel, N.D. Rizzo, J. Salter,23 | P a g e

Chapter 1

M. Durlam, R.W. Dave, J. Janesky, B. Butcher, K. Smith, G. Grynkewich, Proc. IEEE91, 703 (2003).
20. J. C. Slonczewski, J. Magn. Magn. Mater. 159, L1 (1996).
21. L. Berger, Phys. Rev. B 54, 9353 (1996).
22. E. B. Myers1, D. C. Ralph, J. A. Katine, R. N. Louie, and R. A. Buhrman, Science
285, 867 (1999).
23. R. Ramaswamy, J. M. Lee, K. Cai, and H. Yang, Appl. Phys. Rev. 5, 031107 (2018).
24. S. V. Aradhya, G. E. Rowlands, J. Oh, D. C. Ralph, and R. A. Buhrman, Nano Lett.
16, 5987 (2016).
25. K. Garello, C. O. Avci, I. M. Miron, M. Baumgartner, A. Ghosh, S. Auffret, O. Boulle,
G. Gaudin, and P. Gambardella, Appl. Phys. Lett. 105, 212402 (2014).
26. S. H. Yang, K. S. Ryu, and S. Parkin, Nat. Nanotechnol. 10, 221 (2015).
27. S. S. P. Parkin, M. Hayashi, L. Thomas, Science 320, 190 (2015)28. J. S. Meena, S. M. Sze, U. Chand, and T. Y. Tseng, Nano. Re. Lett. 9, 526 (2014).
29. Y. Ando, J. J. Appl. Phys. 54, 070101 (2015).
30. M. Tsoi, A. G. M. Jansen, J. Bass, W. C. Chiang, M. Seck, V. Tsoi, and P. Wyder,Phys. Rev. Lett. 80, 4281 (1998).
31. J. E. Wegrove, D. Kelly, P. Guitienne, Y. Jaccard, and J. P. Ansermet, Europhys. Lett.
45, 626 (1999).
32. E. B. Myers, D. C. Ralph, J. A. Katine, R. N. Louie, and R. A. Buhrman, Science 285,
867 (1999).
33. T. L. Gilbert, IEEE Tran. Magn. 40, 3443 (2004).
34. V. M. Edelstein, S. S. Comm. 73, 233 (1990).
35. A. Chernyshov, M. Overby, X. Liu, J. K. Furdyna, Y. L. Geller, and L. P, Nat. Phys.,
5, 656 (2009).

24 | P a g e

Chapter 1

36. I. M. Miron, K. Garello, G. Gaudin, P. J. Zermatten, M. V. Costache, S. Auffret, S.
Bandiera, B. Rodmacq, A. Schuhl, and P. Gambardella, Nature 476, 189 (2011).
37. Y. K. Kato, R. C. Myers, A. C. Gossard, and D. D. Awschalom, Science 306, 1910
(2004).
38. L. Liu1, C. F. Pai, Y. Li, H. W. Tseng, D. C. Ralph, R. A. Buhrman, Science 336,
555(2012).
39. Q. Hao, and Xiao, Phys. Rev. Appl. 3, 034009 (2015).
40. S. Fukami, C. Zhang, S. DuttaGupta, A. Kurenkov, H. Ohno, Nat. Mater. 15, 535(2016).
41. Y. W. Oh, S. C. Baek, Y. M. Kim, H. Y. Lee, K. D. Lee, C. G. Yang, E. S. Park, K.
S. Lee, K. W. Kim, G. Go, J. R. Jeong, B. C. Min, G.W. Lee, K. J. Lee, B. G. Park, Nat.
Tech. 11, 878 (2016).
42. K. U. Demasius, T. Phung, W. Zhang, B. P. Hughes, S. H. Yang, A. Kellock, W. Han,
A. Pushp, and S. S. P. Parkin, Nat. Commun. 7, 10644 (2016)
43. K. S. Ryu, L. Thomas, S. H. Yang, and S. Parkin. Nat. Nanotech. 8, 527 (2013).
44. S. Emori, U. Bauer, S. M. Ahn, E. Martinez, and G. S. D. Beach. Nature Mater. 2,
611 (2013).
45. J. Torrejon, J. Kim, J. Sinha, S. Mitani, M. Hayashi, M. Yamanouchi, and H. Ohno,Nat. Commun., 5, 2014.
46. S. Mühlbauer, B. Binz, F. Jonietz1, C. Pfleiderer, A. Rosch, A. Neubauer, R. Georgii,
P. Böni, Science 323, 915 (2009).
47. W. Jiang, G. Chen, K. Liu, J. Zang, S. G.E. Velthuis, A. Hoffmann, Phys. Rep. 704,
1 (2017).
48. C. O. Avci, “Current-induced effects in ferromagnetic heterostructures due to spinorbit coupling”, PhD thesis, 7 (2015).

25 | P a g e

Chapter 1

49. Y. Ando, J. Phys. Soc. J. 82, 102001 (2013).
50. M. König, S. Wiedmann, C. Brüne, A. Roth, H. Buhmann, L. W. Molenkamp, X. L.
Qi, and S. C. Zhang, Science 318, 766 (2007).
51. A. R. Mellnik, J. S. Lee, A. Richardella, J. L. Grab, P. J. Mintun, M. H. Fischer, A.
Vaezi, A. Manchon, E.-A. Kim, N. Samarth, and D. C. Ralph, Nature 511, 449 (2014).
52. Y. Fan, P. Upadhyaya, X. Kou, M. Lang, S. Takei, Z. Wang, J. Tang, L. He, L. T.
Chang, M. Montazeri, G. Yu, W. Jiang, T. Nie, R. N. Schwartz, Y. Tserkovnyak, and K.
L. Wang, Nat. Mater. 13, 699 (2014).
53. J. Han, A. Richardella, S. A. Siddiqui, J. Finley, N. Samarth, and L. Liu, Phys. Rev.
Lett. 119, 077702 (2017).
54. J. C. Y. Teo, L. Fu, C. L. Kane, Phys. Rev. B 78, 045426 (2008).
55. Y. Ueda, N. H. D. Khang, K. Yao, P. N. Hai, Appl. Phys. Lett. 110, 062401 (2017).
56. D. Hsieh, Y. Xia, L. Wray, D. Qian, A. Pal, J. H. Dil, J. Osterwalder, F. Meier, G.
Bihlmayer, C. L. Kane, Y. S. Hor, R. J. Cava, and M. Z. Hasan, Science 323, 919 (2009).
57. T. Hirahara, Y. Sakamoto, Y. Saisyu, H. Miyazaki, S. Kimura, T. Okuda, I. Matsuda,
Phys. Rev. B. 81, 165422 (2010).
58. A. Nishide, A. A. Taskin, Y. Takeichi, T. Okuda, A. Kakizaki, T. Hirahara, K.
Nakatsuji, F. Komori, Y. Ando, and I. Matsuda, Phys. Rev. B 81, 041309(R) (2010).
59. A. A. Taskin, and Y. Ando, Phys. Rev. B 80, 085303 (2009).
60. A. A. Taskin, K. Segawa, and Y. Ando, Phys. Rev. B 82, 121302 (R) (2010).

26 | P a g e

Chapter 2

Chapter 2

Fundamental Physics of Spin-Orbit Interaction
In this chapter, overview of spin-orbit interaction will be presented as the key
concept of many interesting phenomena observed in spintronics. As consequences ofspin-orbit interaction, the spin Hall effect, the Dzyaloshinskii-Moriya interaction and theunidirectional magnetoresistance will be explained.

2.1. Spin-orbit interaction (SOI)
Spin-orbit interaction (SOI), also called as spin-orbit effect or spin-orbit coupling,is the concept describing the interaction between a particle’s intrinsic angular momentum(spin) and its orbital degree of freedom. In the atomic regime, SOI is described in the
picture of an electron motion around nucleus and its self-rotation. The orbiting of anelectron around nucleus in the laboratory frame can be transferred to the orbiting of
nucleus around the electron in the electron rest frame. As the results, the magnetic field
B appearing in the rest frame of the electron can be expressed asB0 Zev4 r 2(2.1)

where 0 is the permeability of free space, Ze and v are the charge and velocity of nucleus,
respectively and r is the radius of nucleus motion. In the Lorentz transformation, theequation (2.1) is reformed as [1]

B

1
Ev
2
2 c 1  v2 / c2

(2.2)

where E is electric field, c is light velocity in free space.
Because the electron has a spin magnetic moment , it can interact with themagnetic field rising in the electron rest frame, and its energy Einter is written as

27 | P a g e

Chapter 2

Einter  .B

(2.3)

This type of interaction is named as SOI. In the quantum mechanical description for theorbital angular momentum (L) and spin angular momentum (S) of the electron, SOI canbe described by the following Pauli spin-orbit coupling term [2]

H SO   L.S ,(2.4)

where  is the SOC energy, L̂ and Ŝ are the dimensionless operators of orbital angularmomentum and spin angular momentum of the electron, respectively. As the consequenceof SOI, the orbital degree of freedom can couple with the electron spin.

Figure 2.1: Schematic illustrations of (a) an electron orbiting around nucleus in the
nucleus rest frame and (b) the nucleus orbiting around the electron in the electron rest
frame. The electron in the rest frame of the electron feels the magnetic field B due tocyclic motion of the nucleus, while its spin is locked. This gives rise to the spin-orbit
interaction.

2.2. Spin-orbit torque (SOT)
2.2.1.

Spin current

28 | P a g e

Chapter 2

Figure 2.2 illustrates one of the basic concepts of spintronics, the spin current. The
flow of electrons will be merely a charge current, if their different directions of spins are
mixed up and cannot be distinguished (Fig. 2.2(a)). However, there are situations that one
spin population is larger than the other. The Figure 2.2(b) illustrates this kind of
circumstance that the density of spin-up electrons is higher than the density of spin-down
electrons. In this case, the charge current is accompanied by a spin current called “spinpolarized current”. The net spin current will be the current of spin-up minus the currentof spin-down.
More interestingly, Figure 2.2(c) shows a special case of spin current that the spinup current flows to the right, while the spin-down current flows to the left. This situation
makes the charge current, which is the total current of spin-up and spin-down in opposite
direction, zero. In contrast, the net spin current is the sum of spin-up and spin-downcurrent. This is called “pure spin current” [3] and poses new ideas about creating a spincurrent without a charge current.

Figure 2.2: Schematic illustrations of (a) charge current, (b) spin-polarized current and(c) pure spin current.

So far, spin injection is a particular example of spin-polarized current generated bypassing a charge current through a ferromagnetic layer, and can be directly applied to
STT-MRAM. However, spin injection is limited by the maximum spin polarization P =29 | P a g e

Chapter 2

1 of the ferromagnetic layer. Recently, the Rashba-Edelstein effect or the spin Hall effectemerge as new ways to generate pure spin current with improved charge-to-spin
conversion efficiency.

2.2.2.

The Rashba-Edelstein effect

Under a broken inversion symmetry at the interface of NM/FM as shown in Fig.
2.3(a), an uncompensated electric field E appears along the z axis, and a conducting
electron travelling with velocity v will experience an effective magnetic field B in the
direction Ev.

B   (v  E ) / c 2(2.5)

where   1/ 1  v 2 / c 2 is the Lorentz factor. This field will couple to the electron spin,
and its interaction can be expressed by the following Hamiltonian

HR 

R

( E  p)(2.6)

where  R is the Rashba parameter, p̂ and ˆ are the momentum operator and electron
spin operator, respectively. This type of interaction is named as the Rashba effect [4]originating from an interfacial SOI [5, 6, 7]. Under this situation, an in-plane current willbe spin-polarized with the spin-polarization perpendicular to the current direction. Thisis called Rashba-Edelstein effect (REE) (Fig. 2.4).

30 | P a g e

Chapter 2

Figure 2.3: Schematic illustrations of (a) the Rashba-Edelstein effect and (b) the spin
Hall effect. Reproduced with permission [8].

Figure 2.4 shows the spin redistribution under (a) the Rashba effect and (b) the
Rashba-Edelstein effect with an electric current. The Rashba-Edelstein effect gives a nonequilibrium k-dependent spin polarization as the results of the electric field and scatteringthat leads to redistribution of carriers on the Fermi surface. The in-plane spin polarizationis perpendicular to the direction of the charge current [9].

Figure 2.4: Schematic illustrates the microscopic picture of (a) the Rashba effect and(b) the Rashba-Edelstein effect. Reproduced with permission [9]31 | P a g e

2.2.3.

Chapter 2

The spin Hall effect (SHE)

While the Rashba-Edelstein effect mainly exploits the interface SOI, a pure spincurrent can also arises inside NM thank to the bulk SOI. This effect is known as the spin
Hall effect (SHE) with two main mechanisms: extrinsic mechanism (skew and side-jump
scattering) and intrinsic mechanism (Berry phase of the band structure) [10, 11, 12].
Figure 2.3(b) illustrates the spin current generated from the spin Hall effect of NM. The
direction of the spin polarization is perpendicular to the direction of the charge current.
The extrinsic contribution of SHE is from impurity SOI that leads to many spindependent scattering events. This SOI arises from the interaction between electrons withthe electrostatic potential of the scatters V(r) similar to the interaction between electrons
with the Coulomb potential of nucleus in the atomic SOI. Therefore, this interaction canbe expressed by the Hamiltonian

H scat  [kV (r )]

(2.7)

where  is the modified SOI parameter. The extrinsic contribution can be classified intoskew-scattering or side-jump scattering. However, although the side-jump is classified as
an extrinsic contribution, when addressing materials with strong SOI, the side-jump
scattering is separated into two dependent sub-mechanisms: extrinsic side jump andintrinsic side jump. In the heavy metal such as Pt or Ta, intrinsic side jump is believed as
the main contribution of SHE.
The contribution of SHE can also come from the Berry phase effect of the band
structure (intrinsic contribution). This effect is first confirmed by observing polarized spinof GaAs though Kerr microscopy in 2004 [12, 13]. SHE from the bulk band structure due
to strong SOI in TIs is also an example for the intrinsic contribution [14, 15,16].
In order to evaluate the intrinsic strength of SHE, the spin Hall angle SH is definedas32 | P a g eSH 

Chapter 22e

J s / Jc

(2.8)

where Jc is the charge current density, Js is the spin current density. The magnitude ofSH gives the spin current generation efficiency in NM, and its sign defines the directionof spin accumulating at the in NM/FM interface.
If a pure spin current is created by a charge current by SHE, the reverse process canalso happen and is called the inverse spin Hall effect (ISHE); that is, a charge current isgenerated by a spin current (Fig. 2.5). In general, the SHE can be considered as theconcept borrowing from the well-established anomalous Hall effect (AHE) in
ferromagnets. While a polarized transverse charge current is generated by a charge current
in the case of AHE, a transverse pure spin current is generated in the case of SHE, andboth of them arise from the same SOI mechanisms (Fig. 2.5). However, in contrast to
AHE whose signal can be detected electrically in ferromagnet due to the difference
between majority and minority spin population, the SHE required another ferromagnetic
layer on which the spin current exerts a spin-orbit torque (SOT) that can be measured.

Figure 2.5: The schematic illustrates the connection between the anomalous Hall
effect, the spin Hall effect and the inverse spin Hall effect. Reproduced with permission[9].

33 | P a g e

2.2.4.

Chapter 2

Spin orbit torque (SOT)In NM/FM bilayers, spins can accumulate at the NM/FM interface and can exert an
SOT on FM thanks to the REE or SHE. Depending on spin accumulation’s mechanism,
SOT (per unit moment) can be decomposed into two components, as shown in Fig. 2.6[17, 18]:(1) The field-like torque (FL) associated to Rashba-Edelstein effect can be written as

 FL  m  H FL

(2.9)

where HFL is the field-like effective field (HFL//), and m is unit vector of FM
magnetization.
(2) The antidamping-like torque (AD) associated to the SHE can be expressed by anantidamping-like effective field (HAD) as following

 AD  m  H AD

(2.10)

The antidamping-like effective field (HAD) is given by

H AD  

2eM stJ s (  m)

(2.11)

where  is the spin polarization unit vector of the spin current, Ms and t are thesaturation magnetization and thickness of FM, respectively.
Since both effects can generate SOT, classifying the contribution of these effects
therefore, is necessary. There are many different techniques, such as spin torqueferromagnetic resonance (ST-FMR) [19, 20], differential planar Hall effect [21, 22] andharmonic voltage measurement [ 23 , 24] that can be employed to evaluate theirmagnitudes.

34 | P a g e

Chapter 2

Figure 2.6: Schematic illustrates the field-like torque (FL) and antidamping-like torque(AD) with their respective effective field. Reproduced with permission [24].

2.3. The Dzyaloshinskii-Moriya interaction (DMI)
2.3.1.

The Dzyaloshinskii-Moriya interaction (DMI)

In magnetic systems which lack inversion symmetry, SOI can combine with theexchange interaction to create the Dzyaloshinskii-Moriya interaction or antisymmetricexchange interaction which can be expressed by the following Hamiltonian

H DMI   D12 (S1  S2 )(2.12)

where D12 is the DMI characteristic vector, S1 and S2 are two neighboring atomic spins.
This type of interaction was discovered by I. Dzyaloshinskii in 1958 [25], and its
mechanism based on SOI was completed by T. Moriya in 1960 [26]. The DMI can beclassified into two types, as illustrated in Fig. 2.7: the bulk DMI and the interfacial DMI.
B20-type ferromagnets, such as MnSi, are examples of materials with bulk DMI.
In these materials, the inversion symmetry is broken at each unit cell. This leads to theinterplay of two atomic spins with a neighboring atom having strong SOI, and the DMI

35 | P a g e

Chapter 2

vector D12, as a result, will point out of the film’s plane. Comparing with the Heisenberg
exchange interaction which prefers the parallel or antiparallel configuration, DMI energy
is minimized when neighboring spins are perpendicular to each other. As a consequence,a finite angle between each atomic spin arises and plays as the origin of non-collinear
spin textures, such as spin spirals, chiral magnetic domain walls, and skyrmions.
The domain wall energy with DMI can be expressed as [27]  4 AK   D(2.13)

where A is the exchange constant, K is the anisotropy constant, and D is the DMI energy
constant. In the normal case when D is small, the domain wall energy  is positive.
However, when D is large enough,  can be negative and chiral domain walls emerge. If
those chiral domain walls are rounded in space, they form skyrmions. However,skyrmions due to bulk DMI usually exist at low temperatures and need an external
magnetic field to be stable.
The situation is little different for the interfacial DMI. Although the inversion
symmetry can be maintained in each layer (FM or NM), it is broken at the interface of
NM/FM. This makes two atomic spins in the FM layer exchange with a neighboring atom
having strong SOI in the NM layer resulting in the interfacial DMI. The strength of DMI
can be drastically enhanced by utilizing multilayers of NM/FM. DMI in these cases thus,
can be strong and can compete with other exchange interactions even at room temperature.
The domain wall energy will become zero or even negative leading to the turbulence ofspin geometry mainly governed by the interfacial DMI.

36 | P a g e

Chapter 2

Figure 2.7: The schematic illustrations of (a) DMI generated by indirect exchange in atriangle composed of two atomic spins and an atom with strong SOC (bulk DMI) and(b) DMI generated by indirect exchange in a triangle composed of two atomic spins inferromagnetic layer and an atom with strong SOC in the non-ferromagnetic layer(interfacial DMI). Reproduced with permission [28].

2.3.2.

Skyrmion

Skyrmion or topologically protected spin texture is a key results of spinreconfiguration to minimize the system energy under strong DMI. The easiest way toevaluate skyrmion state is based on the skyrmion number S which can be written asS m m 
1
m

dxdy

4
 x y (2.14)

where m is normalized magnetic vector. In one dimension, this function can be simplified
as
S

1 
dx
2  xwhere  is the angle between adjacent moments.

(2.15)

37 | P a g e

Chapter 2

Figure 2.8: Skyrmion number in one-dimension (left side) and in two-dimension (rightside) of (a-b) the ferromagnetic system, (c-d) the ferromagnetic system with two
opposite domain walls and (e-f) the skyrmion system. Reproduced with permission[29].

Figure 2.8 illustrates the spin profile of three different magnetic sates in the onedimension (left figure) and in two-dimension (right figure). In the ferromagnetic system,
magnetization is homogeneous as illustrated by the gray line in the below graph, and theskyrmion number S is zero. The situation is same in the case of the ferromagnetic systemwith two opposite domain walls that cancels each other. However, the circumstance iscompletely different in the skyrmion state with two chiral domain walls, whose skyrmion
number is non-zero (S = 1). Its inner domain can be shrunk but it is very hard to annihilate
even by applying a magnetic field. This is known as topological protection, which meansa small deformation of the system cannot change its spin structure. Moreover, skyrmions

38 | P a g e

Chapter 2

have small size (~5-80 nm [30, 31]) and can be moved with an ultra-low driving current
density (~102 A/cm2 [32]). Thus, skyrmions can enable the manipulation of information
with high bit density and low power consumption. As a consequence, it has become very
attractive candidate for the next generation magnetic memory, especially in racetrack
memory.

2.3.3.

Topological Hall effect (THE)The non-collinear topological spin texture of skyrmions gives rise to an extra
fictitious field. Interestingly, conduction electrons can also “feel” this fictitious field. In
the Hall effect measurement, besides the ordinary Hall effect due to the Lorentz force andthe anomalous Hall effect (AHE) driven by magnetization, there isan additional

analogous component known as the topological Hall effect (THE) [33].
The THE resistivity can be phenomenologically expressed as

THE  PR0 H fic(2.16)

where P is the spin polarization, R0 is the normal Hall coefficient, and H fic is thefictitious magnetic field.
Comparing with other techniques of probing skyrmion, such as Lorentz
transmission electron microscopy (TEM) [34] or X-ray microscopy [35], the THE has
received a lot of attention due to its simplicity. The fictitious field is theoreticallyestimated around 1000 kOe for a 10-nm size skyrmion [36] and experimentally confirmed
to be approximately 600 kOe [37].

39 | P a g e

Chapter 2

2.4. The unidirectional magnetoresistance (UMR)
2.4.1.

MagnetoresistanceIn a perfect crystal at zero temperature, electrons move in the periodic potential oflattices and experience no collision. However, at temperature above zero withimperfection of crystal, electrons often collisions with other carriers or atoms and as theresults, give rise to non-zero resistivity. The resistance of material also can be changed
by applying a magnetic field (Lorentz force) or by spin-disorder scattering that originatesfrom the s, p-d exchange interactions in magnetic materials. Magnetoresistance (MR) is
named as a result of the dependence of resistance on the external magnetic field.
The Lorentz force mechanism occurs in both ferromagnetic and paramagnetic
materials because of the electron’s cyclotron motion under external magnetic field. On
the other hand, the spin-disorder MR arises from suppression of the electron-magnon
scattering at high external magnetic field. This mechanism therefore, occurs only inferromagnets. In addition, there is another MR effect, whose magnitude depends on therelative orientation between the magnetization direction and the current called anisotropic
magnetoresistance (AMR). Figure 2.9 illustrates the microscopic origin of AMR. Its
origin can be simply considered as a results of SOI and reorientation of the atomic orbitals.
The AMR resistivity  xx can be expressed as

 xx     (     ) sin 2  cos 2 (2.17)

where  and  are the resistivity when magnetization M is perpendicular and parallelwith current direction, respectively,  and  are the polar and azimuthal angle ofmagnetization direction.

