Detection of edge magnetic state by a ballistic bend resistance measurement
Takahiro Matsunaga, Kohsuke Furukawa, Yuhsuke Kanda, Masahiro Hara, Tatsuya Nomura, and Takashi
KimuraCitation: Applied Physics Letters 102, 252405 (2013); doi: 10.1063/1.4812729
View online: http://dx.doi.org/10.1063/1.4812729
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APPLIED PHYSICS LETTERS 102, 252405 (2013)

Detection of edge magnetic state by a ballistic bend resistance measurement
Takahiro Matsunaga,1 Kohsuke Furukawa,1 Yuhsuke Kanda,1 Masahiro Hara,1,a)Tatsuya Nomura,2 and Takashi Kimura2

1Graduate School of Science and Technology, Kumamoto University, 2-39-1 Kurokami,
Kumamoto 860-8555, Japan
2
Advanced Electronics Research Division, INAMORI Frontier Research Center, Kyushu University,
744 Motooka, Fukuoka 819-0395, Japan(Received 15 March 2013; accepted 16 June 2013; published online 27 June 2013)
We have investigated a magnetization process of a permalloy nanowire by using a ballistic microHall sensor consisting of GaAs/AlGaAs two-dimensional electron gas. Although a conventionalbi-stable hysteresis loop with a rectangular shape was observed in the Hall resistance measurement,unexpected extra resistance changes were observed in a bend resistance measurement. These
unconventional features are quantitatively explained by the magnetic transitions among themeta-stable edge-domain structures in the ferromagnetic wire. The geometrical dependence of
these resistance changes and their application possibility for the multiple-valued memory were also
C 2013 AIP Publishing LLC. [http://dx.doi.org/10.1063/1.4812729]
discussed. V
Magnetic field sensors are widely utilized in commercial
electrical and biomedical devices as well as in the fundamental analysis of the functional magnetic materials.1 Various
types of the magnetic sensors have been developed and still
continue to grow with improving the performance and thecost reduction. Fluxgate sensor using a magnetic core is
known to provide high sensitivity with a reliable roomtemperature operation. However, complexities of the device
structures make it difficult to reduce the device dimension. In
addition, it is not suitable to detect the spatially non-uniform
magnetic field. Superconducting quantum interference device(SQUID) sensor yields the highest field sensitivity less thanpico Tesla. However, its operation is limited to low temperature because of the necessity of the superconductivity, leading to high running cost and large system size. The use ofspin-dependent transports such as giant and tunnel magnetoresistances (MRs) enables to create a nano-sized magnetic
sensor with a high sensitivity. However, the nonlinear fielddependence of the magnetization and the hysteresis in themagnetization process are serious obstacles for the precise
detection of the magnetic field. Therefore, a breakthroughtechnology based on a different sensing mechanism isrequired for the innovation of magnetic sensing devices.
As an alternative approach for the sensitive detection ofa tiny magnetic field with a high spatial resolution, we are focusing on the ballistic transports in mesoscopic structures.
Since the trajectory of the ballistic electron is stronglyaffected by the external magnetic field, the transport properties of the electrons collimated by patterned nanostructures
yields highly sensitive magnetic field response. In fact, themagnetization reversal process of submicron-sized patterned
ferromagnets was precisely investigated from ballistic bend
resistance measurements using a micro-Hall cross in GaAs/
AlGaAs two-dimensional electron gas (2DEG) systems.2–4
Moreover, a ballistic bend resistance measurement using a30-nm wide Hall cross was found to show a high spatial resolution of less than 100 nm very recently.5 Although theabove demonstration using GaAs/AlGaAs 2DEG system isa)Electronic address: mhara@sci.kumamoto-u.ac.jp0003-6951/2013/102(25)/252405/4/$30.00