40 | P a g e

Chapter 2

Figure 2.9: Schematic illustrates the microscopic of anisotropic magnetoresistance(AMR). The changing of atomic orbital’s shape changes the number of scattering
between electron and atom. Reproduced with permission [38].

2.4.2.

The spin Hall magnetoresistance (SMR)

The MR effect becomes much more interesting in bilayers of a paramagnetic
material with strong SOI and a ferromagnetic material. One example is the spin Hall
magnetoresistance (SMR), as shown in Fig. 2.10. The spin current created by SHE in the
NM layer accumulates at the interface of NM/FM. Depending on the relative direction
between the polarization direction of spins at interface and the magnetization direction in
the FM layer, the spin current is partly absorbed in the FM layer, and the rest of spincurrent will be reflected back to NM layer. This backflow of spin current generates anelectric current by the inverse spin Hall effect (ISHE), which contributes to thelongitudinal current and gives rise to the SMR. Since the SMR effect originates from thebackflow of spins, its magnitude can be enhanced by using insulator ferromagnets, suchas the yttrium iron garnet (YIG) [39].

41 | P a g e

Chapter 2

Figure 2.10: Illustration of spin Hall magnetoresistance as the result of the backflow
of the spin current and the inverse spin Hall effect when (a) magnetization aligns withpolarization of spin current, (b) magnetization is perpendicular with the polarization ofspin current. Reproduced with permission [39].

2.4.3.

The unidirectional magnetoresistance (UMR)

Recently, there is a new effect relating to an unusual behavior of MR occurring in
FM/NM system such as Co/Pt or Co/Ta [40] named as unidirectional magnetoresistance(UMR). This effect poses the features of the GMR effect that the spin accumulation at theinterface of FM/NM can be considered as an FM layer. However, unlike the GMR effectand the SMR effect, the dependence of resistance on the charge current in UMR isnonlinear. In the metallic bilayers, such as Co/Pt, UMR is classified into two types [41]:spin-dependent scattering and magnon scattering mechanism as shown in the Fig. 2.11.
In the first mechanism, a pure spin current generated from the SHE or REE is injected to
FM layer and accumulates at the near interface. A GMR-like UMR signal is generated as
the result of the spin transmission and reflection depending on direction of the spinpolarization  and magnetization M. The second mechanism on the other hand, comesfrom the spin-disorder scattering generated from absorption or emission of magnon, aquantized spin wave in ferromagnets as illustrated in Fig. 2.12.

42 | P a g e

Chapter 2

Figure 2.11: The schematic illustrates (a) the spin-dependent scattering mechanismand (b) the magnon scattering mechanism. Reproduced with permission [41].

Figure 2.12: The schematic illustrates the simple picture of magnon in (a) side viewand (b) top view.

UMR not only provides useful information that shed light on the SOI properties but
also plays as a new method to detect the magnetization direction. By utilizing UMR for
readout, the reference layer and the tunnel barrier in SOT-MRAM can be completely
omitted. Thus, UMR can greatly simplify the structure of SOT-MRAM.

43 | P a g e

Chapter 2

2.5. Summary
In this chapter, the concept of SOI and related effects, such as the Rashba-Edelsteineffect, the spin Hall effect, etc. were introduced. Each of them gives spintronics (spinorbitronics in particular) novel ideas that can improve or even completely change
spintronic device technologies. For example, the SHE can improve the power
consumption, the writing speed, and the bit density in STT-MRAM. The THE can help
detect skyrmions for the racetrack memory, and UMR can be employed to greatly simply
the structure of SOT-MRAM devices. Further study to fully understand theircharacteristics as well as enhance their performances, especially in new materials, play avital role. For this reason, study of spin-related phenomena in BiSb-ferromagnet bilayers
is the main topic in the rest parts of this thesis.

44 | P a g e

Chapter 2

References
1. L. H. Thomas, Nature 117, 514 (1926).
2. J. M. D. Coey, Cam. Uni. Pre. 3, 66 (2010).
3. Y. Ando, J. J. Appl. Phys. 54, 070101 (2015).
4. V. M. Edelstein, Solid State Commun. 73, 233 (1990).
5. G. Dresselhaus, Phys. Rev. 100, 580 (1955).
6. Yu. A. Bychkov, and E. I. Rashba, JETP Lett. 39, 78 (1984).
7. A. Manchon, H. C. Koo, J. Nitta, S. M. Frolov, and R. A. Duine, Nat. Mater. 14, 871(2015).
8. R. Ramaswamy, J. M. Lee, K. Cai, and H. Yang, Appl. Phys. Rev. 5, 031107 (2018).
9. J. Sinova, S. O. Valenzuela, J. Wunderlich, C. H. Back, T. Jungwirth, Rev. Mod.
Phys. 87, 1213 (2015).
10. M. I. Dyakonov, and V. I. Perel, Phys. Lett. A 35, 459 (1971).
11. J. E. Hirsch, Phys. Rev. Lett. 83, 1834 (1999).
12. Y. K. Kato, R. C. Myers, A. C. Gossard, and D. D. Awschalom, Science 306, 1910
(2004).
13. J. Sinova, and T. Jungwirth, Phys. Today 70, 38 (2017).
14. D. Hsieh, Y. Xia, L. Wray, D. Qian, A. Pal, J. H. Dil, J. Osterwalder, F. Meier, G.
Bihlmayer, C. L. Kane, Y. S. Hor, R. J. Cava, and M. Z. Hasan, Science 323, 919(2009).
15. T. Hirahara, Y. Sakamoto, Y. Saisyu, H. Miyazaki, S. Kimura, T. Okuda, I.
Matsuda, Phys. Rev. B. 81, 165422 (2010).
16. N. H. D. Khang, Y. Ueda, and P. N. Hai, Nat. Mater. 17, 808 (2018).
17. K. W. Kim, S. M. Seo, J. Ryu, K.-J. Lee, and H. W. Lee, Phys. Rev. B 85, 180404(2012).

45 | P a g e

Chapter 2

18. P. M. Haney, H. W. Lee, K.-J. Lee, A. Manchon, and M. D. Stiles, Phys. Rev. B 87,
174411 (2013).
19. L. Q. Liu, T. Moriyama, D. C. Ralph, and R. A. Buhrman, Phys. Rev. Lett. 106,
036601 (2011).
20. A. R. Mellnik, J. S. Lee, A. Richardella, J. L. Grab, P. J. Mintun, M. H. Fischer, A.
Vaezi, A. Manchon, E. A. Kim, N. Samarth, and D. C. Ralph, Nature 511, 449 (2014).
21. M. Kawaguchi, K. Shimamura, S. Fukami, F. Matsukura, H. Ohno, T. Moriyama, D.
Chiba, and T. Ono, Appl. Phys. Exp. 6, 113002 (2013).
22. M. Jamali, Z. Zhao, DC. Mahendra, D. Zhang, H. Li, A. K. Smith, and J. P. Wang,
J. Appl. Phys. 119, 133902 (2016).
23. J. Kim, J. Sinha, M. Hayashi, M. Yamanouchi, S. Fukami, T. Suzuki, S. Mitani, and
H. Ohno, Nat. Mater. 12, 240 (2013).
24. K. Garello, I. M. Miron, C. O. Avci, F. Freimuth, Y. Mokrousov, S. Blugel, S.
Auffret, O. Boulle, G. Gaudin, and P. Gambardella, Nat. Nanotechnol. 8, 587 (2013).
25. I. Dzyaloshinskii, J. Phys. Chem. Solids 4, 241 (1958).
26. T. Moriya, Phys. Rev. 120, 91 (1960).
27. S. Rohart, and A. Thiaville, Phys. Rev. B 88, 184422 (2013).
28. A. Fert, V. Cros, and J. Sampaio, Nat. Nanotech. 8, 152 (2013).
29. K. Bergman, A. Kubetzka, O. Pietzsch, and R. Wiesendanger, J. Phys. Condens.
Matter. 26, 394002 (2014).
30. G. Chen, A. Mascaraed, A.T. N’Diaye, A.K. Schmid, Appl. Phys. Lett. 106,242404 (2015).
31. O. Boulle, J. Vogel, H. Yang, S. Pizzini, D. de Souza Chaves, A. Locatelli, T.O.
Mentes, A. Sala, L.D. B. Prejbeanu, O. Klein, M. Belmeguenai, Y. Roussigne, A.

46 | P a g e

Chapter 2

Stashkevich, S.M. Cherif, L. Aballe, M. Foerster, M. Chshiev, S. Auffret, I.M. Miron,
G. Gaudin, Nat. Nanotechnol. 11, 449 (2016).
32. F. Jonietz, S. Mühlbauer, C. Pfleiderer, A. Neubauer, W. Münzer, A. Bauer, T.
Adams, R. Georgii, P. Böni, R. A. Duine, K. Everschor, M. Garst, A. Rosch, Science17, 1648 (2010).
33. A. Neubauer, C. Pfleiderer, B. Binz, A. Rosch, R. Ritz, P. G. Niklowitz, and P.
Bo ̈ni, Phys. Rev. Lett. 102, 186602 (2009).
34. W. Wang, Y. Zhang, G. Xu, L. Peng, B. Ding, Y. Wang, Z. Hou, X. Zhang, X. Li,
E. Liu, S. Wang, J. Cai, F. Wang, J. Li, F. Hu, G. Wu, B. Shen, and X. X. Zhang, Adv.
Mat. 28, 6887 (2016).
35. K. Litzius, I. Lemesh, B. Krüger, P. Bassirian, L. Caretta, K. Richter, F. Büttner, K.
Sato, O. A. Tretiakov, J. Förster, R. M. Reeve, M. Weigand, I. Bykova, H. Stoll, G.
Schütz, Geoffrey, S. D. Beach, and M. Kläui, Nat. Phys. 13, 170 (2017).
36. P. Bruno, V.K. Dugaev, and M. Taillefumier, Phys. Rev. Lett. 93, 096806 (2004).
37. K. K. Meng, X. P. Zhao, P. F. Liu, Q. Liu, Y. Wu, Z. P. Li, J. K. Chen, J. Miao, X.
G. Xu, J. H. Zhao, and Y. Jiang, Phys. Rev. B 97, 060407 (2018).
38. C. O. Avci, “Current-induced effects in ferromagnetic heterostructures due to spinorbit coupling”, PhD thesis, 7 (2015).
39. H. Nakayama, M. Althammer, Y. T. Chen, K. Uchida, Y. Kajiwara, D. Kikuchi, T.
Ohtani, S. Gepra ̈gs, M. Opel, S. Takahashi, R. Gross, G. E. W. Bauer, S. T. B.
Goennenwein, and E. Saitoh, Phys. Rev. Lett. 110, 206601 (2013).
40. C. O. Avci, K. Garello, A. Ghosh, M. Gabureac, S. F. Alvarado, and P.
Gambardella, Nat. Phys. 11, 570 (2015).
41. C. O. Avci, J. Mendil, G. S. D. Beach, and P. Gambardella, Phys. Rev. Lett. 121,
087207 (2018).

47 | P a g e

Chapter 3

Chapter 3

Sample Preparation and Characterization
Techniques
In this chapter, fabrication and characterization techniques of BiSb-ferromagnet
bilayers will be described in details. Section 3.1 gives details of sample preparation’s
procedure, and the characterization as well as experimental setup will be shown in Section
3.2.

3.1. Sample preparation
3.1.1.

Molecular beam epitaxy (MBE)

In order to fabricate high quality BiSb-ferromagnet bilayers, the molecular beam
epitaxy (MBE) was employed in this study for sample preparation. MBE is a crystal
growth technique that can grow atomic layer by atomic layer in an ultra-high vacuum(UHV) condition and based on reaction of molecular (or atomic beam) with a heatedsubstrate [1]. Here, the term “epitaxy” describes the ordered growth of crystalline layers.
Unlike other crystal-growth methods, MBE allows to fabricate samples with precise
composition, high purity and real-time monitoring. As a consequence, MBE can produce
samples with extremely high crystal quality, and is employed to grow metals, insulatorsor semiconductors with sharp interfaces and precise composition.
Figure 3.1 shows the schematic illustration of the growth chamber of a MBE system (Fig.
3.1(a)) and the real image of the Anelva MBE-620 system used in my study (Fig. 3.1(b)).
The UHV (~10-7 Pa) in this MBE was achieved by employing an ion pump, an Tisublimation pump and a liquid nitrogen shroud to prevent atom’s re-evaporation. The

48 | P a g e

Chapter 3

samples, mounted to molybdenum holders by indium, were loaded to the growth chamberby a transfer rod. The samples were heated by a resistance-type heater and theirtemperature was controlled by thermal couple feedback. The grown materials (Ga, As,
Bi, Sb and Mn) were stored in Knudsen cells (or K-cells) and deposited on sample’s
substrate by heating the materials to given temperatures.

Reflection high-energy electron diffraction (RHEED)The layer-by-layer growth also permits real-time in situ surface observation by
RHEED [2, 3]. The electrons emitted from a heated tungsten filament are accelerated tohigh speed and energy (~20 – 23 keV), strike and diffract on the sample’s surface at a
grazing angle of less than a few degree, and form the RHEED patterns on a fluorescentscreen. From the position and shape of the streaks in the RHEED patterns, the informationof surface crystallography such as the surface orientation and the surface roughness canbe observed in real-time. RHEED as the results, has become an indispensable tool in MBE
systems.

49 | P a g e

Chapter 3

Figure 3.1: (a) Schematic illustration of the growth chamber of a MBE system.
(b) Photograph of the Anelva MBE-620 system used in this work.

50 | P a g e

Chapter 3

GaAs buffer layer’s preparation
Because the surface condition of the starting crystal (substrate) plays a vital role inepitaxial growth by MBE, preparing the substrate surface with high crystal quality isnecessary in my experiments. The GaAs substrates were used for all fabricated samples,
and the substrate preparation is described as follows(1) Heat the GaAs substrates from 150oC to 580oC at a ramping rate of 20oC/min toremove the oxidized layer (GaAsO3 and GaAsO4 [4]) (Fig. 3.2(a) and Fig. 3.2(d)).
(2) Keep GaAs at 580oC under As exposure to completely remove oxidized layer andcompensate the lost As atoms from the substrate (Fig. 3.2(b) and Fig. 3.2(e)).
(3) Grow a thick GaAs film (~ 80 – 100 nm) until high quality of GaAs surface wasconfirmed (Fig. 3.2(c) and Fig. 3.2(f)).

Figure 3.2: RHEED patterns of a GaAs(001) substrate taken along [ 110 ] azimuth (a)before deoxidation, (b) after deoxidation, and after growing a thick buffer GaAs layer.
(d-f) same as (a-c) but for a GaAs(111)A substrate.

51 | P a g e

3.1.2.

Chapter 3

Hall bar device fabrication

For the electrical measurement, Hall bar devices were fabricated with the process
shown in Fig. 3.3.
(1) In the first step, the Hall bar pattern, made from a positive photoresist (OFPR)
mask was formed on the sample’s surface by conventional photolithography
process. After milling process (Ar+ ion), the photoresist mask was removed bygentle ultrasonic cleaning in warm acetone. The Hall bars with size of 100 m 
50 m or 100 m  25 m were fabricated as shown in Fig. 3.4(a).
(2) In the second step, the electrode mask, made from OFPR was formed on thesample’s surface by the same photolithography process. After that, Cr (5 nm)/Au(50~150 nm) bilayers were deposited on the sample by electron-beam evaporation.
Finally, the electrode was obtained by lift off as shown in Fig. 3.4(b).

Figure 3.3: Schematic illustrates (a) Hall bar preparation and (b) electrode preparation
for a Hall bar device.

52 | P a g e

Chapter 3

Figure 3.4: (a) Micrograph of a 100 m  50 m Hall bar after the milling process. (b)Final device after deposition of a Cr (5 nm)/Au (50 nm) pad for the contact electrodes.

3.2. Characterization techniques
3.2.1.

X-ray diffraction (XRD) measurement

To evaluate the crystal characteristics, X-ray diffraction (XRD), a non-destructive
technique for analyzing material’s structure, was employed. As its name implies, XRD isbased on diffraction of X-rays that are irradiated toward the sample. The XRD peak
positions satisfy the Bragg’ law (Fig. 3.5(a)):

2d sin   k (3.1)

where d is the distance between diffraction planes,  and  are the wavelength ( =0.15406 nm for K1 of Cu) and its incident angle, respectively, and k is an integer (k =1, 2, 3,…).
The 2 scanning (Fig. 3.5(a)) measures the dependence of the XRD intensity on 
and gives the basic information of the sample’s crystal characteristics. For the detailed
crystal characterization, - scanning (Fig. 3.5(b)) is used. By measuring the XRD
intensity at each  and  value, the crystallography of sample can be determined.

53 | P a g e

Chapter 3

Figure 3.5: (a) Illustration of the Bragg equation. (b) Schematic of XRD measurement
setup (2 scanning and - scanning).

3.2.2.

Magnetotransport measurement

Sample characterization by magnetotransport measurement is an indispensable stepfor all topics of spin-related phenomena in BiSb/FM bilayers. Fig. 3.6 (a) illustrated theschematic setup of Hall measurement, and its actual experiment setup is shown in Fig.
3.6(b). In these measurements, the samples are biased with a DC current (or a pulse
current), and the Vxx or Vxy signal are measured by voltmeters under a magnetic field.
Moreover, for the measurements at low temperatures, the samples were cooled down bya cryogenic system. There are three types of magnetotransport measurement performedin my study:(1)

Hall effect measurement

This measurement was employed in order to detect the normal Hall effect as wellas the anomalous Hall and the topological Hall effect. The DC current was applied in thelongitudinal direction, and the transverse Vxy voltage was detected as the output signal.

54 | P a g e

Chapter 3

The Hall resistivity  H can be expressed as H  O  AHE  R O H eff  RAHE M(3.2)

where O is the ordinary Hall resistivity, AHE is the anomalous Hall resistivity, R O
and RAHE are the coefficient of the ordinary Hall and anomalous Hall effects,
respectively, Heff is the effective magnetic field, and M is the sample’s magnetization.
For the SOT switching in BiSb/MnGa bilayers, pulse currents ( = 100 ms) wereapplied. The final state of the MnGa magnetization was confirmed by Hallmeasurement with a small DC current.
There is a third term, the topological Hall effect, in the case of skyrmions. The Hall
resistivity therefore, can be rewritten as H  O  AHE  THE

(3.3)

where THE is the topological Hall resistivity.
(2)

UMR measurement

This measurement was used to evaluate the UMR ratio. The DC current was appliedin the longitudinal direction, while MR was measured by the longitudinal Vxx voltage.
UMR was defined as the difference of MR between positive and negative current.
(3)

Differential planar Hall effect measurement

This measurement was used in order to separate SOT and thermal effect’s
contribution. The external magnetic field Hext was rotated when a DC current wasapplied, and the differential planar Hall effect was measured as the difference ofplanar Hall resistivity between the positive and negative current.

55 | P a g e

Chapter 3

Figure 3.6: (a) Schematic illustration of the Hall effect measurement. (b) Photographof the Hall effect measurement system.

56 | P a g e

3.2.3.

Chapter 3

Magneto-optical measurement(1) Magnetic circular dichroism (MCD)
Figure 3.7 shows the schematic setup of the MCD measurement. The light
generated from a Xenon lamp is passed through a monochromator toward the surface ofsample. The light is modulated by a photoelastic modulator (PEM). The detector collects
the intensity of reflected light, and measures the difference in optical reflectivity between
right and left circular polarization. This measurement gives information of spin splittingof the band structure under an external magnetic field applied perpendicular to the film
plane, and its intensity is written as
MCD 

90 dR
E
 dE

(3.4)

where R is the optical reflectivity, E is the photon energy and E is the spin-splittingenergy by the Zeeman effect [5]. Because the MCD intensity is proportional to sample’s
perpendicular magnetization (E  M), MCD measurement is used to evaluate themagnetization of samples.

Figure 3.7: Schematic illustration of MCD measurement

57 | P a g e(3)

Chapter 3

Longitudinal magneto-optic Kerr effect (in-plane MOKE)

To confirm the titling magnetization of Mn0.45Ga0.55 thin film in chapter 5, in-plane
MOKE, a unique tool for the determination of the in-plane magnetization is employed[6]. A linearly polarized light is focused on the sample’s magnetic domains by anobjective lens. This light is reflected off the sample surface, and its polarization direction
is rotated by the interaction with the sample’s magnetic domains. The detector will collect
the reflected light, and analyses the local magnetization by the magnitude of the polarized
light’s rotation.

3.2.4.

Magnetization measurement

In order to evaluate the magnetization of samples, superconducting quantum
interface device (SQUID), a very sensitive device based on the Josephson effect was usedin my measurement. Figure 3.8 shows the schematic diagram of magnetic property
measurement system (MPMS-5S Quantum Design). The SQUID is located in the bottom
position of the MPMS system and detects the sample’s magnetization throughsuperconducting detection coils, which are connected to the SQUID. The current
generated by the magnetization of the sample flows in this detection coil, and asconsequence, an output voltage proportional to the detection coil’s current is evaluatedby SQUID [7].

3.2.5.

Atomic force microscopy (AFM) measurement

AFM was employed in my measurement to observe the surface morphology of
MnGa thin films. Figure 3.9 illustrates its operation mechanism. An oscillating cantileverwith a sharp tip in nanometer, is brought near the sample surface. According to Hooke’s
law, the cantilever is deflected due to the atomic force between the tip and sample. The
deflection of the cantilever is measured by a laser beam system. AFM can map the surface

58 | P a g e

Chapter 3

sample without using a conductive surface as in scanning tunneling microscope (STM).
AFM therefore, can image almost any type of surface and has been widely used.

Figure 3.8: The schematic diagram of SQUID magnetometer MPMS XL-5S.
Reproduced with permission [8].

Figure 3.9: The schematic illustration of AFM measurement. Reproduced withpermission [9].

59 | P a g e

Chapter 3

3.3. Summary
In this chapter, the fabrication process of BiSb/FM bilayers and characterization
techniques were presented. Fabrication based on MBE and real-time RHEED observation
help us ensure the best crystal growth condition. Hall bar devices were fabricated formagnetotransport measurement. To fully understand the characteristics of samples,
various kinds of measurements were used.

60 | P a g e

Chapter 3

References
1. K. Alavi, Ency. Mater. Sci. Tech., 5765 (2001).
2. F. Tang, T. Parker, G. C. Wang, and T. M. Lu, J. Phys. D: Appl. Phys. 40, R427
(2007).
3. M. D. Szata, Mater. Chem. Phys. 81, 257 (2003).
4. D. A. Allwooda, R. T. Carlineb, N. J. Masona, C. Pickering, B. K. Tannerc, P. J.
Walker, Th. Sol. Fil. 364, 33 (2000).
5. P. N. Hai, L. D. Anh, S. Mohan. T. Tamegai, M. Kodzuka, T. Ohkubo, K. Hono, and
M. Tanaka, Appl. Phys. Lett. 101, 182403 (2012).
6. T. Haider, Inter. J. Elec. Appl. 7, 17 (2017).
7. R. L. Fagaly, Rev. Sci. Instrum. 77, 101101 (2006).
8. A. Barth, “Magnetic and structural properties of the Gd/Ni-bilayer-system”, PhD
thesis, 32 (2007).
9. A. Passian, and G. Siopsis, Phys. Rev. A 95, 043812 (2017).

61 | Page

Chapter 4

Chapter 4

MnGa

Thin

Magnetic

Films

Anisotropy

with

Perpendicular

Grown

on

BiSb

Topological Insulator
In order to study spin-related phenomena in BiSb/FM bilayers, the first step in my
Ph.D. thesis is to grow a FM layer on BiSb. Here, MnGa was chosen as a candidate for
the FM layer, because of its unique characteristics. MnGa shows small magnetization (Ms< 400 emu/cm3) [1-12] and small damping factor ( < 0.008 ) [13], which are promising
for low-power magnetization switching. Furthermore, MnxGa1-x thin films also show
large PMA (Ku > 10 Merg/cm3) and high TC [1], which are essential for long time thermal
stability. Recent studies have shown that MnxGa1-x is a potential candidate not only forconventional STT-MRAM [14] but also for SOT-MRAM with heavy metal (Pt or Ta) /MnGa bilayers [15,16].
In this chapter, the crystal growth, structural and magnetic properties of Bi0.8Sb0.2
topological insulator (TI) / MnxGa1-x bilayers grown on GaAs(111)A substrates bymolecular beam epitaxy (MBE) will be reported. By optimizing the growth condition and
Mn composition, I show that MnxGa1-x thin films can be grown on Bi0.8Sb0.2 withcrystallographic orientation of Bi0.8Sb0.2(001)[1 1 0] // MnGa (001)[100]. Using MCD
spectroscopy, both L10 phase ( x  0.6 ) and D022 phase ( x  0.6 ) of MnxGa1-x was
detected. For 0.50  x  0.55 , ferromagnetic L10-MnGa thin films with clear
perpendicular magnetic anisotropy (PMA) were confirmed by MCD hysteresis,
anomalous Hall effect (AHE) as well as SQUID measurement.

62 | Page

Chapter 4

4.1. Growth of BiSb - MnxGa1-x bilayers by MBE
There are two main concerns about the growth of BiSb/MnxGa1-x bilayers by MBE.
First, the crystal structure of BiSb and MnxGa1-x is completely different from each other.
BiSb has a three-fold symmetric crystal structure as shown in Figure 4.1(a) [17]. In
contrast, MnxGa1-x has two phases: the L10 ferromagnetic phase for 0.43  x  0.66 (Mn2Ga) and the D022 ferrimagnetic phase for 0.66  x  0.75 (Mn2Ga, Mn3Ga), but both ofthem have four-fold symmetric tetragonal crystal structure [1], as shown in Figure 4.1(b).
While there are several attempts for growth of MnGa thin films on various substrates,
such as GaAs(001) [2], GaN(0001) [18, 19], GaSb(111) or Al2O3(0001) [20], MgO [1, 6],
and ScN [21], only a few of those thin films grown on four-fold symmetric GaAs(001)and MgO(001) substrates show clear PMA. In addition to difference in crystal symmetry,the lattice mismatch between MnxGa1-x (aMnGa ~ 0.39 nm) [22, 23] and BiSb (aBiSb ~ 0.46
- 0.43 nm) [24] is larger than 10%. These pose a big challenge for growing MnxGa1-x thinfilm with high PMA on BiSb.
To overcome these problems, I employed a growth technique of the BiSb/MnGabilayers on GaAs(111)A substrates by the MBE method as shown in Fig. 4.2(a). Afterremoving the surface oxide layer of GaAs(111)A substrate at 570oC, a 40 nm-thick GaAs
buffer layer was grown to obtain an atomically smooth surface. Then, the substrate wascooled to 150oC for growing a 20 nm-thick Bi0.8Sb0.2 layer at a rate of 8 nm/min. For
growing MnxGa1-x thin films on top of the Bi0.8Sb0.2 layer, the template method, originallydeveloped by M. Tanaka et. al [25] for growth of MnGa thin films on GaAs(001)substrates, was employed. First, the substrate temperature Tsub was reduced to 40oC, and4 monolayers (MLs) of Mn-Ga-Mn-Ga were deposited on top of Bi0.8Sb0.2. Then, the 4MLs were heated up to 230oC for crystallization so as a thin Mn0.5Ga0.5 template wasformed on the surface of Bi0.8Sb0.2. Finally, MnxGa1-x thin films with the total thickness

63 | Page

Chapter 4of 8 nm and the Mn composition between 0.45 and 0.74 were grown at a rate of 0.5
nm/min. The growth process was monitored in situ by RHEED. Figure 4.2(b) shows the
RHEED patterns observed along the GaAs[1 1 0] direction during the growth of
BiSb/MnxGa1-x bilayers on GaAs(111)A substrates for x = 0.74, 0.55 and 0.45. The
Bi0.8Sb0.2 thin films show bright RHEED with Kikuchi lines, confirming that the Bi0.8Sb0.2
thin films were epitaxially grown on GaAs (111)A as reported in [26]. The RHEED
patterns of 4 MLs of Mn-Ga-Mn-Ga deposited on top of Bi0.8Sb0.2 at 40oC were weak,
but becomes bright with mixing streaky and dotty patterns after annealing at 230oC. This
indicates that a crystallized template of Mn0.5Ga0.5 was formed. The MnxGa1-x layersgrown on this template remain crystalline, but their RHEED patterns become dim withincreasing the MnxGa1-x thickness. The RHEED pattern of the 8 nm-thick MnxGa1-x canstill be observed for x = 0.74 and 0.55, but disappears for x = 0.45.

Figure 4.1: (a) Crystal structure of BiSb. (b) Crystal structures of L10 ferromagnetic
phase (left) and D022 ferrimagnetic phase (right) of MnGa. The red and blue arrows
represent the direction of Mn atoms’ magnetic moments.

64 | Page

Chapter 4

Figure 4.2: (a) Growth condition of Bi0.8Sb0.2/MnxGa1-x bilayers on GaAs(111)A
substrates. (b) RHEED patterns observed along GaAs[1 1 0] direction during the
growth of Bi0.8Sb0.2/MnxGa1-x bilayers.

65 | Page

Chapter 4

4.2. Crystal structure analysis
4.2.1.

Crystal orientation of MnxGa1-x on BiSb thin films

After the growth, the crystal orientation of MnxGa1-x thin films was evaluated by
XRD measurements. Figure 4.3(a) shows the -2 XRD spectra of Bi0.8Sb0.2/MnxGa1-x
bilayers with different Mn composition x ranging from 0.45 to 0.74. Here, the hexagonal
coordinate indexing was used for BiSb, and cubic coordinate indexing was used for GaAs
and MnGa. Besides the Bi0.8Sb0.2(003), Bi0.8Sb0.2 (006), and (009) peaks, clear MnxGa1x(001) and MnxGa1-x(002) peaks for all x was observed. A MnxGa1-x(200) peak was also

observed for high Mn composition (x > 0.6), but gradually decreases to the noise level
for low Mn composition (x < 0.6). This indicates that it is possible to grow MnGa(001)on top of Bi0.8Sb0.2(001) despite their differences in crystal symmetry and lattice constant.

4.2.2.

In-plane crystallographic relationships

In order to investigate the in-plane crystallographic relationship between
MnGa(001) and BiSb(001), I measured the scan XRD pattern of the Mn0.5Ga0.5 thinfilm at 43.7o and 2 = 36.6o (Fig. 4.3(b)), and compare it to that of GaAs(111) at

70.3o and 2 = 27.3o (Fig. 4.3(c)). As shown in Fig. 4.3(b), three equivalent sets offour-fold symmetric Mn0.5Ga0.5(011), (101), (0 1 1) and ( 1 01) peaks were observed witheach set shifted by 60o from each other. Comparing these peaks with those of GaAs(1 11), GaAs(11 1 ), and GaAs( 1 11), and taking into account the fact that BiSb[1 10](001)//GaAs[1 1 0](111) [26], the in-plane crystallographic relationships between
MnGa and BiSb as MnGa[100]//BiSb [1 1 0] can be identified.
This relationships is reasonable because the lattice constant of BiSb along the
BiSb[1 1 0] direction (d ~ 7.8Å) is exactly twice of aMnGa ~ 3.9Å, as shown in Fig. 4.3(d).
Note that there are also two other equivalent MnGa in-plane crystallographic orientation,

66 | Page

Chapter 4

shifted by 60o from that illustrated in Fig. 4.3(d), reflecting the three-fold symmetry of
the hexagonal BiSb(001) surface. Figure 4.3(e) shows the measured lattice constant c of
MnxGa1-x grown on Bi0.8Sb0.2 as a function of x, compared with those of bulk [27, 28] and
MnxGa1-x thin films grown on MgO(001) [1] and GaAs(001) substrates [29]. At high x, cof MnxGa1-x grown on Bi0.8Sb0.2 is close to those of bulk or thin films grown on MgO and
GaAs. However, at low x, c of MnxGa1-x grown on Bi0.8Sb0.2 is significantly smaller thanthe others. This suggests that MnxGa1-x grown on Bi0.8Sb0.2 at low x may be under tensilestress, i.e. the relationships 2aMnGa = d was kept even for low x.

67 | Page

Figure 4.3: (a)  - 2Chapter 4

XRD spectra of Bi0.8Sb0.2/MnxGa1-x bilayers with Mncomposition x ranging from 0.45 to 0.74. The XRD spectrum of a single Bi0.8Sb0.2 layer(bottom) is shown for reference. (b), (c) scan XRD pattern of the Mn0.5Ga0.5 thinfilm and GaAs(111) substrate, respectively. (d) In-plane crystallographic orientation of
MnGa (blue) on BiSb (green). (e) c lattice constant of MnxGa1-x grown on Bi0.8Sb0.2
thin films as a function of x (this work), compared with those of bulk [22, 23], and
MnxGa1-x thin films grown on MgO(001) [11] and GaAs(001) substrate [29].

68 | Page

Chapter 4

4.3. Magnetic properties
4.3.1.

Magneto-optical properties

Next, the magnetic properties of MnxGa1-x thin films grown on Bi0.8Sb0.2 were
investigated. It is known that there is a magnetic phase transition from the DO22
ferrimagnetic phase (x  0.66) to the L10 ferromagnetic phase (x < 0.66). In this study,
the MCD spectroscopy technique was used to investigate such a magnetic phase transition.
Here, MCD measures the difference between the reflectivity for right (𝑅σ+ ) and left (𝑅σ− )circular polarizations: MCD( E ) 

90 R  ( E )  R  ( E ) , where R is the optical
2 R( E )reflectivity, and E is the photon energy. Here, 𝑅σ+ (𝐸) is determined by the opticaltransitions from the occupied spin-down band to the unoccupied spin-up band, while𝑅σ− (𝐸) is determined by the optical transitions from the occupied spin-up band to theunoccupied spin-down band. That means the MCD spectrum reflects the spin-polarizedband structure, and each specific magnetic material has its own MCD signature. Thus, it
is possible to distinguish the DO22 ferrimagnetic phase (x  0.66) and the L10
ferromagnetic phase (x < 0.66) of MnGa, even when their crystal structure and lattice
constant are very similar. Furthermore, since the MCD intensity is proportional to zdirection magnetization Mz, it is also possible to measure the magnetization hysteresis byinvestigating the magnetic field dependence of the MCD intensity. Note that the MCD
spectrum of the D022 and L10 phase of MnGa have never been reported so far.
Figures 4.4(a) and 4.4(b) show the normalized MCD spectra of various MnxGa1-x
thin films with x = 0.74 and 0.65, and x = 0.59, 0.55, 0.50, and 0.45, respectively. Here,the spectra were measured at 300 K with a magnetic field of 1 T applied perpendicular to
the film plane. Two different spectral shapes were confirmed. The spectra of thin films

69 | Page

Chapter 4

with x = 0.74 and 0.65 show a broad plateaus at 3.5 ~ 5 eV, while those with x = 0.59,
0.55, 0.50, and 0.45 show a peak around 3.2-3.5 eV. The transition of the MCD spectral
shape at about x ~ 0.6 agrees well with that of magnetic phase transition between the D022
and L10 phase of MnGa. These indicate that the spectral shape of thin films with x = 0.65,
0.74 reflects the D022 phase, while that of thin films with x = 0.59, 0.55, 0.50, and 0.45
reflects the L10 phase. Here, once can see that the spectral shapes in Figs. 4.4(a) and 4.4(b)are consistent with the band structures of D022 and L10-MnGa. Figures 4.4(c) and 4.4(d)show the spin-resolved density of states (DOS) of D022 and L10-MnGa, respectively,
calculated by first principles [6]. The arrows in those figures indicate the opticaltransitions from the occupied spin-down band to the unoccupied spin-up band underirradiation of right circular polarized photons (+). (For clarity, the optical transitions
from the occupied spin-up band to the unoccupied spin-down band under irradiation ofleft circular polarized photons (-) are omitted). For the D022-MnGa phase, the spin-down
DOS under the Fermi energy spread over a broad band from -1 eV to -4 eV, while thespin-up DOS above the Fermi energy spread over a small band centering at about 1.5 eV.
Therefore, the corresponding spectra of the optical transitions between them are broad,which explains the observed broad plateaus at 3.5 ~ 5 eV in Fig. 4.4(a). In contrast, thespin-down DOS of the L10-MnGa phase is localized around -1.3 eV, which explains theobserved peaks around 3.2-3.5 eV in Fig. 4.4(b). These results show that MCD is a
powerful tool to distinguish the L10 and the D022 phase of MnGa.

70 | Page

Chapter 4

Figure 4.4: Normalized MCD spectra of BiSb/MnxGa1-x bilayers for (a) x = 0.74 and
0.65, and (b) x = 0.59, 0.55, 0.50, and 0.45. Spin-resolved density of states (DOS) of(c) D022 and (d) L10-MnGa, calculated by first principles.

71 | Page

4.3.2.

Chapter 4

Magnetization properties

Next, the MCD intensity-magnetic field (MCD-H) characteristics were investigated,which reflects the hysteresis of perpendicular magnetizations Mz. Figure 4.5(a) shows thenormalized MCD-H hysteresis for various MnxGa1-x thin films. Poor squareness of thehysteresis of DO22-MnxGa1-x thin films (x = 0.65, 0.74) was observed. In contrast, goodsquareness of the hysteresis of L10-MnxGa1-x thin films was obtained. In particular, the
MnxGa1-x thin films with x = 0.50 and 0.55 exhibit good PMA characteristics with 100%of remanence factor. We also evaluated the hysteresis of these two samples by using
SQUID and AHE measurements. Figures 4.5(b) and 4.5(c) compare the normalized
hysteresis obtained by MCD, SQUID, and AHE measurements for sample with x = 0.50
and 0.55, respectively. The hysteresis curves obtained by different methods agree wellwith each other. The coercive force is about 0.6 T for x = 0.50, and 0.5 T for x = 0.55,
which are close to those reported for Pt/MnGa or Ta/MnGa bilayers [30, 16].
Figure 4.6(a) and 4.6(b) show the out-of-plane and in-plane M-H curves up to 70 kOe of
two BiSb/MnxGa1-x bilayers with x = 0.50 and 0.55. From these data, the uniaxial
magnetic anisotropy constant (Ku) of the MnxGa1-x layers was calculated to be around 2.2
Merg/cc and 2.3 Merg/cc for x = 0.50 and 0.55, respectively. Those values of Ku are small
compared with those of stand-alone MnGa layers grown on MgO(001). Note that
reduction of Ku is due to the small saturation magnetization MS of the MnGa layers (87emu/cc and 78 emu/cc for x = 0.50 and 0.55, respectively), rather than by reduction of theuniaxial anisotropy magnetic field. Indeed, the in-plane saturation magnetic field is ashigh as 55 ~ 60 kOe, which is similar to those of high-quality stand-alone MnGa thinfilms grown on MgO(001).

72 | Page

Chapter 4

Figure 4.5: (a) Normalized MCD hysteresis of BiSb/MnxGa1-x bilayers. (b) and (c)Normalized hysteresis obtained by MCD, SQUID, and AHE measurements for
BiSb/MnxGa1-x bilayer with x = 0.50 and 0.55, respectively.

73 | Page

Chapter 4

Figure 4.6: Out-of-plane (blue) and in-plane (red) M-H curves of BiSb/MnxGa1-x
bilayers with (a) x= 0.50 and (b) x = 0.55 at room temperature.

4.3.3.

Discussion

There are two reasons for the small MS observed in BiSb/MnxGa1-x bilayer system.
First, it is known that high substrate temperature of 450–500C is needed for obtaining
high-quality MnGa thin films with high MS [13]. However, the melting temperature of
BiSb is low (280C for Bi0.9Sb0.1), thus low substrate temperature of 230C had to be used
to grow MnGa layers on top of BiSb, resulting in low chemical ordering of MnGa as
indicated by the dim RHEED patterns in Fig. 4.2(b). One solution of this problem is to
grow a high-quality MnGa layer first on suitable substrates, such as GaAs(001) or
MgO(001), and then grow the BiSb layer on top of the high-quality MnGa layer. Anotherproblem is the existence of the three equivalent in-plane crystallographic domains of
MnGa on BiSb, each shifted by 60o from each other, as indicated by the scan XRD
pattern in Fig. 4.3(b). Because MnGa has a tetragonal crystal structure, a large amount ofcrystal defects would exist at the interfaces between neighboring MnGa domains toabsorb this 60o shift. Such crystal defects at various MnGa domain boundaries would
significantly reduce the crystal quality and the MS of the overall MnGa layer. To solve

74 | Page

Chapter 4

this problem, it is necessary to break the in-plane three-fold symmetry of the BiSb(001)surface. This may be done by applying an in-plane uniaxial stress to the substrates, orusing substrates with lower crystal symmetry, such as those with orthorhombic crystal
structures.

4.4. Summary
In conclusion, crystalline MnxGa1-x thin films was grown on Bi0.8Sb0.2 layer despite
their differences in crystal symmetry and lattice constant. XRD analysis indicates that
MnxGa1-x grows on Bi0.8Sb0.2 with the crystallographic orientation of Bi0.8Sb0.2(001)[1 10]//MnGa(001)[100]. In addition, L10 ( x  0.6 ) and D022 phase ( x  0.6 ) of MnxGa1-x
were distinguished by using MCD spectroscopy. For 0.50  x  0.55 , MnGa thin films
showed large PMA characteristics confirmed by MCD, AHE, and SQUID measurements.
These results show that BiSb/MnxGa1-x bilayer system is promising for perpendicularmagnetization switching using giant spin Hall effect in TIs. This technique can possibly
be applied to growth of other ferromagnetic materials with a similar crystal structure andhigh PMA, such as FePt, FePd, MnGe, and MnAl, on other TIs, such as Bi2Se3 and Bi2Te3.

75 | Page

Chapter 4

References
1. L. J. Zhu, S. H. Nie, and J. H. Zhao, Chin. Phys. B 22, 118505 (2013).
2. M. Tanaka, J. P. Harbison, J. DeBoeck, T. Sands, B. Philips, T. L. Cheeks, and V. G.
Keramidas, App. Phys. Lett. 62, 1565 (1993),
3. S. Zhao, and T. Suzuki, AIP Adv. 6, 056025 (2016).
4. W. Y. Zhang, P. Kharel, S. Valloppilly, R. Skomski, and D. J. Sellmyer, J. Appl.
Phys. 117, 17E306 (2015).
5. K. Wang, E. Lu, J. W. Knepper, F. Yang, and A. R. Smith, Appl. Phys. Lett. 98,
162507 (2011).
6. S. Mizukami, T. Kubota, F. Wu, X. Zhang, T. Miyazaki, H. Naganuma, M. Oogane,
A. Sakuma, and Y. Ando, Phys. Rev. B 85, 014416 (2012).
7. F. Wu, E. P. Sajitha, S. Mizukami, D. Watanabe, T. Miyazaki, H. Naganuma, M.
Oogane, and Y. Ando, Appl. Phys. Lett. 96, 042505 (2010).
8. M. Tanaka, Mater. Sci. Eng. B 31, 117 (1995).
9. A. Köhler, I. Knez, D. Ebke, C. Felser, and S. S. P. Parkin, Appl. Phys. Lett. 103,
162406 (2013).
10. J.N. Feng, W. Liu, W.J. Gong, X.G. Zhao, D. Kim, C.J. Choi and Z.D. Zhang, J.
Mater. Sci. Tech. 33, 291 (2017).
11. L. J. Zhu, S. Nie, K. Meng, D. Pan, J. Zhao, and H. Zheng, Adv. Mater. 24, 4547
(2012).
12. W. Feng, D. V. Thiet, D. D. Dung, Y. Shin, and S. Cho, J. Appl. Phys 108, 113903(2010).
13. S. Mizukami, F. Wu, A. Sakuma, J. Walowski, D. Watanabe, T. Kubota, X. Zhang,
H. Naganuma, M. Oogane, Y. Ando, and T. Miyazaki, Phys. Rev. Lett. 106, 117201(2011).

76 | Page

Chapter 4

14. K. Z. Suzuki, R. Ranjbar, J. Okabayashi, Y. Miura, A. Sugihara, H. Tsuchiura, and
S. Mizukami, Sci. Rep. 6, 30249 (2016).
15. R. Ranjbar, K. Z. Suzuki, Y. Sasaki, L. Bainsla, and S. Mizukami, Jpn. J. Appl.
Phys 55, 120302 (2016).
16. K. K. Meng, J. Miao, X. G. Xu, J. X. Xiao, J. H. Zhao, and Y. Jiang, Phys. Rev. B
94, 214413 (2016).
17. B. Stegemann, C. Ritter, B. Kaiser, and K. Rademann, Phys. Rev. B 69, 155432(2004).
18. E. Lu, D. C. Ingram, A. R. Smith, J. W. Knepper, and F. Y. Yang, Phys. Rev. Lett.
97, 146101 (2006).
19. A. Bedoya-Pinto, C. Zube, J. Malindretos, A. Urban, and A. Rizzi, Phys. Rev. B 84,
104424 (2011).
20. W. Fenga, D. V. Thiet, D. D. Dung, Y. Shin, and S. Chob, J. Appl. Phys. 108,
113903 (2010).
21. K. Wang K, A. Chinchore A, W. Lin, D.C. Ingram, A. R. Smith, A. J. Hauser, andF. Yang, J. Cryst. Growth 311, 2265 (2009).
22. T. A. Bither and W. H. Cloud, J. Appl. Phys. 36, 1501 (1965).
23. J. Winterlik, B. Balke, G. H. Fecher, C. Felser, M. C. M. Alves, F. Bernardi, and J.
Morais, Phys. Rev. B 77, 054406 (2008).
24. H. Berger, B. Christ, and J. Troschke, Crys. Res. Tech. 17, 1233 (1982).
25. M. Tanaka, J. P. Harbison, J. DeBoeck, T. Sands, B. Philips, T. L. Cheeks, and V.
G. Keramidas, Appl. Phys. Lett. 62, 1565 (1993).
26. Y. Ueda, N. H. D. Khang, K. Yao, and P. N. Hai, Appl. Phys. Lett. 110, 062401(2017).
27. T. A. Bither and W. H. Cloud, J. Appl. Phys. 36, 1501 (1965).