limited at low temperature, it is not unrealistic in several systems such as graphene to make a device with a channellength less than the mean free path even at room temperature.6 Thus, the ballistic transport in 2DEG systems may
open an avenue for the development of more functional andhigher performance magnetic sensors. Here, we demonstrated that metastable edge domain structures in a ferromagnetic nanowire were sensitively detected by using 2DEG
ballistic transports. The study of the edge magnetization isimportant not only in fundamental physics but also in device
applications since the magnetic behavior in tiny magnets
strongly depends on the edge condition.7–10 Moreover, theratio of the edge region relatively increases in smaller nanomagnets, which calls for a sensitive magnetic sensor with ahigh spatial resolution. An anisotropic magneto-resistance(AMR) measurement11,12 and a local Hall measurement13,14
are well-known methods for electrically detecting a change inthe bulk magnetization, however, is difficult to catch up aslight change in the local edge magnetization. In this letter, weshow a clear detection of edge magnetic structure in the bend
resistance, which indicates that the spatial resolution is muchhigher than those of other methods. The importance of the ballistic bend signal grows up since the miniaturization of themagnetic sensor is reaching a technological limit nowadays.
A 2DEG cross was fabricated from a GaAs/AlGaAs
single-heterojunction wafer. The density and mobility of the2DEG before processing at 5 K were 4:25  1015 =m2 and76:5 m2 =Vs, respectively. The depth of the 2DEG planefrom the surface is 65 nm. The cross structure 1.2 lm
 1.2 lm was fabricated by means of Ar plasma etching.
A scanning electron microscopy (SEM) image of the sample
is shown in Fig. 1. The electron mean free path of the 2DEG
is 8:2 lm at 5 K, which is larger than the size of the cross.
A rectangular permalloy (Py) with thickness of 50 nm, widthof 900 nm, and length of 10 lm is placed on the top of thecross. 4-terminal resistance measurements were carried out
using a low-frequency ac technique at 5 K.
We measured a Hall resistance R13;42 and a bend resistance R14;23 as a function of in-plane magnetic field. We precisely aligned the magnetic field in the 2DEG plane so that102, 252405-1

C 2013 AIP Publishing LLC
V

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252405-2

Matsunaga et al.

Appl. Phys. Lett. 102, 252405 (2013)

FIG. 1. SEM image of the fabricated device. The 2DEG was etched into across structure by Ar plasma etching. The edge of the rectangular Py wasplaced at the center of the cross. 4-terminal resistance of the 2DEG wasmeasured at 5 K as a function of in-plane magnetic field.

the change in the resistance originates only from a straymagnetic field from the ferromagnet. As shown in Fig. 2(a),the change in the Hall resistance reveals the magnetization
reversal of the bulk region. From the local Hall measurement, the reversal field is about 610 mT. The change in thebend resistance shown in Fig. 2(b) significantly differs fromthe Hall resistance and shows a resistance jump at higher
fields. These indicate that the bend resistance detects a spatial variation of the stray field from the rectangular Py, which
is not apparent in the Hall signal.
In order to analyze the resistance behavior, the magnetization pattern of the rectangular Py was calculated byOOMMF simulator.15 And then, we estimated the pattern of
the stray field normal to the plane of the 2DEG and the totalmagnetic flux U inside the cross. Figure 3(a) shows the magnetic flux as a function of in-plane magnetic field. The magnetic flux dominantly depends on the magnetization of thebulk region. The change in the flux DU with the magnetization reversal of the bulk region is 3:03  1014 Wb. Thechange in the Hall resistance DR13;42 is roughly estimated asthe following:13,14

FIG. 3. (a) Estimated magnetic flux U in the 1:2 lm  1:2 lm cross as a function of in-plane magnetic field. (b) and (c) Schematic illustration of the devicestructure. (d) and (e) Magnetization patterns of the rectangular Py and thestray field profiles in the cross at the sweeping points indicated in (a).

DR13;42 ’

FIG. 2. (a) Hall resistance R13;24 as a function of in-plane magnetic field.
(b) Bend resistance R14;23 as a function of in-plane magnetic field. The offsets are subtracted for clarity.

1 DU 30:9 X;
ne S(1)

which shows a good agreement with the experimental value
in Fig. 2(a). Here, S and n are the area of the cross and theelectron density of the 2DEG, respectively. The change inthe magnetization in this reversal process corresponds toFig. 3(d) (i ! ii). In the reversal process, a vortex nucleatesat the top or the bottom side near the edge and moves to theother side. Here, the direction of the vortex movement
depends on the nucleation site of the vortex determined by
the sample asymmetry. At higher fields, the vortex annihilates and then the magnetization only near the edge is not

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252405-3

Matsunaga et al.