77 | Page

Chapter 4

28. J. Winterlik, B. Balke, G. H. Fecher, C. Felser, M. C. M. Alves, F. Bernardi, and J.
Morais, Phys. Rev. B 77, 054406 (2008).
29. L. J. Zhu, D. Pan, S. H. Nie, J. Lu, and J. H. Zhao, Appl. Phys. Lett. 102, 132403(2013).
30. K. Meng, J. Miao, X. Xu, Y. Wu, J. Xiao, J. Zhao and Y. Jiang, Sci. Rep. 6, 38375(2016).

78 | Page

Chapter 5

Chapter 5

Spin Hall Effect in BiSb Topological Insulator
SOT using the SHE in heavy metal and topological insulators has great potential
for ultra-low power SOT-MRAM. To be competitive with conventional STT-MRAM, apure spin current source with large spin Hall angle (SH > 1) and high electricalconductivity ( > 105 -1m-1) is required. However, this requirement cannot be satisfied
in heavy metals (such as Pt, Ta, and W) with high  but small θSH (~ 0.1) [1, 17, 23], and
TIs with large θSH but low . There is no spin Hall material so far that can satisfy
both conditions simultaneously.
This chapter will focus on evaluation of the SHE in the topological insulator Bi1xSbx (0.07  x  0.22) with strong spin orbit coupling [4]. Thanks to its high carrier

mobility (~104 cmV-1s-1), our previous work showed that the average conductivity of BiSb
thin films is as large as 2.5×105 Ω-1m-1 [5], which is compatible to other metallic materials
used in realistic MRAM. On the other hand, its non-trivial topologically protected surface
states have been confirmed by the angle-resolved photoemission spectroscopy (ARPES)[6, 7, 8] and magneto-transport measurements [9, 10]. Thus, BiSb promises large SHE.
In this work, the performance of thin BiSb films as a pure spin current source in various
BiSb / MnGa bilayers will be investigated. The large spin Hall angle in BiSb will be
evaluated and compared with other spin Hall materials. Finally, prospective applicationsof SOT-MRAM based on BiSb will be discussed.

79 | Page

Chapter 55.1. Thin film growth and crystal structure characterizations
The BiSb / MnGa bilayer thin films were grown on semi-insulating GaAs(001)substrates by using ultrahigh vacuum MBE system. After removing the surface oxide
layer of the GaAs substrate at 580oC, a 100 nm-thick GaAs buffer layer was grown toobtain an atomically smooth surface. The substrate was cooled down to room temperaturefor deposition of a 4 monolayer Mn-Ga-Mn-Ga template. Then, the substrate was heated
up to 250oC for deposition of a MnGa thin film with the total thickness of 3 nm. A
Bi0.1Sb0.9 layer was grown on top of the MnGa layer at 200oC with the rate of 1 nm/min.
Finally, the samples were cooled down again to room temperature for deposition of an As
thin cap layer. The growth process was monitored in situ by reflection high energy
electron diffraction.
By optimizing the growth condition, high quality BiSb / MnGa bi-layers withsmooth interface can be obtained, despite the large lattice mismatch between MnGa(001)
and BiSb(012). Figure 5.1 shows the RHEED patterns during growth of the BiSb / MnGa
bi-layers. The RHEED patterns of both MnGa (3) and BiSb (10) are streaky (the numbers
in parentheses present layer’s thickness in nanometers), indicating good crystal quality.
To check the crystallographic orientation of the BiSb / MnGa bilayers, a thick BiSb (20)/ MnGa (10) bilayer was grown in the same condition and checked by X-ray diffraction
measurements. Figure 5.2 shows the -2 XRD spectrum of the BiSb (20) / MnGa (10)bi-layer. The XRD spectrum indicates that the crystallographic orientation isBiSb(012)//MnGa(001)//GaAs(001).

80 | Page

Chapter 5

Figure 5.1: RHEED patterns during growth of the BiSb / MnGa bilayers (a) after
deposition of the 4 monolayer Mn-Ga-Mn-Ga template, (b) after annealing the template
at 250oC, (c) after growth of the 3 nm-thick MnGa layer, (d) after growth of a 1 nmthick BiSb layer at 200oC, and (e) after growth of the 10 nm-thick BiSb layer.

Figure 5.2: -2 XRD spectrum of a BiSb (20) / MnGa (10) bilayer. The
crystallographic orientation is BiSb(012)//MnGa(001)//GaAs(001).

81 | Page

Chapter 55.2. Magnetic properties and SOT effect in Bi0.9Sb0.1Mn0.6Ga0.4 bilayers
5.2.1.

Magnetic properties

MnGa was employed as a model ferromagnet because its large perpendicularmagnetic anisotropy (> 10 Merg/cc), large uniaxial anisotropy field (> 40 kOe), large
coercive force (> 1.5 kOe), and high conductivity (5×105 Ω-1m-1) represent well thosewould be used in futuristic ultra-high density SOT-MRAM [ 11 ]. Furthermore, by
adjusting the Mn composition, I can grow Mn0.6Ga0.4 layers with perfect perpendicularmagnetization and Mn0.45Ga0.55 layers with titling magnetization which are convenient forevaluation of the spin-orbit field generated by the BiSb layer.
Figure 5.3 (a) shows the schematic Bi0.9Sb0.1 (10) / Mn0.6Ga0.4 (3) (thickness in nm)
bi-layer and the coordinate system used in this work. An electric current was appliedalong the x direction, while an external magnetic field Hext was applied in the z-x plane atan angle  with respect to the z axis. Figure 5.3 (c) shows the out-of-plane magnetization
curve of the bilayer measured at various temperatures. The magnetization of the 3 nmthick Mn0.6Ga0.4 layer in this bi-layer is the same as that of high quality stand-alone
Mn0.6Ga0.4 thin films grown on GaAs(001), indicating that there is no interfacial magnetic
dead layer.

5.2.2.

SOT effect

The bi-layers are then patterned into 100m-long and 50 m-wide Hall bars fortransport measurements, as one shown in Fig. 5.3(b). The Hall bars are mounted inside aliquid nitrogen cryostat which acts as a heat sink to minimize the effect of Joule heating.
Figure 5.3 (d) shows the Hall resistance RH of a Hall bar under a perpendicular magnetic

82 | Page

Chapter 5field (= 0 at 150 K, measured with various current density J = 0.2 – 15.4105 A/cm2.
Here, J is the nominal current density of the Hall bar, defined asJ  I / [w(tBiSb  tMnGa )](5.1)

where I is the applied current (10 mA maximum), w = 50 m is the width of the Hall bar,tBiSb = 10 nm and tMnGa = 3 nm are the thickness of the BiSb and MnGa layer, respectively.
The Hall resistance is dominated by the anomalous Hall effect which reveals theperpendicular magnetization component of the Mn0.6Ga0.4 layer. A systematic reductionof the coercive force Hc of the Mn0.6Ga0.4 layer was observed with increasing J. The
reduction Hc is as large as 2 kOe at a modest J =15.4105 A/cm2. To make sure that thisreduction of Hc is not the result of Joule heating of the Mn0.6Ga0.4 layer, a Hall bar froma stand-alone Mn0.6Ga0.4 (3) layer was prepared, and its Hall resistance was measured
under various J. As seen in Fig. 5.3(e), no clear change of Hc up to J = 46.7105 A/cm2
was confirmed, which is 3 time higher than the highest current density applied in Fig.
1(d). This indicates that the reduction of Hc shown in Fig. 5.3(d) is not the result of Joule
heating. Indeed, for the Joule heating to be the origin of the large Hc = 2 kOe, theMn0.6Ga0.4 layer temperature had to increase from 150 K to 250 K (see Fig. 5.3(c)), whichis unlikely given the very small J used in our experiments, comparing with J ~ 107 - 108
A/cm2 used in previous studies using heavy metals as the spin Hall layer. Furthermore, asignificant reduction of the remanent RH at J =15.4105 A/cm2 was observed. This was
not observed in the magnetization curve at 250 K. Therefore, the large reduction of Hc isthe result of an in-plane spin-orbit field generated by spin current injection from the BiSb
layer. Figure 5.3(f) shows Hc as a function of the current density JBiSb in the BiSb layer.
Here, JBiSb is calculated using BiSb2.5×105 Ω-1m-1and MnGa5×105 Ω-1m-1. The
gradient Hc/JBiSb is as large as 3700 Oe/(MA/cm2) at high JBiSb (dashed line in Fig.
5.3(f)).

83 | Page

Chapter 5

Figure 5.3: (a) Schematic structure of the Bi0.9Sb0.1 (10) / Mn0.6Ga0.4 (3) (thickness innm) bi-layer and the coordinate system used in this work. (b) Micrograph of a 100 m
 50 m Hall bar device. (c) Out-of-plane magnetization curves of the bilayer at
different temperatures. (d) Hall resistance RH of a Hall bar under a perpendicularmagnetic field Hext (= 0 at 150 K, measured with various current density J = 0.2 –15.4105 A/cm2. (e) RH of a Hall bar of a stand-alone MnGa (3) layer. (f) Reduction of
the coercive force Hc of the bi-layer as a function of the current density JBiSb in the
BiSb layer.

84 | Page

Chapter 55.3. Magnetic properties and SOT effect in Bi0.9Sb0.1Mn0.45Ga0.55 bilayers
5.3.1.

Magnetic properties

In order to quantitatively evaluate the spin Hall angle of BiSb, another bilayer
Bi0.9Sb0.1 (10) / Mn0.45Ga0.55 (3) with tilting magnetization was prepared. The blue andthe red curves in Fig. 5.4(a) show the in-plane and out-of-plane magnetization curve of
Bi0.9Sb0.1 (10) / Mn0.45Ga0.55 (3) bilayers. Because of the tilting magnetization, the outof-plain magnetization does not saturate until a perpendicular Hext ~ 20 kOe is applied.
The in-plane magnetization shows small remanence, but rapidly increases up to an inplane Hext ~ 4 kOe, then slowly increases and saturates at an in-plane Hext ~ 50 kOe.
The magnetic domains of the Mn0.45Ga0.55 layer was investigated by an in-planemagneto-optical Kerr effect (MOKE) microscope. Unfortunately, the MOKE effect of
MnGa is weaker than the resolution of the MOKE microscope, thus individual magnetic
domains of the Mn0.45Ga0.55 layer could not be distinguished. Indeed, the magnetic
circular dichroism (MCD) intensity (equivalent to MOKE ellipticity) of the Mn0.45Ga0.55
is only 20 mdeg, while the MOKE microscope requires at least 100 mdeg for working.
However, the horizontal component of the stray field from the Mn0.45Ga0.55 layer
can be detected, indicating the existence of tilting domains. The experiment setup is asfollows. First, a MOKE sensor with large MOKE effect was prepared, so that individual
domains of the sensor are visible under our in-plane MOKE microscope. The in-planemagnetization of the sensor is known to saturate at about 400 Oe, and the sensor is used
to visualize magnetic fields larger than 400 Oe. Then, the domains of the sensor wasobserved with and without contact with the Mn0.45Ga0.55 layer under in-plane magnetic
fields. Figure 5.4(b) show the MOKE images of the sensor in contact with the Mn0.45Ga0.55
layer, while Figure 5.4(c) show those of the sensor without contact with the Mn0.45Ga0.55

85 | Page

Chapter 5

layer. In Fig. 5.4(b), the sensor is saturated (i.e. all domains disappear and the MOKE
image becomes dark) when an in-plane magnetic field of 300 Oe is applied. In contrast,
in Figs. 5.4(c), the sensor is saturated at 400 Oe. This indicates that there is an in-planecomponent of the stray field from Mn0.45Ga0.55 when an external Hext = 300 Oe is applied,which gives evidence that the tilting domains in the Mn0.45Ga0.55 layer rapidly reorientate
toward the magnetic field direction.

86 | Page

Chapter 5

Figure 5.4: (a) In-plane (blue) and out-of-plane (red) magnetization curve of Bi0.9Sb0.1(10) / Mn0.45Ga0.55 (3) bilayers. Inset shows the tilting magnetic domains of the
Mn0.45Ga0.55 layer. (b) In-plane MOKE images of the sensor in contact with the
Mn0.45Ga0.55 layer. (c) In-plane MOKE images of the sensor without contact with the
Mn0.45Ga0.55 layer. Here, the magnetic field is applied in-plane.

87 | Page

Chapter 55.3.2.

Magnetic anisotropy of the tilting magnetic domains in

Mn0.45Ga0.55
In order to see the detail picture of the tilting magnetization in the Mn0.45Ga0.55 (3)layer, the anisotropy magnetic energy density of a single domain is studied. It can be
expressed by
Eani  KuK
cos 2  4 cos 4
2
4

(5.2)

where  is the angle between the magnetization vector of the domain and the z axis, Ku is
the anisotropy constant (including the shape anisotropy) representing the uniaxial easy
axis along the z axis, and K4 is the anisotropy constant representing the biaxial easy axes
at = 45, respectively.
Ku and K4 can be estimated as follows. When the magnetic field is applied in-plane (H//x),the total magnetic energy density is given by
E

Ku
K
cos 2  4 cos 4  MH sin 
2
4

(5.3)

At a given H,  is determined by solving the equationordE
 K u sin 2  K 4 sin 4  MH cos   0
d

(5.4)

2Ku sin   4K4 cos 2 sin   MH  0(5.5)

which is further simplified to

H u sin   H 4 cos 2 sin   H  0(5.6)

where Hu the uniaxial anisotropy field and H4 the biaxial anisotropy field defined by
Ku 

1
1
H u M , K 4  H 4 M . When H approaches the in-plane saturation magnetic field2
4

Hs-x,  reaches 90, thus

88 | Page

Chapter 5

H u  H 4  H s-x(5.7)

Similarly, when the magnetic field is applied out-of-plane (H//z), the total magnetic
energy density is given by
E

Ku
K
cos 2  4 cos 4  MH cos 
2
4

Solving

or

dE
d

(5.8)

 0 , Eq. 5.8 can be rewritten as

2Ku cos   4K4 cos 2 cos   MH  0(5.9)

H u cos   H 4 cos 2 cos   M  0(5.10)

When H approaches the out-of-plane saturation magnetic field Hs-z,  reaches 0,thus H u  H 4  H s-z .

(5.11)

Hu = 10 kOe and H4 = 30 kOe were obtained by solving Eq. 5.7 and Eq. 5.11 using Hs-x
= 40 kOe, and Hs-z = 20 kOe (see Fig. 5.4(a)).
This magnetic energy density function captures most of the important features ofthe magnetization curves in Fig. 5.4(a). Figure 5.5(a-d) plot the E/M of the domain as afunction of  when (a) no magnetic field is applied, (b) an in-plane magnetic field of 4
kOe is applied, (c) an in-plane magnetic field of 40 kOe is applied, and (d) an out-ofplane magnetic field of 20 kOe is applied. In Fig. 5.5(a), the magnetization vector has 4
equivalent stable positions at = 35 and 145. The potential barrier between +35/ 35 domains is much smaller than that between 35/145 domains. This suggests thecoexistence of 35 domains as schematically shown in the inset of Fig. 5.4(a). Figure5.5(b) shows that when an in-plane magnetic field of 4 kOe is applied, the barrier between+35/ -35 domains disappears. Thus, Figs. 5.5(a) and 5.5(b) explain the observation thatthe in-plane magnetization shows small remanence, but rapidly increases up to an in-

89 | Page

Chapter 5plane magnetic field of 4 kOe. When a large in-plane magnetic field of 40 kOe is applied,
the magnetization vector approaches 90 as shown in Fig. 5.5(c). Similarly, when a large
out-of-plane magnetic field of 20 kOe is applied, the magnetization vector approaches 0
as shown in Fig. 5.5(d).

Figure 5.5: E/M of a single domain of the Mn0.45Ga0.55 layer as a function of  , when(a) no magnetic field is applied, (b) an in-plane magnetic field of 4 kOe is applied, (c)an in-plane magnetic field of 40 kOe is applied, and (d) an out-of-plane magnetic fieldof 20 kOe is applied.

90 | Page

Chapter 5

Figures 5.6(a) and 5.6(b) compare the magnetization hysteresis curves of the
Mn0.45Ga0.55 layer in Fig. 5.4(a), measured by SQUID (circles) and theoretical calculation
results using the single domain model (solid lines), when the magnetic field was applied
in-plane and out-of-plane, respectively. One can see that the theoretical curves reproduce
the experiment results when the magnetic field is higher than 4 kOe (in-plane) or 12 kOe(out of plane). However, at low magnetic fields, clear deviation from the single domain
model is observed. Particularly, the remanences and the coercive forces are smaller thanthose predicted by the single domain model. These indicates that the sample should be in
the multi domain structure at low magnetic fields so that the static magnetic energy canbe reduced, and the magnetization reversal process occurs through domain wall
movement rather than single domain coherent rotation.

Figure 5.6: Magnetization hysteresis curves of the Mn0.45Ga0.55 layer measured by
SQUID (circles) and theoretical calculation results (solid lines) using the single domain
model, when the magnetic field is applied (a) in-plane and (b) out-of-plane,
respectively.

91 | Page

5.3.3.

Chapter 5

SOT effect in Bi0.9Sb0.1 - Mn0.45Ga0.55 bilayers under a titlingexternal magnetic field
The initial rise of the in-plane magnetization at the small in-plane Hext indicatesreorientation of the magnetic domains toward the in-plane Hext direction, while the slow
increase at the in-plane Hext > 4 kOe reflects their tilting toward the horizontal direction.
This unique magnetic behaviors of the Mn0.45Ga0.55 layer allow us to directly evaluate Hso.
Figure 5.7(a) shows the RH of a 100 m × 50 m Hall bar made from the bilayer in Fig.
5.4(a) under nearly perpendicular Hext at room temperature. Before the measurements, anin-plane magnetic field of +8 kOe is applied to induce a small remanent in-plane Mx
component of the Mn0.45Ga0.55 layer (see Fig. 5.3(a) and the inset in Fig. 5.4(a)), then 
was reduced to ~ 2 and the magnetic field was swept from +8 kOe to – 8 kOe and viceverse. Since the direction of the damping-like spin-orbit field Hso is given by   m ,where  is the spin polarization unit vector of the spin current along the y direction andm is the unit vector of the magnetization direction, there is an out-of-plane component
Hso-z of the spin-orbit field associating with Mx.
The existence of such Hso-z component can be seen in Fig. 5.7(a); the remanence
and coercive force of the RH hysteresis systematically increase with increasing positive J.
This clearly cannot be explained by Joule heating which can only reduce but not enhance
the remanent RH and coercive force. On the other hand, the RH hysteresis was reduced
remanence and coercive force at a negative J = -7.7105 A/cm2.
In addition to the damping-like spin-orbit field Hso, there is possibly a field-likespin-orbit field HFL generated by BiSb. However, HFL can be neglected by analyzing themagnitude of the RH loops of the Bi0.9Sb0.1 (10) / Mn0.45Ga0.55 (3) Hall bar under a slightly
tilting perpendicular magnetic field (= 2 toward the x direction Here, a situation wasconsidered when HFL was comparable with Hso, i.e. its strength was ~ 1 kOe at the highest

92 | Page

Chapter 5

J = 13.8105 A/cm2. Since HFL is along the y direction, it can generate a non-zero My
component for the Mn0.45Ga0.55 (3) layer. Therefore, there would be contribution from theplanar Hall resistance RPHE in addition to the anomalous Hall resistance RAHE to the total
Hall resistance RH. Unlike Hso, however, the direction of HFL depends only on the
direction of J, but not M. Figures 5.7(c) and 5.7(d) show the direction of Mx, My, and Mz
at a perpendicular Hext = 8 kG and -8 kG, respectively. In Fig. 5.7(c), Mx > 0, My > 0, and
Mz > 0, thus

RH (8 kOe)  RPHE sin 2  RAHE

(5.12)

where  tan-1(My/Mx). In Fig. 5.7(d), Mx < 0, My > 0, and Mz < 0, thus

RH (8 kOe)  RPHE sin[2(   )]  RAHE   RPHE sin 2  RAHE

(5.13)

That means the magnitude of the RH loop is given by RPHE sin 2  RAHE , and would
be enhanced by the amount of RPHE sin 2 . As a result, one would expect that themagnitude of the RH loops would systematically increase with increasing J. However, as
seen in Fig. 5.7(a), the magnitude of the RH loops does not change when J is increased
from 0.2105 A/cm2 to 13.8105 A/cm2. This indicates that HFL is negligible, and that RH
has only contribution from RAHE.

93 | Page

Chapter 5

Figure 5.7: (a) RH of a 100 m  50 m Hall bar of the bilayer under a slightly tilting
perpendicular magnetic field (= 2, measured with various current density J = -7.7
– 13.8105 A/cm2 at 300 K. Inset shows the perpendicular spin-orbit field Hso acting
on the magnetization vector M at Hext = -Hc (coercive force) in the macrospin picture.
(b) Coercive force Hc and its change ΔHc as functions of the current density JBiSb in theBi0.9Sb0.1(10)/Mn0.45Ga0.55(3) bilayer. (c), (d) Direction of Mx, My, and Mz under aslightly tilting perpendicular magnetic field Hext (= 2 toward the x direction),assuming a non-zero field-like spin-orbit field HFL at Hext = 8 kOe and Hext = -8 kOe,
respectively.

94 | Page

5.3.4.

Chapter 5

SOT effect in Bi0.9Sb0.1 - Mn0.45Ga0.55 bilayers under an in-plane

external magnetic field
To further confirm the effect of Hso-z, RH was measured under an in-plane Hext
(=90). Figures 5.8(a) and 5.8(b) show the RH-Hext (=90) hysteresis at J = 13.8105
A/cm2 and J = -13.8105 105 A/cm2, respectively. One can see that RH rapidly increases
up to Hext ~ 4 kOe, and then gradually decreases at Hext > 4 kOe. This behavior isconsistent with the in-plane magnetization curve shown in Fig. 5.4(a); at Hext = 0~4 kOe,
the magnetic domains are rapidly reoriented toward the x-directions, so that Hso-z and RH
reach their maximum value at 4 kOe. At Hext > 4 kOe, the whole MnGa layer becomes asingle domain, while the magnetization begins tilting toward the x direction and RH
decreases.
Furthermore, Hso-z and RH switch its directions when direction of Mx or J is changed.
As shown in Fig. 5.8(c), the Hso direction can be switched between 4 different
configurations by changing the direction of Mx (by sweeping the in-plane external fieldfrom positive to negative and vice-verse), or by changing the direction of the spinpolarization of the spin Hall current (changing the charge current direction from positive
to negative). These results definitely demonstrate that the symmetry of Hso follows thatof M×σ, consistent with the symmetry of SOT.
Note that the polarity switching of RH when direction of Mx or J is changed wasobserved not only in the low field range of |Hext| <4 kOe (multi-domain state), but also in
the high field range of |Hext| > 4 kOe (single domain state). This eliminates the possibilityof artifacts due to the topological Hall effect [12, 13, 14] or the tunneling planar Hall
effect [15], since those effects require inhomogeneous magnetization to occur in our
device, either in the form of spatially varying magnetic domains or skyrmions.

95 | Page

Chapter 5

Figure 5.8: (a), (b) RH as a function of an in-plane Hext (= 90at J = +13.8105
A/cm2 and -13.8105 A/cm2, respectively. (c) Symmetry of 𝐻SO ∼ 𝑀 × 𝜎 confirmedby switching the in-plane magnetic field direction or the current direction.

96 | Page

5.3.5.

Chapter 5

Spin Hall angle evaluation

Next, the spin Hall angle was evaluated from data in Fig. 5.7(a). For the sake ofsimplicity, a macrospin model with coherent magnetization rotation was first assumed.
At Hext = -Hc(J) (the coercive force at a given J), the net perpendicular magnetization
component is zero, so there is only the in-plane magnetization component. The situation
at Hext = -Hc(J) is shown in the inset of Fig. 5.7(a). At this point, Hso points to the z
direction and counters Hext. Thus, the macrospin model predicts that the shift of thecoercive Hc is equal to Hso. In reality, however, the Mn0.45Ga0.55 layer is in a multidomain state at low magnetic fields, and magnetization reversal occurs through domain
wall movement rather than coherent magnetization rotation. Nevertheless, fullmicromagnetic simulations have shown that the relation Hso = Hc gives a good
estimation for Hso with less than 5% of uncertainty in a Pt/BaM ferrite bi-layer [16].
Furthermore, the macroscopic model has been used to remarkably reproduce theexperimental switching phase diagram due to SOT effect in Pt/Co bilayers [17]. Thisconfirms the validity of this relation even though it is derived from a simple macrospin
coherent rotation model.
Hso can also be estimated from the RH-Hext data in Figs. 5.8(a)-2(b) in the high inplane field range (|Hext| > 4 kOe), when the Mn0.45Ga0.55 layer becomes a single domain
and the macrospin model is applicable. The obtained average value of |Hso| = 2.9 – 3.4
kOe for J = 13.8 105 A/cm2 are within 10% of uncertainty from that obtained byassuming Hso = Hc = 3.1 kOe for J =13.8 105 A/cm2 in Fig. 5.7(a) (see appendix A).
Thus, in the following, the relation Hso = Hc was used to estimate the spin Hall angle.
Figure 5.7(b) plots Hc obtained in Fig. 5.7(a) as a function of JBiSb. The slope Hso/JBiSb= 2.3 kOe/(MA/cm2) was obtained at room temperature. This value is much larger thanthose of heavy metals and TIs reported before, such as Ta ~ 6.8 Oe/(MA/cm2) in Fe (1.1)

97 | Page

Chapter 5/ Ta (7.2), Pt ~ 2.9 Oe/(MA/cm2) in Fe (0.5) / Pt (2.3) [ 18 ], and BixSe1-x ~100
Oe/(MA/cm2) in CoFeB (5) / BixSe1-x (4) [3]. The room-temperature spin Hall angle SH ,calculated by

SH 

2e

M MnGa tMnGa

H SO
J BiSb

(5.14)

where M MnGa and tMnGa are the magnetization and thickness of Mn0.45Ga0.55, respectively,

J BiSb is the current density flowing in BiSb layer. The estimated spin Hall angle is 52,
which is the highest value reported so far. Our data also show that SH of BiSb has thesame sign as those of (Bi0.5Sb0.5)2Te3 [19], Bi2Se3 [2] and Pt [17].

5.4. Magnetization switching by ultra-low current density
In order to demonstrate magnetization switching by ultra-low current density using
the large spin Hal effect of BiSb, a 100 m × 50 m Hall bar of a Bi0.9Sb0.1 (5) /Mn0.45Ga0.55 (3) bilayer was prepared. Figure 3(a) and 3(b) demonstrate the SOT
switching of the MnGa layer when applying 100 ms pulse currents to the Hall bar and an
in-plane Hext = + 3.5 kOe and -3.5 kOe, respectively. One can see that clear switching at
an average critical current density of J = 1.5×106 cm2 (JBiSb = 1.1×106 cm2). Here,the critical current density is defined at which the Hall resistance changes sign. Note thatthe switching of RH between 1  corresponds to full magnetization switching.
Furthermore, the switching direction is reversed when the in-plane Hext direction isreversed, consistent with the behavior of SOT switching. The observed critical current
density is much smaller than those of Ta (5) / MnGa (3) (J = 1.1108 A/cm2) [20], IrMn
(4) / MnGa (3) (J = 1.5108 A/cm2) [ 21] and Pt (2) / MnGa (2.5) (J = 5.0107 A/cm2)[22].

98 | Page

Chapter 5

Figure 5.9: (a), (b) RH of a 100 m  50 m Hall bar of the Bi0.9Sb0.1 (5) / Mn0.45Ga0.55(3) bilayer under 100 ms pulse currents and an in-plane Hext of +3.5 kOe and -3.5 kOe,
respectively.

Table 5.1: Room-temperature spin Hall angle SH, conductivity , and spin Hall
conductivity SH of several heavy metals and TIs.

SH



SH

(-1m-1)(𝟐𝒆-1m-1)ℏ

-Ta [1]0.15

5.3105

0.8105

-W [23]

0.4

4.7105

1.9105

Pt [17]0.08

4.2106

3.4105

Bi2Se3 [2]

2-3.5

5.7104

1.1-2.0105

BixSe1-x [3]

18.8

7.8103

1.47105

Bi0.9Sb0.1 (this work)52

2.5105

1.310799 | Page

Chapter 55.5. Comparisons with other spin Hall materials
BiSb has many characteristics that make it the best candidate for the pure spincurrent source in SOT-MRAM. Its conductivity is comparable to typical ferromagnetic
and non-magnetic metals used in MRAM, while its spin Hall angle is as large as 52 atroom temperature. It can be grown well on ferromagnetic metals without creating amagnetic dead layer. Table 5.1 summarizes , SH, and SH of several heavy metals and
TIs at room temperature. In term of SH, which is considered as the figure of merit for
spin Hall materials, BiSb outperforms other TIs by a factor of 100 and the nearest
competitor (Pt) by a factor of 30. Although there are reports of room-temperature SOT
switching by other TIs in Bi2Se3/CoTb [24], Bi2Se3/NiFe [25], and BixSe1-x/CoFeB [3],the ferromagnets used in those works have a low coercive force of only a few 10 Oe ~ afew 100 Oe, which is much smaller than that (a few kOe) in realistic MRAM. Using BiSb,
both very large spin-orbit field of 2.3 kOe/(MA/cm2) and SOT switching at a low criticalcurrent density of 1.5×106 cm2 have been demonstrated by using the MnGa as
ferromagnetic layer with much higher PMA (40 ~ 50 kOe) and coercive force ( > 1.6
kOe) than those used in previous experiments. These double check the very large spin
Hall effect of BiSb.
The observation of the very large spin Hall effect in BiSb leaves many open
questions about the physics of the spin Hall effect in TIs. Even though stronger spin-orbit
interaction and larger spin Hall effect are expected for BiSb than Bi3Se2 or (Bi,Sb)3Te2ℏ

thanks to its very small band gap, the observation of SH = 1.3107 2𝑒-1m-1 is unexpected.
Because of the very small band gap, the electric current flows in both the surface and thebulk of BiSb, thus contribution of both surface and bulk spin Hall effect should beconsidered. However, first-principle calculation of the bulk intrinsic spin Hall effect of

100 | Page

Chapter 5ℏBiSb yields a maximum value of 9.8×104 2𝑒-1m-1 when the Fermi level is in the bandgap, which can account for only 0.74% of the observed value (although very large bulk
intrinsic SH 

2e  SHis possible from the calculation since the bulk  ~ 0 at zero 

temperature) [26]. Furthermore, the bulk extrinsic mechanism such as side-jump or skewscattering is unlikely the main mechanism given the high carrier mobility and low
scattering rate in BiSb alloys. Therefore, this suggests that the topological surface statesof BiSb(012) are mainly responsible for the observed very large spin Hall effect in BiSb.
It was theoretically predicted [ 27 ] and later experimentally confirmed by ARPES
measurement [28] that the BiSb(012) surface has three Dirac cones at the  , X , and M
point, while there is only one Dirac cone at the  point on the BiSb(001), Bi2Se3(001),
and Bi2Se3(012) surface. This unique “valley degree of freedom” of the BiSb(012) surface
may be related to the origin of the observed SHE. Detailed observation of the BiSb(012)surface states by spin-resolved ARPES is needed for unlocking the secret of the very large
spin Hall effect in BiSb(012).

Figure 5.10: (a), (b) Topological prediction for the surface electronic structure of
Bi2Se3 and Bi1-xSbx (0.09 < x < 0.22), respectively. Reproduced with permission [28].

101 | Page

Chapter 55.6. Summary
In this chapter, the huge spin Hall angle in BiSb thin films with SH ~ 52, and spinℏHall conductivity SH ~ 1.3107 2𝑒-1m-1 at room temperature was observed. BiSb not
only has large  ~ 2.5105 -1m-1 but also can generate a very large spin-orbit field of
2.3 kOe/(MA/cm2) in Bi0.9Sb0.1 / MnGa bi-layers. These results underline the potential of
BiSb as good spin Hall material in SOT-MRAM. As over ten years have passed from the
proposals [29, 30] and the realization of TIs [31], BiSb emerges as a promising candidate
for SOT-MRAM based on TIs.

102 | Page

Chapter 5

References
1. L. Liu, C. F. Pai, Y. Li, H. W. Tseng, D. C. Ralph, and R. A. Buhrman, Science 336,
555 (2012).
2. A. R. Mellnik, J. S. Lee, A. Richardella, J. L. Grab, P. J. Mintun, M. H. Fischer, A.
Vaezi, A. Manchon, E.-A. Kim, N. Samarth, and D. C. Ralph, Nature 511, 449 (2014).
3. DC. Mahendra, R. Grassi, J. Y. Chen, M. Jamali, D. R. Hickey, D. Zhang, Z. Zhao, H.
Li, P. Quarterman, L. Yang, M. Li, A. Manchon, K. A. Mkhoyan, T. Low, and J. P. Wang,Nat. Mater. 17, 800 (2018).
4. J. C. Y. Teo, L. Fu, and C. L. Kane, Phys. Rev. B 78, 045426 (2008).
5. Y. Ueda, N. H. D. Khang, K. Yao, and P. N. Hai. Appl. Phys. Lett. 110, 062401 (2017).
6. D. Hsieh, D. Qian, L. Wray, Y. Xia, Y. S. Hor, R. J. Cava, and M. Z. Hasan, Nature
452, 970 (2008).
7. T. Hirahara, Y. Sakamoto, Y. Saisyu, H. Miyazaki, S. Kimura, T. Okuda, I. Matsuda,

S. Murakami, and S. Hasegawa, Phys. Rev. B. 81, 165422 (2010).
8. A. Nishide, A. A. Taskin, Y. Takeichi, T. Okuda, A. Kakizaki, T. Hirahara, K.
Nakatsuji, F. Komori, Y. Ando, and I. Matsuda, Phys. Rev. B 81, 041309 (2010).
9. A. A. Taskin, Y. Ando, Phys. Rev. B 80, 085303 (2009).
10. A. A. Taskin, K. Segawa, and Y. Ando, Phys. Rev. B 82, 121302 (2010).
11. L. J. Zhu, S. H. Nie, and J. H. Zhao, Chin. Phys. B 22, 118505 (2013).
12. P. Bruno, V. K. Dugaev, and M. Taillefumier, Phys. Rev. Lett. 93, 096806 (2004).
13. K. Yasuda, R. Wakatsuki, T. Morimoto, R. Yoshimi, A. Tsukazaki, K. S. Takahashi,
M. Ezawa, M. Kawasaki, N. Nagaosa, and Y. Tokura, Nat. Phys. 12, 555 (2016).
14. B. M. Ludbrook, G. Dubuis, A. H. Puichaud, B. J. Ruck, and S. Granville, Sci. Rep.
7, 13620 (2017).
15. B. Scharf, A. M. Abiague, J. E. Han, E. M. Hankiewicz, and I. Žutić, Phys. Rev. Lett.

103 | Page

Chapter 5117, 166806 (2016).
16. P. Li, T. Liu, H. Chang, A. Kalitsov, W. Zhang, G. Csaba, W. Li, D. Richardson, A.
DeMann, G. Rimal, H. Dey, J. S. Jiang, W. Porod, S. B. Field, J. Tang, M. C. Marconi,A. Hoffmann, O. Mryasov, and M. Wu, Nature Comm. 7, 12688 (2015).
17. L. Liu, T. Moriyama, D. C. Ralph, and R. A. Buhrman, Phys. Rev. Lett. 106, 036601(2011).
18. M. Kawaguchi, K. Shimamura, S. Fukami, F. Matsukura, H. Ohno, T. Moriyama, D.
Chiba, and T. Ono, Appl. Phys. Exp. 6, 113002 (2013).
19. Y. Fan, P. Upadhyaya, X. Kou, M. Lang, S. Takei, Z. Wang, J. Tang, L. He, L. T.
Chang, M. Montazeri, G. Yu, W. Jiang, T. Nie, R. N. Schwartz, Y. Tserkovnyak, and K.
L. Wang, Nat. Mater. 13, 699 (2014).
20. K. K. Meng, J. Miao, X. Xu, Y. Wu, J. Xiao, J. Zhao, and Y. Jiang, Sci. Rep. 6, 38375(2016).
21. K. K. Meng, J. Miao, X. G. Xu, Y. Wu, X. P. Zhao, J. H. Zhao, and Y. Jiang, Phys.
Rev. B 94, 214413 (2016).
22. R. Ranjbar, K. Z. Suzuki, Y. Sasaki, L. Bainsla, and S. Mizukami, J. J. Appl. Phys.
55, 120302 (2016).
23. C. F. Pai, L. Liu, Y. Li, H. W. Tseng, D. C. Ralph, and R. A. Buhrman, Appl. Phys.
Lett. 101, 122404 (2012).
24. J. Han, A. Richardella, S. A. Siddiqui, J. Finley, N. Samarth, and L. Liu, Phys. Rev.
Lett. 119, 077702 (2017).
25. Y. Wang, D. Zhu, Y. Wu, Y. Yang, J. Yu, R. Ramaswamy, R. Mishra, S. Shi, M.
Elyasi, K. L. Teo, Y. Wu, and H. Yang, Nature Commun. 8, 1364 (2017).
26. C. Sahin, and M. E. Flatté, Phys. Rev. Lett. 114, 107201 (2015).
27. J. C. Y. Teo, L. Fu, and C. L. Kane. Phys. Rev. B 78, 045426 (2008).

104 | Page

Chapter 5

28. X. G. Zhu, M. Stensgaard, L. Barreto, W. S. Silva, S. Ulstrup, M. Michiardi, M.
Bianchi, M. Dendzik, and P. Hofmann. New J. Phys. 15, 103011 (2013).
29. C. L. Kane, and E. J. Mele, Phys. Rev. Lett. 95, 226801 (2005).
30. B. A. Bernevig, T. L. Hughes, and S. C. Zhang, Science 314, 1757 (2006).
31. M. König, S. Wiedmann, C. Brüne, A. Roth, H. Buhmann, L. W. Molenkamp, X. L.
Qi, S. C. Zhang, Science 318, 766 (2007).

105 | Page

Chapter 6

Chapter 6

Topological Hall Effect and Skyrmions in
BiSb - MnGa Bilayers

Besides SOT-MRAM, racetrack memory is a very promising candidate for highdensity and low-cost magnetic memory. One of innovative types of race track memory
utilizes the topological magnetic objects knows as skyrmions. Thanks to their small size(~5-80 nm [1, 2]) and low driving current density (~102 A/cm2 [3]), skyrmions can enable
manipulation of information with ultra-low power consumption.
Dzyaloshinskii-Moriya-Interaction (DMI) is the key ingredient to stabilize chiraldomains wall of skyrmions, which can give to rise a fictitious magnetic field and can bedetected by the topological Hall effect (THE) [4]. Recently, skyrmion-driven THE wasobserved in B20 compounds [5 - 8] and SrRuO3-SrIrO3 bilayers [9]. Since then, the THE, 6, 7,has become an important tool for probing skyrmions. However, although skyrmions
generated by bulk DMI have been found in different B20 compounds, they exist only at
low temperature. Interfacial DMI in multilayers such as Pt/CoFeB, Pt/Co/Ni/Co and
Pt/Co can generate skyrmions even at room temperature [10-14]. Unfortunately, theseskyrmions are still meta-stable at zero magnetic field. For realistic application ofskyrmions to racetrack memory, stable skyrmions at room temperature under absence ofan external magnetic field are required. , 11, 12, 13, 14]This chapter will study the topological Hall effect (THE) in BiSb topologicalinsulator / MnGa bilayers. The interfacial DMI is modulated by controlling the annealing
temperature of the MnGa template. The THE observed at room temperature even under106 | Page

Chapter 6

absence of an external magnetic field is the strong evidence for the existence ofthermodynamically stable skyrmions in MnGa/BiSb bilayers. These results shed light on
the role of the interfacial DMI tailored by suitable material choice and growth techniquefor generation of skyrmions at room temperature.

107 | Page

Chapter 6

6.1. Sample preparation
The BiSb/MnGa bilayers were grown by MBE on semi-insulating GaAs(001)substrate with orientation of BiSb(012) // MnGa(001) // GaAs(001). In order to modulate
the interfacial DMI, an additional annealing step was added into the growth process asshown in Fig. 6.1. The whole growth process was described as follows. After a thick
GaAs buffer layer was grown at 550oC, the substrate was cooled down to 50oC to grownalternative monolayers of Mn-Ga-Mn-Ga. Then, the template of MnGa bilayer wasformed by annealing for in 1 min at two different annealing temperatures: tan = 350oC(sample A), and tan = 400oC (sample B). The samples were cooled down again to grow athick MnGa with a total thickness of 5 nm at 250oC. Finally, a 10-nm BiSb thin film wasgrown under the substrate temperature of 200oC. The growth of the BiSb/MnGa bilayers
was monitored in situ by RHEED, and the thickness of BiSb(10)/MnGa(5) (the numbers
in parentheses present layer’s thickness in nanometers) thin films were controlled by theirfluxes and the growing time. To further understand the role of interface between BiSb
and MnGa thin film, samples of MnGa(5) thin film without BiSb layer andBiSb(10)/MnGa(5) bilayer without annealing step were also prepared.

Figure 6.1: Schematic illustration of the growth process. An additional annealing stepof the MnGa template layer was employed to tailor the DMI strength.

108 | Page

Chapter 6

6.2. Topological Hall effect (THE)The Hall resistivity can be expressed as H  R0 H  AHE  T

(6.1)

where the first, second and third terms are the ordinary Hall effect, the anomalous Hall
effect (AHE) and the THE, respectively. H of the BiSb/MnGa bilayers was measured byusing 50×50 m2 Hall bars fabricated by convention ultraviolet photolithography and Ar
ion milling. Since the THE coexists with the ordinary Hall effect and the AHE, it isnecessary to estimate the AHE by measuring the magnetic circular dichroism (MCD)
intensity-magnetic field (MCD-H) characteristics. The sample’s magnetization was alsomeasured by a superconducting quantum interface device (SQUID).
Figure 6.2(a-b) show the Hall resistivity (blue line), the AHE (red line) estimatedby MCD, and the THE (green line) of the MnGa/ BiSb bilayers annealed at 350oC (Fig.
6.2a) and 400oC (Fig. 6.2b) at room temperature. In the Hall resistivity curve, two humps
which can be attributed to the THE were clearly observed. While the sample A shows two
humps between 0 and 3.5 kOe, the sample B shows two humps between -3 kOe and 3
kOe. This characteristic can be further confirmed in the THE curves. While the peak in
the THE curve of the sample A appears at around 1.5 kOe, that of the sample B appears
at zero external magnetic field. The existence of the THE in sample B under zero external
magnetic field was observed at different temperatures. The magnetic phase diagram ofsample B as a function of the external magnetic field (H) and temperature (T) is shown in
Fig. 6.2(c). The full Hall resistivity data at each temperature are shown in Fig. 6.3(a-i).
The THE amplitude of sample B decreases with decreasing temperature and disappeared
at about 125 K as showed in Fig. 6.3(g).

109 | Page

Chapter 6

Figure 6.2: (a-b) Room-temperature topological Hall effect (THE) (green lines)
extracted from the total Hall effect resistivity (blue lines) and the anomalous Hall effect(AHE) resistivity derived from magnetic circular dichroism intensity-magnetic fieldmeasurement (red lines) of MnGa(5 nm)/BiSb(10 nm) bilayers with different MnGa
template annealing temperature tan of 350oC (sample A) and 400oC (sample B),
respectively. (c) Magnetic phase diagram of sample B as a function of the external
magnetic field (H) and temperature (T). (d) The topological Hall resistivity T ofsample B as a function of temperature.

110 | Page

Chapter 6

Figure 6.3: (a-i) The Hall resistivity (blue line) and magnetic circular dichroism
intensity-magnetic field measurement (red line) of sample B at different temperatures.

111 | Page

Chapter 6

Figure 6.4(a) sketches the zero-field magnetic potential in sample A and B. The
topological magnetic states can be described by the skyrmion number (S). In the sample
A, the energetically lower state is ferromagnet (S = 0), and the higher state is skyrmion(S = 1). As the results, for the skyrmions to be observed, the skyrmion state potential must
be changed from the higher state to the lower state by applying an external magnetic field(H). The meta-stable skyrmion state under zero magnetic field can also be realized byheating or applying a bi-polar pulse magnetic field, or by “blowing” through a wire [15]at room temperature [16]. However, such meta-stable skyrmions are easily erased byapplying a large magnetic field. In contrast, the situation in the sample B is quite different.
The energetically lower state is skyrmion (S = 1), while the higher state is ferromagnet (S= 0). As the results, the skyrmions can be stable at zero external magnetic field (H = 0
kOe) at room temperature. The stable skyrmions cannot be erased by just applying a large
magnetic field; as long as the field is reduced to zero, the skyrmions emerge again.
To prove that the observed THE is due to skyrmions generated by the interfacial
DMI of BiSb and MnGa, I measured the Hall resistivity of a reference MnGa(5) single
layer annealed at 400oC and a BiSb(10)/MnGa(5) bilayer (sample C) without theannealing step, which are shown in Fig. 6.4(b) and Fig. 6.4(c), respectively. No THE is
detected in both samples, confirming that the THE observed in Fig. 6.2(a-b) is due to theinterfacial DMI between BiSb and MnGa thin film, not by the bulk DMI in the MnGa
thin film, and that strength of their interfacial DMI depends on the annealing condition.
Moreover, the critical DMI constant for skyrmion generation Dc can be modulated bychanging the thickness of MnGa thin film. The Hall resistivity of a BiSb(10)/MnGa(10)bilayer annealed at 400oC (sample D) is shown in Fig. 6.4(d) and compared with its MCDH characteristics (as shown Fig. 6.5(a-i)). Only AHE was observed, and there is no THE

112 | Page

Chapter 6

detected because of the larger Dc as discussed later. All of these observation are consistent
with the existence of skyrmions generated by the interfacial DMI.