Appl. Phys. Lett. 102, 252405 (2013)aligned with the direction of in-plane field as shown inFig. 3(d)(iii). The tilt direction of the edge magnetization isthe same as the direction of the vortex movement. Furtherincrease of the magnetic field leads to a discrete change ofthe magnetization into a so-called flower state (iii ! iv).16
This causes a noncontinuous spatial shift of the stray field
while the amplitude of the magnetic flux is almost constant.
The change in the magnetic flux due to the transition in theedge region is about 1  1016 Wb. It is quite difficult to
detect the transition by a local Hall measurement since thechange in the Hall signal is estimated to be about 0.1 X.
For reproducing the high sensitivity of the bend resistance to the edge magnetic transition, we made a simple simulation based on a semiclassical billiard model.17 The bend
resistance R14;23 is described in terms of transmission coefficients between the probes as
R14;23 ¼h T23 T34  T24 T31;
D2e2(2)where D is a factor independent of the current/voltage terminal configuration.18 In the simulation, electrons are injectedfrom each probe like a billiard ball with an angular distribution PðaÞ ¼ cos a=2. Classical trajectories of electrons aremodified by the stray field estimated by the OOMMF simulator. We then calculated transmission probabilities by counting number of the transmitted electrons into each probe.
Figure 4(a) shows the calculated change in the bend resistance DR14;23 in the process of the transition between

FIG. 4. (a) Calculated change in the bend resistance DR14;23 in the processof the transition between meta-stable edge magnetic states. (b)Magnetization patterns near the edge at the sweeping points indicated in (a).

meta-stable edge magnetic states, where the bulk magnetization in the wire is fully aligned in the external field.
Corresponding magnetization patterns are shown in
Fig. 4(b). Just above the reversal field of the bulk magnetization, there are two possible edge magnetic states (A and A0 ).
The tilt direction of the edge magnetization in the actual
sample is determined by an unavoidable sample asymmetry.
At higher field, a transition into a more stable flower state
occurs in the both paths (C ! D and C0 ! D). A bend resistance jump due to the edge magnetic transition at B ¼ 54 mT
is clearly seen in Fig. 4(a). The change in the resistance isabout 2 X which is comparable to the experimental value inFig. 2(b). Importantly, we can distinguish whether the edge
magnetization tilts upward or downward. Comparison withthe resistance trace in the experiment reveals that the tilt
direction of the edge magnetization before the transition into
a flower state was downward in the actual sample, whichcorresponds to A ! B ! C in the simulation. This implies
that a vortex nucleated at the top side and then moved to thebottom side in the process of bulk magnetization reversal as
shown in Fig. 3(d). If we intentionally make a vortex nucleation site at the bottom, we will observe the other edge magnetization path (A0 ! B0 ! C0 in the simulation).
We also calculated the bend resistance behavior for different widths of the rectangular Py to evaluate the spatial resolution for detecting the edge magnetization. Figure 5
shows the calculated change in the bend resistance DR14;23
around the transition to a flower state. The transition field
increases with decrease of the width of the Py. The shift inthe bend resistance between the different edge states isobservable even in the narrower cases although the amplitude of the stray field becomes smaller.
Finally, we would like to mention that the present bend
resistance measurement is applicable for a multiple-valued
magnetic memory.19,20 In the present study, the Hall signal
reflects the direction of the bulk magnetization (left or right).
By contrast, the bend signal is sensitive to the abovementioned edge magnetic states. Therefore, the combined
local Hall/bend measurement enables us to distinguish multiple magnetic states including a slight difference in the edge
region. We believe that an approach to a multiple-valued
magnetic memory realizes a drastic increase of stored information in magnetic storage devices and the bend resistance

FIG. 5. Calculated change in the bend resistance DR14;23 for different widthsof the rectangular Py.

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252405-4

Matsunaga et al.

measurement plays an important role in reading out thedifferent values.
In summary, we study the behavior of Hall/bend resistance of 2DEG cross in the presence of stray field from theedge of a rectangular Py. The Hall signal is less sensitive tothe profile of the stray field and dominantly depends on themagnetization in the bulk region. On the other hand, thebend resistance reveals a magnetic structure in the edge
region, which is difficult to detect by the Hall measurement.
We would like to thank the financial support from theIndustrial Technology Research Grant Program from NEDO.
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