113 | Page

Chapter 6

Figure 6.4: (a) Sketch of the zero-field potential for (1) sample A and (2) sample B.
(b-d) Hall resistivity of a MnGa(5) single layer annealed at 400oC, a BiSb(10)/MnGa(5)bilayer without the annealing step (sample C) and a BiSb(10)/MnGa(10) bilayer
annealed at 400oC (sample D).

114 | Page

Chapter 6

Figure 6.5: The Hall resistivity (blue line) and magnetic circular dichroism intensitymagnetic field measurement (red line) of the BiSb(10)/MnGa(10) bilayer (sample D)
annealed at 400oC under different temperatures. No THE was observed.

115 | Page

Chapter 6

The domain wall energy with DMI is expressed as DW  4 AK u   D(6.2)

where D is the effective DMI constant, A is the exchange constant, and Ku is anisotropy
constant. When  DW comes to zero, skyrmions can emerge. The critical DMI energy
constant can be estimated as
Dc  4 AK / (6.3)

The exchange constant A is calculated from [17]A  (a 2TC  M s ) / (2g B )(6.4)

where TC, Ms, g and B is Curie temperature, saturation magnetization, Landé factor and
Bohr magneton constant, respectively. Figures 6.7(a-h) show both the out-of-plane andin-plane magnetization of the reference MnGa(5) single layer annealed at 400oC (Fig.
6.6(a-b)), the BiSb(10)/MnGa(5-10) bilayers annealed at 400oC (sample B and sample D)(Fig. 6.6(c-d) and Fig. 6.6(g-h), respectively) and the MnGa(10)/BiSb(10) bilayer without
the annealing step (sample C) (Fig. 6.6(e-f)). For annealed samples, the exchange constant
A and anisotropy constant Ku are estimated to be about 5.4 pJ/m and 1.2×105 J/m3,
respectively, and the critical DMI constant Dc is 1 mJ/m2.
Table 6.1 summarizes the THE, the exchange constant A, the anisotropy constantKu, and the critical DMI energy constant Dc for the reference MnGa(5) and the sample BD. By comparing sample B with sample C, one can see that the critical DMI energy
constant was reduced over 2 times by the annealing step. For the sample D with thicker
MnGa(10) thin film grown at the same condition, Dc ~ 7.0 mJ/m2 which is nearly 7 times
higher than that of sample B due to much larger Ms, and THE cannot be detected.
In multilayers, a critical interfacial DMI parameter Ds can be expressed as [13]116 | Page

Ds  Dc  tMnGa

Chapter 6(6.5)

The interfacial DMI constant is estimated Ds = 5.1 pJ/m for the sample B. For the
sample C, Ds = 12.1 pJ/m (Dc = 2.43 mJ/m2) which is two times larger than that of sample
B. The vanishing of THE in sample C demonstrates the role of the annealing step oncontrol of the critical DMI strength.
The domain wall width   A / K of sample B is estimated to be 5.4 nm and its
fictitious magnetic field is estimated from

H eff  T / ( P  R0 )(6.6)

where P denotes the spin polarization of MnGa (P = 42%), and R0 is the normal Hall
coefficient (R0 = 0.6×10-5 cm/Oe). Hence, Heff ~ 5.7 kOe is estimated.
Table 6.2 compares Dc, and the critical interfacial DMI constant Ds of the sample
B with previous works. A much larger Ds of 5.1 pJ/m was achieved in sample B. These
results confirm that BiSb topological insulator is a promising candidate with large spinorbit-torque [18] and huge interfacial DMI for generation and manipulation of skyrmion.

117 | Page

Chapter 6

Figure 6.6: (a), (b) The out-of-plane and in-plane magnetization of a reference
MnGa(5) single layer annealed at 400oC. (c), (d) for sample B BiSb(10)/ MnGa(5)bilayers annealed at 400oC. (e), (f) for sample C BiSb(10)/ MnGa(5) bilayers without
annealing step. (g), (h) for sample D BiSb(10)/MnGa(10) bilayers annealed at 400oC.

118 | Page

Chapter 6

Table 6.1: The THE effect, the exchange constant A, the anisotropy constant Ku andthe critical DMI energy constant Dc in the 400oC annealed reference MnGa(5) sample
and sample B-D.
A

Ku

Dc

SampleStack

Annealed

THE

Ref.

MnGa(5)

O

X

10.89

1.29

-

B

BiSb(10)/MnGa(5)

O

O

5.40

1.19

1.02

C

BiSb(10)/MnGa(5)

X

X

11.72

3.11

2.43

D

BiSb(10)/MnGa(10)

O

X

19.60

15.20

6.95

(pJ/m) (105 J/m3) (mJ/m2)

Table 6.2: Comparison of Dc and the critical interfacial DMI constant Ds observedin this work and other bilayers reported sofar.
Dc (mJ/m2)

Ds (pJ/m)

Co/Pt

1.30-2.05

1.37-2.17

CoFeB/Pt

1.0

0.8

MnGa/Pt or Ta

0.65-1.08

2.60-4.32

1.02

5.1

MnGa/BiSb(this work)

119 | Page

Chapter 6

For the sample A, the critical DMI energy constant Dc of 1.08 mJ/m2 is only slightly
larger than that of sample B, and this cannot explain the difference in their potential
landscape (Fig. 6.4 (a)). Here, I think that the surface roughness of the MnGa layer at
different annealing temperatures plays an important role. Indeed, as shown in Fig. 6.7(ac), the RHEED patterns are improved with annealing. To evaluate the surface roughnessof MnGa, AFM was employed, and the measurement results are shown in Fig. 6.7(d-f).
One can see that the root mean square value of the surface roughness Rq of MnGa was
improved by annealing at higher temperatures.

Figure 6.7: (a-c) RHEED patterns observed along the GaAs[ 1 10] direction of MnGa
thin films for as grown and with annealing at 350oC and 400oC, respectively. (d-f)
Surface of MnGa thin films measured by atomic force microscopy (AFM). The root
mean square value of the surface roughness Rq of each film is 1.7 nm, 1.4 nm and 1.2
nm, respectively.

120 | Page

Chapter 6

6.3. Condition of DMI constant D and anisotropy constant Ku
for generation of skyrmions
The existence of skyrmions is influenced not only by the DMI constant D but also
by the anisotropy constant Ku as reported in previous work. Indeed, the typical value of
Ku of MnGa thin film is estimated from 1.0×106 J/m3 to 2.0×106 J/m3[19, 20], but oursamples only show THE for Ku = 1.2×105 J/m3. Therefore, in order to further understandthe condition of Ku and D for generation of skyrmions, the finite difference time domain
micromagnetic simulation by MuMax3 was employed [21]. The simulation follows steps
proposed by M. Mruczkiewicz et al [22]. Bloch skyrmion is assumed in the initial state,
and the final state is evaluated after relaxation to the ground state under zero magnetic
field. The topological number is calculated as S  m m 1mdxdy [23]. The S4 x y 

value of uniform state, vortex state and skyrmion state are 0, 0.5, 1, respectively (seeappendix B). The simulation parameters are the disk radius R = 64 nm, thickness t = 5
nm, saturation magnetization Ms = 108.6 emu/cc, exchange constant A = 5.4 pJ/m,
damping factor  = 0.008, DMI constant D = 1.0 - 2.2 mJ/m2 and magnetic anisotropy
constant Ku = 1.0×105 - 5.0×105 J/m3 which are similar to that of the 400oC annealed
samples. The results of simulation are showed in Fig. 6.9. The white squares present
unconverged simulation, and the white line presents the Dc position where the THE wasobserved. One can see that the maximum Ku for generation of skyrmions is around
3.2×105 J/m3. For Ku above this value, the disk changes to uniform state (S = 0). These
results is consistent with my experiment results (Ku = 1.2×105 J/m3 for sample B) andinterestingly, consistent with K. K. Meng et al [24] who show the largest value of Ku forobserving THE in MnGa/heavy metal bilayers is approximately 3.0×105 J/m3. Thus, myexperimental results are consistent with the micromagnetic simulation results.

121 | Page

Chapter 6

Figure 6.8: The skyrmion number S as a function of magnetic anisotropy constant Ku
and DMI constant D. The white squares indicate unconverged simulator.

6.4. Summary
In this chapter, by combining the strong spin-orbit-interaction of BiSb and the small
magnetization of MnGa, a large interfacial Dzyaloshinskii-Moriya-Interaction (DMI) (Ds= 5.1 pJ/m) was tailored by controlling the annealing temperature tan of the MnGa
template. Moreover, THE can be observed at room temperature even under absence of an
external magnetic field, demonstrating field-free ground-state skyrmions. A large criticalinterfacial DMI constant of 5.1 pJ/m was obtained. These results confirm that BiSb
topological insulator can generate not only colossal spin-orbit-torque, but also hugeinterfacial DMI for generation and manipulation of skyrmions.

122 | Page

Chapter 6

References
1. G. Chen, A. Mascaraed, A. T. N’Diaye, and A. K. Schmid, Appl. Phys. Lett. 106,242404 (2015).
2. O. Boulle, J. Vogel, H. Yang, S. Pizzini, D. de Souza Chaves, A. Locatelli, T.O.
Mentes, A. Sala, L. D. B. Prejbeanu, O. Klein, M. Belmeguenai, Y. Roussigne, A.
Stashkevich, S.M. Cherif, L. Aballe, M. Foerster, M. Chshiev, S. Auffret, I.M. Miron,and G. Gaudin, Nat. Nanotechnol. 11, 449 (2016).
3. F. Jonietz, S. Mühlbauer, C. Pfleiderer, A. Neubauer, W. Münzer, A. Bauer, T.
Adams, R. Georgii, P. Böni, R. A. Duine, K. Everschor, M. Garst, and A. Rosch,
Science 17, 1648 (2010).
4. P. Bruno, V. K. Dugaev, and M. Taillefumier, Phys. Rev. Lett. 93, 096806 (2004).
5. A. Neubauer, C. Pfleiderer, B. Binz, A. Rosch, R. Ritz, P. G. Niklowitz, and P. Böni,
Phys. Rev. Lett. 102, 186602 (2009).
6. N. Kanazawa, Y. Onose, T. Arima, D. Okuyama, K. Ohoyama, S. Wakimoto, K.
Kakurai, S. Ishiwata, and Y. Tokura, Phys. Rev. Lett. 106, 156603 (2011).
7. T. Yokouchi, N. Kanazawa, A. Tsukazaki, Y. Kozuka, M. Kawasaki, M. Ichikawa, F.
Kagawa, and Y. Tokura, Phys. Rev. B 89, 064416 (2014).
8. D. Liang, J. P. DeGrave, M. J. Stolt, Y. Tokura, and S. Jin, Nat. Comm. 6, 8217 (2015).
9. J. Matsuno, N. Ogawa, K. Yasuda, F. Kagawa, W. Koshibae, N. Nagasa, Y. Tokura,and M. Kawasaki, Sci. Adv. 2, e1600304 (2016).
10. S. Woo, K. Litzius, B. Krüger, M. Y. Im, L. Caretta, K. Richter, M. Mann, A. Krone,
R. M. Reeve, M. Weigand, P. Agrawal, I. Lemesh, M. A. Mawass, P. Fischer, M. Kläui,and G. S. Beach, Nat. Mater. 15, 501 (2016).
11. C. M. Luchaire, C. Moutaﬁs, N. Reyren, J. Sampaio, C. A. F. Vaz, N. Van Horne, K.
Bouzehouane, K. Garcia, C. Deranlot, P. Warnicke, P. Wohlhüter, J.-M. George, M.

123 | Page

Chapter 6

Weigand, J. Raabe, V. Cros, and A. Fert, Nat. Nanotech 11, 444 (2016).
12. H. T. Nembach, J. M. Shaw, M. Weiler, E. Jué, and T. J. Silva, Nat. Phys. 11, 825(2015).
13. O. Boulle, J. Vogel, H. Yang, S. Pizzini, D. S. Chaves, A. Locatelli, T. O. Mentes, A.
Sala, L. D. Buda-Prejbeanu, O. Klein, M. Belmeguenai, Y. Roussigné, A. Stashkevich, S.
M. Chérif, L. Aballe, M. Foerster, M. Chshiev, S. Auffret, I. M. Miron, and G. Gaudin,Nat. Nanotech 11, 449 (2016).
14. K. Di, V. L. Zhang, H. S. Lim, S. C. Ng, M. H. Kuok, X. Qiu, and H. Yang, Appl.
Phys. Lett. 106, 052403 (2015).
15. S. Z. Lin, Phys. Rev. B 94, 020402(R) (2016).
16. N. Romming, C. Hanneken. M. Menzel, J. E. Bickel, B. Wolter, K. V. Bergmann, A.
Kubetzka, and R. Wiesendanger, Science 341, 636 (2013).
17. M. Beg, R. Carey, W. Wang, D. C. Ortuno, M. Vousden, M. A. Bisotti, M. Albert, D.
Chernyshenko, O. Hovorka, R. L. Stamps, H. Fangohr, Sci. Rep. 5, 17137 (2015).
18. N. H. D. Khang, Y. Ueda, and P. N. Hai, Nat. Mater. 17, 808 (2018).
19. Z. L. Jun, N. S. Hua, and Z. J. Hua, Chin. Phys. B 22, 118505 (2013).
20. L. J. Zhu, D. Pan, S. H. Nie, J. Lu, and J. H. Zhao, Appl. Phys. Lett. 102, 132403(2013).
21. A. Vansteenkiste, J. Leliaert, M. Dvornik, M. Helsen, F. G. Sanchez, and B. V.
Waeyenberge, AIP Adv. 4, 107133 (2014).
22. M. Mruczkiewicz, M. Krawczyk, and K. Y. Guslienko, Phys. Rev. B 95, 094414(2017).
23. N. Nagaosa, and Y. Tokura, Nat. Nanotechnol. 8, 899 (2013).
24. K. K. Meng, X. P. Zhao, P. F. Liu, Q. Liu, Y. Wu, Z. P. Li, J. K. Chen, J. Miao, X. G.
Xu, J. H. Zhao, and Y. Jiang, Phys. Rev. B 97, 060407(R) (2018).

124 | Page

Chapter 7

Chapter 7

Unidirectional Magnetoresistance in
GaMnAs - BiSb Bilayers

Besides the SHE and the THE, UMR is another attractive spin-related phenomenon,
which can be used for determination of the magnetization direction of a single magnetic
layer, making it possible to design novel SOT-MRAM with an extremely simple stacking
structure and small foot print. Unfortunately, while UMR has been studied extensively inrecent years as an attractive candidate for two-terminal magnetic memories and spin logic
devices, improving its magnitude, which is still far below the practical value, andadequate understanding of the underlying microscopic origins are still required.
This chapter will study the UMR effect in a heterostructure of BiSb topologicalinsulator – GaMnAs ferromagnetic semiconductor. I observed a large UMR ratio of 1.1%
and found that this large UMR is not governed by the giant magnetoresistance (GMR)like spin-dependent scattering, but by magnon emission/absorption and strong spindisorder scattering in the GaMnAs layer. These results provide new insight into thecomplex physics of UMR, as well as a strategy for enhancing its magnitude for device
applications.

125 | Page

Chapter 7

7.1. BackgroundFigure 7.1(a) shows the schematic structure of a two-terminal planar MRAM device
consisting of only a ferromagnetic layer and a spin Hall layer. For data writing, a bipolar
pulse current is applied in plane for magnetization switching by the spin-orbit torqueinduced by SHE in the spin Hall layer. For data reading, a small bias current can beapplied, and a sensing amplifier is used to determine the magnetization direction of theferromagnetic layer by mean of the UMR effect. Such planar two-terminal memory
devices are much simpler than the vertical magnetic tunnel junctions (MTJs) used inconventional MRAM, which involves over ten layers including a synthetic
antiferromagnetic superlattice and a CoFeB layer for the reference layer, a MgO tunnel
barrier, a CoFeB/Ta/CoFeB tri-layer for the free layer, a second MgO layer, and othersupporting layers. Furthermore, there is a great degree of freedom in material choice for
UMR-MRAM, since there is no restriction to the CoFeB/MgO/CoFeB combination as in
the case of MTJs.
However, for the UMR effect to be used in such memory devices, its magnitude has
to be at least a few % (earliest anisotropy magnetoresistance (AMR)-based MRAMs [1]have a typical AMR ratio of 2% for the Co permalloy as the magnetic layer). Previous
studies of UMR in metallic bilayers, such as Ta or Pt/Co [2, 3] reports UMR ratios ofabout 0.005%, which are too small for practical applications. Recent interests have moved
to topological insulator (TI)-based heterostructures, such as Crx(Bi,Sb)2-xTe3/(Bi,Sb)2Te3[4] (Bi,Sb)2Te3/CoFeB and Bi2Se3/CoFeB [5]. Because of the large spin Hall angle in TIs[6, 7, 8, 9, 10], spin accumulation at the interface of those heterostructures can beenhanced, resulting in larger UMR ratios.
The physical origins of UMR are explained as combination of spin-dependent
scattering (SS) and magnon scattering (MS) mechanisms at the interface or in the bulk of126 | Page

Chapter 7

the ferromagnetic layer [11, 12]. Figure 7.1(b) illustrates the SS mechanism in a TI/FM
heterostructure. The SHE or REE in the TI layer generates a pure spin current that is
injected to the FM layer, resulting in spin accumulation near the surface. The transmission
and reflection of spin at the interface depend on direction of the spin polarization  andmagnetization M, generating a GMR-like UMR signal. Furthermore, since the spin
accumulation penetrates to bulk of the FM layer, the bulk spin-dependent scattering(denoted as bulk SS mechanism) of the FM layer also gives rise to a bulk UMR [13]. Notethat this bulk UMR can have opposite polarity to the interfacial GMR-like UMR,
depending on the mobility of majority/minority-spin electrons. Meanwhile, the MS
mechanism involves magnon absorption or stimulated magnon emission in the FM layer
when an accumulated spin flips its orientation (Fig. 7.1(c)). The change of the magnon
temperature as the result of the MS process leads to the change of longitudinal resistance
via the spin-disorder scattering of free carriers in the FM layer. All of these different
mechanisms have recently been observed experimentally [11], but their magnitude varies
with the material combination, and it is not clear how to optimize them to obtain a large
enough UMR ratio for device applications. Recently, a large UMR ratio of 0.5% in
Crx(Bi,Sb)2-xTe3/(Bi,Sb)2Te3 heterostructures was observed and explained as the
manifestation of the enhanced asymmetric magnon scattering in the ferromagnetic TI
Crx(Bi,Sb)2-xTe3 layer [4]. However, such asymmetric magnon scattering is limited toferromagnetic TIs, whose Curie temperature is much lower than room temperature.
Meanwhile, the GMR-like SS is the main mechanism in the (Bi,Sb)2Te3/CoFeB and
Bi2Se3/CoFeB heterostructures [5], but the their UMR ratio is much smaller. Thus, a clear
strategy for reaching over 1% of UMR ratio and a comprehensive understanding of theunderlying microscopic mechanism of UMR in TI-based heterostructures are strongly
required for device applications.

127 | Page

Chapter 7

In this chapter, the UMR effect and their underling physical mechanisms will be
investigated in GaMnAs ferromagnetic semiconductor / BiSb topological insulator
heterostructures. Here, GaMnAs is a prototype ferromagnetic semiconductor with strong
spin-disorder scattering [14], and BiSb is a topological insulator with a giant spin Hall
effect [9, 10]. By varying the conductivity of the BiSb layer, I can change the current
distribution flowing in the GaMnAs layer and the BiSb layer, and selectively study themechanism of UMR in each case. The experiment results confirm that the MS mechanism
is dominant in the GaMnAs layer with a maximum UMR of 1.1%, breaking the 1% barrier
for the first time. The bulk SS mechanism in the GaMnAs layer is also observed with thecorresponding maximum UMR of –0.009%. In addition, I found that other factors, suchas the anomalous Nernst effect (ANE) of the GaMnAs layer and the ordinary Nernst effect(ONE) of the BiSb layer, can dominate the UMR-like signals, when the pure spin current
injection from the BiSb to the GaMnAs layer is suppressed by the conductivity mismatch.
These results provide a strategy to maximize the UMR ratio for practical device
applications.

128 | Page

Chapter 7

Figure 7.1: (a) Two-terminal planar MRAM device with an extremely simple stacking
structure, consisting of only a ferromagnetic layer and a spin Hall layer. Spin-orbit
torque and unidirectional magnetoresistance are utilized for data writing and reading,respectively. (b-c) Schematic illustration of the spin-dependent scattering (SS) andmagnon scattering (MS) mechanism of UMR, respectively. (d) Optical image of aGa0.91Mn0.09As (10 nm) / Bi0.9Sb0.1 (10 nm) Hall bar and magnetoresistancemeasurement configuration.

129 | Page

Chapter 77.2. Preparation of GaMnAs - BiSb bilayers
The 10 nm-thick Ga0.91Mn0.09As (bottom) / 10 nm-thick Bi0.85Sb0.15 (top)heterostructures were grown on insulating GaAs(001) substrates by MBE. After removalof the surface oxide layer of GaAs substrate, a 20 nm-thick GaAs buffer was grown toobtain an atomically smooth surface at 580oC. Then, a 10 nm-thick Ga0.91Mn0.09As layer
was grown on the GaAs substrate at 300oC at the rate of 9 nm/min. The BiSb growth rate
is 3.5 nm/min for both two samples. Finally, these samples were cooled down to the room
temperature for deposition of an As thin cap layer. The growth process was monitored insitu by reflection high electron diffraction.
The samples were patterned into 100 m  25 m Hall bars by optical lithography
and Ar ion milling. A 60 nm-thick Au and a 6 nm-thick Cr adhesion layer were depositedas electrodes by electron beam evaporation, which reduce the effective length of the Hallbars to 50 m. Figure 7.1(d) shows a photograph of a Hall bar with contact electrodes andthe measurement configuration. UMR hysteresis curves were measured by sweeping an
in-plane magnetic field H along the GaAs [110] direction (the y direction) under various
current density J. To extract the UMR hysteresis and eliminate the large even-function
component of the conventional magnetoresistance Rxx(H) of GaMnAs, the odd-function
component Rxx and UMR ratio were measured as follows
Rxx = Rxy(J) - Rxy(-J)(7.1)

UMR ratio = Rxxextr /Rxx(0)(7.2)

where Rxxextr and Rxx(0) are the extremum of Rxx(H0) and the Hall bar resistance atzero magnetic field, respectively. In addition, to evaluate the contribution of the ANE andthe ONE in the UMR signal, Rxx and the odd-function component Rxy of the planar

130 | Page

Chapter 7

Hall resistance Rxy were measured under a rotating in-plane magnetic field. Here, Rxy is
expressed asRxy = Rxy(J) - Rxy(-J)(7.3)

In order to change the current distribution in the heterostructures, I fabricated two
samples whose top BiSb layer has different crystal quality and electrical conductivity
while the Ga0.91Mn0.09As layer is kept the same. The first sample (denoted as sample A)
has a poly-crystalline BiSb layer with low electrical conductivity ( ~ 1.5×104 -1m-1),
which is similar to that of GaMnAs [15]. Thus, roughly half of the bias current flows ineach layer of the sample A. Meanwhile, the second sample (denoted as sample B) has a(001)-oriented BiSb layer [16] with much higher conductivity ( ~ 2×105 -1m-1) [17],so that most of the bias current flows in the BiSb layer, while less than 10% of the bias
current flows in the GaMnAs. In order to change the BiSb thin film’s crystal quality, the
BiSb layer was grown at different substrate temperature: 200oC for the sample A and
150oC for the sample B. This allows us to study the mechanism of UMR in each caseindependently. Figure 7.2(a) and 7.2(b) show a cross-sectional transmission electron
microscope image of sample A and B, respectively, which confirm the contrasting crystal
quality of the BiSb layer between two samples. Figure 7.2(c) shows the temperaturedependence of the resistance R of the Hall bar of sample A. The resistance – temperature
characteristics of the sample A represents that of GaMnAs, with dR/dT singularity at theCurie temperature (TC ~ 85 K) [18]. Below TC, R rapidly decreases as the result ofsuppressed spin-disorder scattering in GaMnAs. Note the large difference between the
maximum and the minimum value of R is as large as 26%. The resistance change ofsample A is strongly governed the resistance change of the GaMnAs rather than by the
BiSb layer. In contrast, the resistance – temperature characteristics of the Hall bar ofsample B, shown in Fig. 7.2(d), represents that of BiSb, showing a plateau at low

131 | Page

Chapter 7

temperatures due to the dominant metallic conduction on the topological surface states of
BiSb [17]. The clear difference between the R-T curves of the two samples is consistent
with the different distribution of the bias current in the two samples.

Figure 7.2: (a-b) Cross-sectional transmission electron microscope image of sample A
and B, respectively. The top BiSb layer is polycrystalline with the electricalconductivity of about 1.5×104 -1m-1 in sample A, while it is (001)-oriented with theelectrical conductivity of about 2 × 105 -1m-1in sample B. (a-b) Temperaturedependence of the resistance R of a Hall bar of sample A and B, respectively.

132 | Page

Chapter 7

7.3. UMR of sample A and its origin
Figure 7.3(a-h) show the UMR hysteresis curves Rxx  Hext for the sample A atthe base temperature Tbase of 4 K and the current density J = 0.2×106 A/cm2  1.6×106
A/cm2. The UMR is negative and has small magnitude (maximum -0.009%) at small J 
6105 A/cm2. However, at higher J  8105 A/cm2, the UMR becomes positive andincreases drastically, reaching 0.55% at J = 1.6106 A/cm2. Such a switching of UMR
polarity as a function of current density has not been observed before, indicating that there
are several competing mechanisms of UMR. Considering that the spin Hall angle of BiSb
has the same sign as that of Pt [9, 10], the negative UMR observed at small J means thatthe longitudinal resistance is larger when the spin polarization  is parallel to M, andsmaller when  is antiparallel to M. This cannot be explained by the interfacial GMRlike SS and the MS mechanism, which should give an ordinary (positive) UMR effect.
The only plausible mechanism of this phenomenon is the bulk SS mechanism, which cangive rise to an inverse UMR when the mobility of the minority electrons is higher thanthat of majority electrons [13]. Such an inverse UMR effect was recently observed in
Co80Cr20 / Pt bi-layers, where the Co80Cr20 is known to have higher mobility for minority
electrons and the MS mechanism was suppressed by applying a strong external magmaticfield [11]. In this case, the bulk SS mechanism in GaMnAs is dominant at low J and low
Tbase, when the MS mechanism is neglectable. At elevating J, the sample temperature
increases due to Joule heating, and the MS mechanism began to take over, resulting in
ordinary UMR.
To further see the competing action between the bulk SS mechanism and the MS
mechanism, the UMR hysteresis at a higher Tbase of 30 K was measured as shown in Fig.
7.4(a-h). One can see that the inverse UMR exists only at J = 2105 A/cm2, and switches

133 | Page

Chapter 7

to the ordinary UMR at J  6105 A/cm2, agreeing with the stronger MS mechanism at
higher temperature. Importantly, the UMR ratio reaches 1.1% at J = 1.6×106 A/cm2,
breaking the 1% barrier for the first time. We concluded that the dominant mechanism in
GaMnAs is MS with the corresponding UMR ratio at the order of 1%, while the bulk SS
mechanism also exists but results in a much smaller UMR ratio at the order of -10-3%.

134 | Page

Chapter 7

Figure 7.3: (a-h) UMR hysteresis curves Rxx  Hext for sample A at the basetemperature Tbase of 4 K and the current density J = 0.2×106 A/cm2  1.6×106 A/cm2.
The magnetic field was applied along the y direction. The inverse (negative) UMR at
low J is governed by the bulk SS mechanism, while the ordinary (positive) UMR athigh J is due to the MS mechanism.

135 | Page

Chapter 7

Figure 7.4: (a-h) The inverse UMR exists only at J = 2105 A/cm2, and switches to theordinary UMR at J  6105 A/cm2 due to stronger MS mechanism at higher
temperature. The UMR ratio reaches 1.1% at J = 1.6×106 A/cm2, breaking the 1%
barrier for the first time.

136 | Page

Chapter 7

Figure 7.5(a) summarizes the UMR ratio as a function of J at various Tbase. One cansee that the UMR ratio rapidly increases with both J and Tbase. Let the contribution of thebulk SS mechanism, the interfacial GMR-like SS mechanism, and the MS mechanism to
the UMR ratio, to the UMR ratio as aJ (a < 0), bJ (b >0), and cJ+dJ3 (c,d > 0), respectively.
The total UMR ratio can be fitted by J + J3, where  = a + b + c represents the linear
contribution from the bulk SS minus that of the interfacial GMR-like SS and the MS
mechanism, while  = d represents the non-linear contribution of the MS mechanism athigh J. The fitting shows reasonably good agreement with the experimental results, except
for those at Tbase = 50 K and J  1.4×106 A/cm2, where Joule heating makes the sample
temperature close to the Curie temperature. Figure 7.5(b) shows the values of , atvarious Tbase.  is negative and nearly unchanged for a wide range of temperature,indicating that the linear component of UMR is dominated by the bulk SS mechanism.
Meanwhile,  gradually increases up to 50 K. Since UMR due to the MS mechanism
depends on magnon absorption/emission, its magnitude is proportional to (dR/dT)Tm,
where Tm ~ J3 at high J is the magnon temperature difference between two
magnetization directions. Thus,  is proportional to dR/dT. This observed -T dependence
is consistent with the increasing dR/dT at elevated temperature near the Curie temperatureof GaMnAs (Fig. 7.2(c)), reconfirming that the observed large UMR ratio at high J
originates from the MS mechanism. The fact that UMR due to the MS mechanism
increases with increasing temperature is quite attractive for device applications, because
other well-known magnetoresistance effects, such as GMR [ 19 , 20 ] or tunnelingmagnetoresistance (TMR) [21, 22] always decreases with increasing temperature. To
further see the MS mechanism in action, Fig. 7.5(c) shows the UMR ratio at the verysmall J of 2105 A/cm2 as a function of Tbase. At Tbase  30 K, the UMR ratio is stillnegative since the bulk SS mechanism is dominant at this small current density and low

137 | Page

Chapter 7

temperatures. However, the UMR ratio becomes positive at Tbase  40 K, where the nonlinear component of the MS mechanism become strong enough.

Figure 7.5: (a) UMR ratio as a function of J at various Tbase. Dashed lines show thefitting curves by J + J3. (b) Values of  (blue) and  (red) at various Tbase.  isnegative and nearly unchanged for a wide range of temperature, indicating that thelinear component of UMR is dominated by the bulk SS mechanism. Meanwhile, gradually increases up to 50 K, consistent with the MS mechanism. (c) UMR ratio atthe very small J of 2105 A/cm2 as a function of Tbase in Fig. 5c, reflecting thecompetition between the bulk SS and MS mechanism.

138 | Page

Chapter 7

There is another mechanism that can results in UMR-like behavior of Rxx: theanomalous Nernst effect (ANE) of the GaMnAs layer with VANE  MT, where T is
the temperature gradient in the GaMnAs layer. The corresponding thermal voltage is Vxx
 MyTz. However, the artifact Rxx due to this thermal effect should be proportional to
J (since Tz  J2), thus it cannot be the origin of the observed J3 dependence of UMR athigh J. Nevertheless, contribution from the thermal effect was quantitatively evaluatedby measuring Rxx and Rxy with an in-plane rotating magnetic field. Figure 7.6(a) and7.6(b) show the magnetic field direction -dependence of Rxx, measured at Tbase = 4 K,
J = 1.6×106 A/cm2, and Hext = 2 kOe and 7.8 kOe, respectively. The amplitude of theRxx - curve (~ 20 ) at Hext = 7.6 kOe is smaller than that (~ 40 ) at Hext = 2 kOe due
to suppression of magnon population under a higher magnetic field, as expected from thedominant MS mechanism. Figure 7.6(c-e) show the representative -dependence of Rxy,
measured at Hext = 2 kOe, 4 kOe, and 7.8 kOe, respectively. The experimental Rxy-
curves can be decomposed to the field-like torque’s contribution (green curves), which is
written as
RFL = RPHE(HFL/Hext)(sin3 - sin)(7.4)

where RPHE is the planar Hall resistance and HFL is the field-like effective field, and theantidamping-like torque and thermal effects’ contribution (blue curves), which isexpressed as
RAD + RT = (cAD/(Hext + Hdem) + cAN + cONHext)sin(7.5)

where cAD, cAN and cON are the coefficient of antidamping-like torque, the ANE of the
GaMnAs layer, the ONE of the BiSb layer, respectively, and Hdem is the demagnetization
field. By fitting to the experimental Rxy- curves, RAD + RT can be extracted. Figure

139 | Page

Chapter 7

7.6(f) shows its amplitude as a function of Hext, which yields cAN = 0.46  and cON = 0.02
kOe-1, respectively. Thus, ANE is the main thermal effect, and its contribution to Rxx
is 0.92  at J = 1.6×106 A/cm2, estimated from the Hall bar’s size. The UMR ratio dueto the ANE effect in sample A is about 0.02% at Tbase = 4 K and J = 1.6×106 A/cm2,
which is much smaller than the observed UMR ratio of 0.56%, and even smaller than theestimated -0.056% from the bulk-SS mechanism. Therefore, while there are thermal
effects contribution to UMR, its magnitude is neglectable in sample A.

140 | Page

Chapter 7

Figure 7.6: (a-b) Magnetic field direction dependence of Rxx, measured at Tbase =4 K, J = 1.6 × 106 A/cm2, and Hext = 2 kOe and 7.6 kOe. respectively. (c-e)

dependence of Rxy under Hext = 2.0, 4.0, and 7.6 kOe, respectively. Blue circles:
experimental data, green lines: contribution from the field-like torque RFL, blue lines:
contribution from the antidamping-like torque and thermal effects RAD + RT, red lines:
cumulative fit curves. (f) RAD + RT amplitude as a function of Hext. Red line shows thefitting curve by cAD/(Hext + HAD) + cAN + cONHext.

141 | Page

Chapter 77.4. UMR of sample B and its origin
In contrast to sample A where the conductivity of the BiSb and the GaMnAs layer
is nearly the same, the conductivity of the BiSb is much higher than that of the GaMnAs
layer in sample B. Such a situation is suitable to study the role of the conductivity
matching in the UMR effect. Figure 7.7(a-h) show the UMR hysteresis curves Rxx  Hextof sample B at Tbase = 4 K and J = 0.2×106 A/cm2  1.6×106 A/cm2 for sample B. In
this sample, most of the bias current flows in the BiSb layer, thus the bulk SS and MS
mechanism in the GaMnAs are not detected. In contrast to sample A, the UMR ratio ofsample B increases slowly, reaching a maximum UMR ratio of 0.020% at J = 1.6×106
A/cm2, which is an order of magnitude smaller than that of sample A measured at thesame condition. In addition, contribution of the ONE can be observed through a linear
dependence with a positive gradient of UMR on the external magnetic field Hext at highJ.

142 | Page

Chapter 7

Figure 7.7: (a-h) UMR hysteresis curves Rxx  Hext of sample B at Tbase = 4 K and J= 0.2×106 A/cm2  1.6×106 A/cm2 for sample B.

143 | Page

Chapter 7

Figure 7.8(a) summarizes the UMR ratio of sample B as a function of J at various
Tbase. The UMR ratio increases linearly with J at all temperatures, and its maximum value
at J = 1.6×106 A/cm2 is nearly temperature-independent. At the first look, this behavior
seems consistent with interfacial GMR-like SS mechanism. However, I found that thisUMR-like signal in the sample B is completely governed by the thermal effects. Figure
7.8(b) shows the  - dependence of Rxy for sample B at J = 1×105 A/cm2 with Hext =1.0 and 7.6 kOe. One can see that Rxy is dominated by the (RAD + RT)sin component
that increases with increasing of Hext, while the field-like torque RFL component is absent.
Figure 7.8(c) shows the extracted RAD + RT amplitude as a function of Hext at J = 1×105
and 2×105 A/cm2, which show that the antidampling-like torque RAD=cAD/(Hext + HAD)
component is also absent, and the thermal component RT = cAN + cONHext is dominant.
At J = 2×105 A/cm2, cAN = 0.075  and cON = 0.016 kOe-1 were obtained. The
corresponding contribution of ANE and ONE to Rxx are 0.15and 0.032 kOe-1 at J
= 2×105 A/cm2. Thus, the thermal effects perfectly describe the UMR hysteresis in Fig.
7.7(a), which means there is no UMR related to the GMR-like SS mechanism. This isconsistent with the absence of the pure spin current injection from BiSb to the GaMnAs
layer, as evidenced by the zero field-like torque and antidamping-like torque effects inthe Rxy curves. The absence of pure spin current injection in sample B, despite better
quality of the top BiSb layer, is the consequence of the well-known “conductivity
mismatch” problem [23], which is known to prevent spin injection in bilayers withsignificantly different conductivity, such as metallic ferromagnet/semiconductor
heterostructures. In the sample B, the conductivity of BiSb is much larger than that of
GaMnAs, thus the spin injection efficiency is close to zero.

144 | Page

Chapter 7

Figure 7.8: (a) UMR ratio of sample B as a function of J at various Tbase. (b)dependence of Rxy, measured at Tbase = 4 K, J = 2×105 A/cm2, and Hext = 1 kOe(blue) and 7.6 kOe (red), respectively. Solid lines show the fitting curves by (RAD +RT). (c) RAD + RT amplitude as a function of Hext at J = 1×105 A/cm2 (blue) and 2×
105 A/cm2(red).

145 | Page

Chapter 77.5. Discussion
These results demonstrate that it is possible to obtain a UMR ratio larger than 1%
in GaMnAs / poly crystalline BiSb heterostructures, which is larger than those in metallic
bilayers and TI / metallic ferromagnet systems by several orders of magnitude. In
particular, these results show that utilizing magnon scattering in ferromagnetic materials
with strong spin disorder scattering and conductivity matching are the key factors to
obtain a large UMR ratio for UMR-MRAM applications. Besides the required strong spin
disorder scattering, the ferromagnetic material should have high enough resistivity to
reduce the effect of parasitic resistance of electrical interconnection. Ferromagnetic
semiconductors, like the GaMnAs material used in this work, are promising. Although
the highest Curie temperature of GaMnAs thin film reported so far (~ 200 K) [24] is still
lower

than

room

temperature,

severalFe-doped

narrow-gap

ferromagnetic

semiconductors with room-temperature ferromagnetism, such as GaFeSb [25] or InFeSb[26, 27], have been realized recently.
On the other hand, topological insulators, such as Bi2Se3 [6], (BiSb)2Te3 [7],sputtered BixSe1-x [8], or poly-crystalline BiSb (this work), are promising as the spin Halllayer, since they have large spin Hall angle and comparable electrical conductivity withferromagnetic semiconductors. In contrast to GMR or TMR effects for which material
combinations have been exhaustedly explored, those for UMR are largely unexplored andopen for development. Further material engineering may improve the UMR ratio to over
10%, which is essential for UMR-MRAM with extremely simple structure and fast
writing/reading. My demonstration of an UMR ratio over 1% is an important step toward
this goal.

146 | Page

Chapter 7

7.6. Summary
This chapter presented the UMR effect in Ga0.91Mn0.09As (10 nm)/Bi0.85Sb0.15 (10nm) bilayers and clarified its origin. The large UMR ratio comes from the MS mechanism,
while the SS mechanism plays a very small role. Moreover, the UMR ratios are several
orders of magnitude larger than that in metallic bilayers and other TIs/FM systems. These
results provide helpful insight into spin transport in strong spin-orbit-couple systems andcan open the door to realistic applications such as two-terminal magnetic storage andspintronic devices based on UMR.

147 | Page

Chapter 7

References
1. J. Daughton, T. Sol. Films 216, 162 (1992).
2. C. O. Avci, K. Garello, J. Mendil, A. Ghosh, N. Blasakis, M. Gabureac, M. Trassin, M.
Fiebig, and P. Gambardella, Appl. Phys. Lett. 107, 192405 (2015).
3. C. O. Avci, K. Garello, A. Ghosh, M. Gabureac, S. F. Alvarado, and P. Gambardella,Nat. Phys. 11, 570 (2015).
4. K. Yasuda, A. Tsukazaki, R. Yoshimi, K. S. Takahashi, M. Kawasaki, and Y. Tokura,Phys. Rev. Lett. 117, 127202 (2016).
5. Lv. Yang, J. Kally, D. Zhang, J. S. Lee, M. Jamali, N. Samarth, and J. P. Wang, Nat.
Commun. 9, 111 (2018).
6. A. R. Mellnik, J. S. Lee, A. Richardella, J. L. Grab, P. J. Mintun, M. H. Fischer, A.
Vaezi, A. Manchon, E. A. Kim, N. Samarth, and D. C. Ralph, Nature 511, 449 (2014).
7. Y. Fan, P. Upadhyaya, X. Kou, M. Lang, S. Takei, Z. Wang, J. Tang, L. He, L. T.
Chang, M. Montazeri, G. Yu, W. Jiang, T. Nie, R. N. Schwartz, Y. Tserkovnyak, and K.
L. Wang, Nat. Mater. 13, 699 (2014).
8. DC. Mahendra, R. Grassi, J. Y. Chen, M. Jamali, D. R. Hickey, D. Zhang, Z. Zhao, H.
Li, P. Quarterman, L. Yang, M. Li, A. Manchon, K. A. Mkhoyan, T. Low, and J. P. Wang,Nat. Mater. 17, 800 (2018).
9. N. H. D. Khang, Y. Ueda, P. N. Hai, Nat. Mat. 17, 808 (2018).
10 .

T.

Shirokura,

K.

Yao,

Y.

Ueda,

and

P.

N.

Hai,

preprint

athttps://arxiv.org/abs/1810.10840 (2018).
11. C. O. Avci, J. Mendil, G. S. D. Beach, and P. Gambardella, Phys. Rev. Lett. 121,
087207 (2018).
12. I. V. Borisenko, V. E. Demidov, S. Urazhdin, A. B. Rinkevich, and S. O. Demokritov,Appl. Phys. Lett. 113, 062403 (2018).

148 | Page

Chapter 7

13. S. S. L. Zhang, and G. Vignale, Phys. Rev. B 94, 140411 (2016).
14. F. Matsukura, H. Ohno, A. Shen, and Y. Sugawara, Physical Review B 57, R2037(1998).
15. K. W. Edmonds, K. Y. Wang, R. P. Campion, A. C. Neumann, N. R. S. Farley, B. L.
Gallagher, and C. T. Foxon, Appl. Phys. Lett. 81, 4991 (2002).
16. K. Yao, N. H. D. Khang, and P. N. Hai, J. Cryst. Growth 511, 99 (2019).
17. Y. Ueda, N. H. D. Khang, K. Yao, and P. N. Hai, Appl. Phys. Lett. 110, 062401(2017).
18. V. Novák, K. Olejník, J. Wunderlich, M. Cukr, K. Výborný, A. W. Rushforth, K. W.
Edmonds, R. P. Campion, B. L. Gallagher, Jairo Sinova, and T. Jungwirth, Phys. Rev.
Lett. 101, 077201 (2008).
19. M. N. Baibich, J. M. Broto, A. Fert, N. V. Dau, F. Petroff, P. Etienne, G. Creuzet, A.
Friederich, and J. Chazelas, Phys. Rev. Lett. 61, 2472 (1988).
20. G. Binasch, P. Grunberg, F. Saurenbach, and W. Zinn, Phys. Rev. B. 39, 4828 (1989).
21. T. Miyazaki, and N. Tezuka, J. Magn. Magn. Mat. 139, L231 (1995).
22. J. S. Moodera, L. R. Kinder, T. M. Wong, and R. Meservey, Phys. Rev. Lett. 74, 3273
(1995).
23. G. Schmidt, D. Ferrand, L. W. Molenkamp, A. T. Filip, and B. J. van Wees, Phys.
Rev. B 62, R4790 (2000).
24. L. Chen, X. Yang, F. Yang, J. Zhao, J. Misuraca, P. Xiong, and S. von Molnár, Nano
Lett. 11, 2584 (2011).
25. N. T. Tu, P. N. Hai, L. D. Anh, and M. Tanaka, Appl. Phys. Lett. 108, 192401 (2016).
26. A. V. Kudrin, Y. A. Danilov, V. P. Lesnikov, M. V. Dorokhin, O. V. Vikhrova1, D.
A. Pavlov, Yu. V. Usov, I. N. Antonov, R. N. Kriukov, A. V. Alaferdov, and N. A.
Sobolev, J. Appl. Phys. 122, 183901 (2017).

149 | Page

Chapter 7

27. N. T. Tu, P. N. Hai, L. D. Anh, and M. Tanaka, Appl. Phys. Exp. 11, 063005 (2018).

150 | Page

Chapter 8

Chapter 8

Conclusions and Future Perspectives
8.1. Conclusions
In this study, various spin-related phenomena in BiSb-ferromagnet bilayers were
investigated for spintronic applications based on TIs. Here, the key results are highlighted
as follows.
In chapter 1, the thesis background was introduced. The primary concepts of spin
spintronics and its applications were reviewed. Spin-orbitronics was introduced as a novel
concept that aims to utilize the spin-orbit interaction (SOI) in spintronic devices and has
expanded spintronic materials to much broader spectra where spin devices utilize not only
magnetic materials but also nonmagnetic materials with strong SOI. Toward exploringnew materials with strong SOI, TIs and BiSb in particular appear as promising candidates.
The motivation and outline of this thesis were introduced.
In chapter 2, fundamental physics of SOI was introduced. SOI-related effects, suchas the Rashba-Edelstein effect, the SHE, THE, etc. were reviewed as new ideas that canhelp improve or even completely change spintronic device technologies. These ideas
inspire my researches of spin-related phenomena in BiSb-ferromagnet bilayers as themain topic in the rest parts of thesis.
In chapter 3, the fabrication process of BiSb/FM bilayer thin films andcharacterization techniques were described in details. The thin film fabrication based on
MBE and real-time monitoring by RHEED played the main role in fabrication process.
For sample characterizations, different types of measurement, such as XRD measurement,
magnetotransportmeasurement,

magneto-opticalmeasurement,

measurement and AFM measurement were briefly introduced.

magnetization

151 | Page

Chapter 8

In chapter 4, growth of MnGa thin layer with high PMA on BiSb thin film despite
their differences in the crystal symmetry and lattice constant were achieved. The high
PMA in BiSb/MnGa bilayers was confirmed by MCD, AHE and SQUID measurements.
In chapter 5, the large spin Hall effect in BiSb thin film was investigated in various
BiSb/MnGa bilayers. A huge spin-orbit field of 2.3 kOe/(MA/cm2) was observed at room
temperature. This value is much larger than those of heavy metals and other TIs by atleast an order of magnitude. The estimated θSH of 52 is the largest value as reported sofar. Comparing with other spin Hall material, BiSb shows the big advantage of large θSHand high electrical conductivity. In term of spin Hall conductivity  SH  ( / 2e)SH  which considered as the figure merit for spin Hall materials, BiSb outperforms the nearest
competitor (Pt) and other TIs by at least an order of magnitude. Finally, the ultra-low
current density of 1.5 MA/cm2 for SOT magnetization switching was demonstrated in
BiSb/MnGa bilayers, even though the MnGa ferromagnet used in this work has higher
PMA energy by an order of magnitude than those used in previous room-temperature
SOT magnetization switching experiments.
In chapter 7, the THE in BiSb topological insulator / MnGa bilayers with anadditional annealing step was observed and provided a firm evidence for the existence ofskyrmions. By combining the strong spin-orbit-interaction of BiSb and the small
magnetization of MnGa, a large critical interfacial Dzyaloshinskii-Moriya-Interaction(DMI) constant (Ds = 5.1 pJ/m) was achieved by controlling the annealing temperature of
the MnGa template. Moreover, field-free ground-state skyrmions were observed for the
first time at room temperature even under absence of an external magnetic field which isalso consistent with micromagnetic simulations. These results confirm that BiSb
topological insulator can generate not only large spin-orbit-torque, but also hugeinterfacial DMI for generation and manipulation of skyrmions.

152 | Page

Chapter 8

In chapter 8, the large UMR in Ga0.91Mn0.09As/Bi0.9Sb0.1 bi-layers was reported. The
observed UMR ratio is many orders of magnitude larger than those observed in metallic
bi-layers and other TIs/CoFeB heterostructures. In addition, I found that the large UMR
ratio comes from the MS mechanism, while the SD mechanism plays a very small role.
These results provide helpful insight into spin transport in strong spin-orbit-couple
systems and can open the door to realistic applications, such as two-terminal magnetic
storage and spintronic devices based on UMR.

153 | Page

Chapter 88.2. Future Perspectives
SOT-MRAM is the main application of BiSb studied in this thesis. Thanks to thehigh conductivity [1] and huge spin Hall angle [2], BiSb is the most promising pure spincurrent source for SOT-MRAM. From my results, the performance of BiSb-based SOTMRAM in nano size of 37 nm was estimated and compared with commercial STTMRAM at the same size (as shown in Fig. 8.1). The writing current can be reduced by atleast an order of magnitude, while the writing speed in SOT-MRAM is 20 times fasterthan in STT-MRAM. The writing energy, therefore, can be reduced by at least two ordersof magnitude. Moreover, the low writing current will help scale down the size of driving
transistors which help increase the bit density of SOT-MRAM. This bench making
demonstrates that BiSb-based SOT-MRAM outperforms STT-MRAM and can be very
competitive with conventional volatile memory technologies.

Figure 8.1: Benchmarking of SOT-MRAM based on BiSb as a spin source. The
estimations are referenced with the performance of STT-MRAM with the same size (~37 nm).

Process integration of BiSb into a realistic MTJ stack remains the challenging
problem for the realization of BiSb-based SOT-MRAM. In particular, because the154 | Page

Chapter 8

BiSb(012) surface is critical to obtain the very large spin Hall effect at room temperature,controlling of the surface orientation is a very important issue. However, the potential
applications of BiSb(012) to realistic MRAM is very optimistic, because BiSb seems togrow with the BiSb(012) orientation on underlying ferromagnetic layers with a cubic
crystal structure, and fortunately, most of the metallic layers used in MRAM has a cubic
crystal structure, just like the MnGa layer in this work.
Furthermore, it is necessary to investigate whether the performance of BiSb(012)surface does not degrade when fabricated by the industry-friendly sputtering method,rather than by the MBE method as in this work. This can be quite challenging since there
are big differences between the lab and industrial conditions. While thin film fabrication
process in my studies was done by MBE to ensure the high quality of BiSb andferromagnetic layers, conventional physical vapor deposition, such as sputtering will be
employed for the industrial mass production, and its final step requires annealing of SOTMRAM devices in 1 hour at 400oC, which is higher than BiSb’s melting temperature andcan may modify its intrinsic transport properties. Therefore, the spin Hall angle θSH andelectrical conductivity σ of BiSb layer can be changed and directly affect the writingenergy of SOT-MRAM devices [3]. Fortunately, recent studies from our group show that
BiSb survives such condition by using a capping layer. Second, the spin Hall angle of TI
seems not to degrade when deposited using the sputtering method. Recently, SH of a
sputtered 4 nm-thick BixSe1-x layer was found to be about 18.8 [4], which is larger thanSH = 2~3 of the MBE-grown Bi2Se3 layer [5]. On the other hand, while MnGa thin film
was used as the magnetic layer in my researches, industrial applications employ othermaterials, such as CoFeB or Co-based multilayers. Therefore, it is important to study the
SHE effect in BiSb/CoFeB or BiSb/Co-based multilayers.

155 | Page

Chapter 8Race track memory based on skyrmions is another application of BiSb. Confirming
the existence of skyrmions by the THE and demonstration of field-free ground state
skyrmions are promising for skyrmion-driven racetrack memory [6, 7]. Future study will
be direct observation of skyrmions and SOT-driven skyrmion motion.
Two terminal SOT-MRAM without a reference layer is another application of BiSb.
The novel UMR-based MRAM is very promising since they require only two layers [8]and two terminals for both reading and writing. This unique advantage cannot be seen inconventional SOT-MRAM and other kinds of MRAM. Observation of the large UMR
ratio up to 1.1% is a milestone toward realistic UMR-based MRAM. The next step will
be realization of the large UMR ratio (> 1%) at room temperature by the magnonscattering mechanism.

156 | Page

Chapter 8

References
1. Y. Ueda, N. H. D. Khang, and P. N. Hai, Appl. Phys. Lett. 110, 062401 (2017).
2. N. H. D. Khang, Y. Ueda, and P. N. Hai, Nat. Mater. 17, 808 (2018).
3. C. F. Pai, Nature Materials 17, 755 (2018).
4. DC. Mahendra, R. Grassi, J. Y. Chen, M. Jamali, D. R. Hickey, D. Zhang, Z. Zhao, H.
Li, P. Quarterman, L. Yang, M. Li, A. Manchon, K. A. Mkhoyan, T. Low, and J. P. Wang,Nat. Mater. 17, 800 (2018).
5. A. R. Mellnik, J. S. Lee, A. Richardella, J. L. Grab, P. J. Mintun, M. H. Fischer, A.
Vaezi, A. Manchon, E.-A. Kim, N. Samarth, and D. C. Ralph, Nature 511, 449 (2014).
6. S. Woo, K. Litzius, B. Krüger, M. Y. Im, L. Caretta, K. Richter, M. Mann, A. Krone,
R. M. Reeve, M. Weigand, P. Agrawal, I. Lemesh, M. A. Mawass, P. Fischer, M. Kläui,and G. S. Beach, Nat. Mater. 15, 501 (2016).
7. C. M. Luchaire, C. Moutaﬁs, N. Reyren, J. Sampaio, C. A. F. Vaz, N. Van Horne, K.
Bouzehouane, K. Garcia, C. Deranlot, P. Warnicke, P. Wohlhüter, J.-M. George, M.
Weigand, J. Raabe, V. Cros, and A. Fert, Nat. Nanotech 11, 444 (2016).
8. K. Olejník, V. Novák, J. Wunderlich, and T. Jungwirth, Phys. Rev. B 91, 180402(2015).

157 | Page

Appendix

Appendix A
Hso obtained by fitting data in Figs. 5.8(a)-5.8(b)in the high in-plane field range (H > 4 kOe)
To further confirm the validity of the relationships Hso = Hc used to estimate Hsofrom data in Fig. 5.7(a), fitting of the experimental RH-H data in Figs. 5.8(a)-(b) was
performed in the high in-plane magnetic field range (|H| > 4 kOe). As dicussed before inchapter section 5.3.1, when an in-plane |H| > 4 kOe is applied, all domains are oriented
toward the magnetic field direction, and the whole sample becomes a single domain(macrospin). Therefore, it is possible to estimate Hso by fitting the RH-H data at |H| > 4
kOe to the single domain model. Note that the field-like spin-orbit field is negligible, thus
the magnetization vector is in the x-z plane. Therefore, all torques acting on M are along
the y direction. The torque balance equation for M becomes a simple scalar equation

TSO  Tani  TH  0(A1)

where Tso = HsoM is the spin-orbit torque, TH = -HMcos is the torque by the in-plane
external field H//x, Tani =dE ani K u sin 2  K 4 sin 4 is the torque by anisotropydmagnetic fields. Equation A1 can be rewritten as
1
1
HSO  H u sin 2  H 4 sin 4  H cos   0
2
4

(A2)

Note that Equation A2 is same as that derived in the pioneering work of L. Liu etal., Phys. Rev. Lett., 109 (2012) 096602, for the Pt/Co bi-layer, except for the term1
 H 4 sin 4 from the bi-axial anisotropy field and the opposite direction of Hso (because
4

BiSb is deposited on top of MnGa, unlike Liu’s Pt/Co bi-layer where Pt is deposited underCo.)158 | Page

Appendix

Using Eq. A2, one can find Hso using a single data point of  (deduce from RH) andH, given that Hu and H4 are known. However, we found that the values Hu = 10 kOe, H4= 30 kOe obtained for the as-grown BiSb/MnGa bi-layer do not give a unique Hso fordifferent data points (RH, H) of the Hall bar. This may be due to the fact that the
BiSb/MnGa bi-layer underwent additional stress and annealing during thephotolithography and ion-milling process for fabrication of the Hall bar, thus Hu and H4of the Hall bar may be different from that of the as-grown bi-layer. Indeed, the coercive
force of the Hall bar at small current densities (1.6 kOe) is smaller than that (4.5 kOe) of
the as-grown bi-layer. Here, Hu and H4 are treated as adjustable parameters and estimate
Hso using the following procedure.
First, Eq. A2 can be rewritten as
1
1
HSO   H u sin 2  H 4 sin 4  H cos   const
2
4

(A2)

At a given current density, Hso is unique and should not change with  or H.
Hso is derived by the following algorithm.
(1)

Assume a pair of Hu and H4.

Calculate Hso from Eq. S5 using the experiment data in Fig. 2(c) or 2(d) at |H| > 4
kG.
(2)

Fitting the calculated |Hso| to a linear a|H| + b function.

(3)

Adjust H4 so that a < 0.001 (i.e. nearly independent from H); thus, b gives theaverage |Hso|.
(4)

Adjust Hu so that the average deviation of Hso for all data points  =(| H so | b) 2 / b becomes less than 5%.
Hu and H4 are adjusted, and the (1)-(5) loop is repeated until a < 0.001 and  < 5%.
If these conditions cannot be satisfied, the calculation loop is stoped and the data isignored.

159 | Page

Appendix

The calculation was performed using data of the forward sweep (H: -8 kOe  + 8kOe) and backward sweep (H: +8 kOe  -8 kOe) in Fig. 5.8(a) and 5.8(b). There arethree sets of data that satisfied these conditions. Other data are too noisy and do not fit
well. The fitting results are summarized in Table. A1 and shown in Figs. A1.
The obtained average |Hso| are 2.9 – 3.4 kOe for J = 13.8 105 A/cm2, which arewithin 10% of uncertainty from that obtained by assuming Hso = Hc = 3.1 kOe for J=13.8 105 A/cm2 in Fig. 5.7(a).

160 | Page

Appendix

Table A1. Fitting results for data in Figs. 5.8(a) and 5.8(b) to Eq. A3.
Data sourceaFig. 2(c)Backward sweep

J = 13.8105 A/cm2

H < -4 kOe

Fig. 2(d)Forward sweep

J = -13.8105 A/cm2

H < -4 kOe

Fig. 2(d)Forward sweep

J = -13.8105 A/cm2

H > 4 kOeb

0.0009 2.9 kOe 4.7%

Ref.
Fig. A1(a)0.0004 3.4 kOe 4.9% Fig. A1(b)0.0001 3.4 kOe 4.8%

Fig. A1(c)Figure A1: Fitting results using Eq. S5 for (a) data in Fig. 5.8(a) with J = 13.8105
A/cm2, backward sweep, H < -4 kOe, (b) data in Fig. 5.8(b) with J = -13.8105 A/cm2,
forward sweep, H < -4 kOe, and (c) data in Fig. 5.8(b) with J = -13.8105 A/cm2,
forward sweep, H > 4 kOe.

161 | Page

Appendix

Appendix B
MuMax3 script for micro magnetic simulation
MuMax3 is an open-source and finite-element micromagnetic simulation software.
MuMax3 is freely distributed under GPLv3 license on http://mumax.github.io.
Representative magnetization configurations in my simulations are shown in Fig. B1.
Results for Ku = 1.2105 J/m3 and D = 1.0 mJ/m2 are presented in Fig. B2. The MuMax3
code is shown as below.
setgridsize(128, 128, 1);// set number of domains

setcellsize(1e-9, 1e-9, 5e-9);// set domain size

SetGeom(Circle(1.28e-07));// set a circular geometry

Msat = 108.64e3;// saturation magnetization

Aex = 5.4e-12;// exchange stiffness

alpha = 0.008;// Landau-Lifshitz damping constant of MnGa

AnisU = vector(0, 0, 1);// uniaxial anisotropy in z direction

Dbulk = 0;// no bulk Dzyaloshinskii-Moriya strength

B_ext = vector(0, 0, 0);// no external magnetic field

tableadd(Dind);tableadd(Ku1);
tableadd(ext_topologicalcharge);
tableadd(LastErr);tableadd(PeakErr);

162 | Page

Appendix

Dind = 0.5e-3;//set Interfacial Dzyaloshinskii-Moriya strengthfor i:=1e5; i<=5e5; i+=0.2e5{
Ku1 = i;m = BlochSkyrmion(1, 1);
relax();
save(m);tablesave();}
Dind = 0.6e-3;
for i:=1e5; i<=5e5; i+=0.2e5{
Ku1 = i;m = BlochSkyrmion(1, 1);
relax();
save(m);tablesave();}…
Dind = 2.5e-3;
for i:=1e5; i<=5e5; i+=0.2e5{
Ku1 = i;m = BlochSkyrmion(1, 1);
relax();
save(m);tablesave();}163 | Page

Appendix

Figure B1: Three representative magnetization configurations. (a) uniform state (S =0), (b) Vortex (S = 0.5), and (c) Néel-like skyrmion (S =1).

Figure B2: (a) Néel-like skyrmion simulated by MuMax3 at Ku = 1.2105 J/m3 and D= 1.0 mJ/m2. (b) Mz profile along the x direction for the Néel-like skyrmion in Fig. B2
at y = 64 nm. The size of the skyrmion is about 55 nm.

164 | Page

Acknowledgments
First of all, I would like to express my gratitude to my supervisor, Prof. Pham Nam
Hai who has greatly supported and constantly guided me with his wisdom, tranquility andprofessionalism in these years. He not only taught me physics, helped me solve theproblems blocking my researches, but also let me know the passion and pleasure whenbecoming a research scientist. 3-year is not a long time but it is enough for me tounderstand that he is a great supervisor and become a researcher under his guidance is awonderful thing. Without his support, this research would not be completed.
I would like to especially thank my co-worker Mr. Yugo Ueda who has been mytutor since the first day of my PhD program. With his patient and thoughtful advice, hetaught me about the fabrication process, device fabrication, measurement setup and many
more things in physics. He shared with me about personal things and endless discussions
that we have enjoyed together.
I wish to express my sincere thankfulness to Dr. Duong Dinh Hiep, Dr. Nguyen
Thanh Tu and Dr. Bui Cong Tinh who always are my best friends and support me in thisPhD research.
I would like to thank other members in my Lab, such as Mr. Yoshida, Mr. Otsuka,
Mr. Nishishima, Mr. Yamane, Mr. Chonan, Mr. Tuo, Mr. Shirokura and especially Mr.
Kenichiro Yao for their help, technical supports and joyful discussions about Japan andlife.
I would like to thank the members of Tanaka Lab at Tokyo University, Munekata
Lab and Nakagawa Lab in Tokyo Institute of Technology who kindly supported me inthe experiment.
I wish to express my thankfulness to Mr. Ida and other members in Ookayama
Materials Analysis Division for their technical supports in the experiment.

165 | Page

I would like to acknowledge the Japanese Government (MEXT) Scholarship for
their financial support in this PhD study.
Finally, I would like to deeply thank my beloved family for your endless supports
and encouragement.

166 | Page

Related publications and presentations

Papers
1. N. H. D. Khang, Y. Ueda, and P. N. Hai, “A conductive topological insulator
with large spin Hall effect for ultralow power spin-orbit torque switching”, Nature
Materials 17, 808 (2018).
2. P. N. Hai, N. H. D. Khang, K. Yao, and Y. Ueda, “Conductive BiSb topologicalinsulator with colossal spin Hall effect for ultra-low power spin-orbit-torque switching”,
Proc. SPIE 10732, 107320U (2018).
3. K. Yao, N. H. D. Khang, P. N. Hai, “Influence of crystal orientation and surface
termination on the growth of BiSb thin films on GaAs substrates”, Journal of Crystal
Growth 511, 99 (2019).
4. N. H. D. Khang, Y. Ueda, K. Yao, and P. N. Hai, “Growth and characterizationof MnGa thin films with perpendicular magnetic anisotropy on BiSb topologicalinsulator”, Journal of Applied Physics 122, 143903 (2017) (selected as feature paperwith an AIP Scilight article).
5. Y. Ueda, N. H. D. Khang, K. Yao, and P. N. Hai, “Epitaxial growth andcharacterization of Bi1-xSbx spin Hall thin films on GaAs(111)A substrates”, Applied
Physics Letters 110, 062401 (2017).
6. N. H. D. Khang, and P. N. Hai, “Giant Unidirectional Magnetoresistance in
topological insulator-ferromagnetic semiconductor heterostructures”, (submitted andunder review).
7. N. H. D. Khang, T. Fan, and P. N. Hai, “Field-free ground-state skyrmions in
BiSb/MnGa bi-layers at room temperature revealed by topological Hall effect”, (inpreparation).

167 | Page

Patent application
Patent name: “Method to fabricate ferromagnets/BiSb heterostructures andmagnetoresistive memory”.
Japanese and PCT patent applications, No. 2017-177564.
Inventors: P. N. Hai, N. H. D. Khang.

Presentations
International Conferences
1. N. H. D. Khang, T. Fan, and P. H. Hai, “Observation of topological Hall effectand field-free stable skyrmions in MnGa/BiSb bi-layers at room temperature”, The 10th
International School and Conference on Spintronics and Quantum Information
Technologies (Spintech X), June 2019.
2. (Invited) N. H. D. Khang, Y. Ueda, and P. N. Hai, “Colossal spin Hall effect ina conductive topological insulator Bi0.9Sb0.1 for ultra-low-power spin-orbit-torqueswitching”, The 11th Vietnam-Japan Scientific Exchange Meeting, September 2018.
3. N. H. D. Khang, Y. Ueda, and P. N. Hai, “Ultra-low-power spin-orbit-torqueswitching using the colossal spin Hal effect in BiSb topological insulator”, Intermag2018,
April 2018.
4. N. H. D. Khang, Y. Ueda, and P. N. Hai, “Magnetic and structural properties of
MnGa thin films grown on Bi0.8Sb0.2 topological insulator”, Junjirou Kanamori Memorial
International Symposium – New Horizon of Magnetism, September 2017.
5. N. H. D. Khang, Y. Ueda, and P. N. Hai, “MnGa thin films grown on BiSb
topological insulator for SOT-MRAM”, The 10th Vietnam-Japan Scientific Exchange
Meeting, September 2017.
6. N. H. D. Khang, Y. Ueda, and P. N. Hai, “MnGa thin films with perpendicularmagnetic anisotropy grown on BiSb topological insulator”, Spintech IX, July 2017.

168 | Page

Domestic Conferences
1. N. H. D. Khang, and P. N. Hai, “Large Unidirectional Magnetoresistance in
GaMnAs/BiSb bilayers”, The 66th JSAP Spring meeting, March 2019.
2. N. H. D. Khang, T. Fan, and P. N. Hai, “Field-free ground-state skyrmions in
BiSb/MnGa bi-layers at room temperature revealed by topological Hall effect”, PASPS23, December 2018 (best student English presentation award).
3. N. H. D. Khang, T. Fan, and P. N. Hai, “Field-free ground-state skyrmions in
BiSb/MnGa bi-layers at room temperature revealed by topological Hall effect”, The 79th
JSAP Autumn Meeting, September 2018.
4. N. H. D. Khang, Y. Ueda, and P. N. Hai, “Room-temperature colossal spin Hall
effect in topological insulator Bi0.9Sb0.1(012) thin films for ultra-low-power spin-orbittorque switching, The 65th JSAP Spring meeting, March, 2018.
5. N. H. D. Khang, Y. Ueda, and P. N. Hai. MnGa thin films with perpendicularmagnetic anisotropy grown on BiSb topological insulator, The Tokyo Tech Spintronics
Symposium 2017, July 2017.
6. N. H. D. Khang, and P. N. Hai, “Growth and characterization of MnGa thin films
on BiSb topological insulator”, The 64th JSAP Spring meeting, March 2017.