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Vol.47 No.4
JournalJournal of the Magnetics Society of Japan
Electronic Journal URL: https://www.jstage.jst.go.jp/browse/msjmag

2023

Review: MSJ Awards 2022
Dynamic Magnetization Process of Magnetic Nanoparticles for Biomedical Applications
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Y. Takemura, S. B. Trisnanto, and S. Ota…84

First-Principles Studies on Spin-Dependent Transport of Magnetic Junctions with Half-Metallic Heusler Compounds
Y. Miura…90

Y. Mori, S. Hatanaka, M. Kambayashi, S. Nakatsuka, K. Hirayama, M. Doi, and T. Shima…103

Hard and Soft Magnetic Materials
Increase in Coercivity of Sm(Fe-Co)-B Thin Films Due To Diﬀusion of Al Element from Cap Layer

Spintronics

Laser Induced Spin Current in GdFeCo/Cu/FeCo Trilayers Triggered by Ultrashort Pulsed Laser
K. Seguchi, E. Watanabe, D. Oshima, and T. Kato

…108

Biomagnetism / Medical ApplicationsFirst-Order Reversal Curve Analysis of Superparamagnetic Nanoparticles with Oriented Easy Axis of Magnetization
E. Sasaoka, C. Yang, S. B. Trisnanto, Z. Song, S. Ota, and Y. Takemura…115

Development of Ultra-Low Field Magnetic Resonance Imaging System at 1 mT
D. Oyama, N. Tsuyuguchi, J. Hirama, Y. Adachi, and J. Kawai

広告◇東英工業株式会社

…118

47

HP: http://www.magnetics.jp/ e-mail: msj@bj.wakwak.com
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Journal of the Magnetics Society of Japan
Vol. 47, No. 4

Electronic Journal URL: https://www.jstage.jst.go.jp/browse/msjmag

CONTENTS
Review: MSJ Awards 2022
Dynamic Magnetization Process of Magnetic Nanoparticles for Biomedical Applications…………………………………………………………………… Y. Takemura, S. B. Trisnanto, and S. Ota

84

First-Principles Studies on Spin-Dependent Transport of Magnetic Junctions with Half-Metallic Heusler
Compounds…………………………………………………………………………………………………………… Y. Miura

90

Hard and Soft Magnetic Materials…

Increase in Coercivity of Sm(Fe-Co)-B Thin Films Due To Diffusion of Al Element from Cap Layer…………Y. Mori, S. Hatanaka, M. Kambayashi, S. Nakatsuka, K. Hirayama, M. Doi, and T. Shima

103

Spintronics…

Laser Induced Spin Current in GdFeCo/Cu/FeCo Trilayers Triggered by Ultrashort Pulsed Laser………………………………………………………… K. Seguchi, E. Watanabe, D. Oshima, and T. Kato

108

Biomagnetism / Medical ApplicationsFirst-Order Reversal Curve Analysis of Superparamagnetic Nanoparticles with Oriented Easy Axis of…

Magnetization……………………………… E. Sasaoka, C. Yang, S. B. Trisnanto, Z. Song, S. Ota, and Y. Takemura

115…

Development of Ultra-Low Field Magnetic Resonance Imaging System at 1 mT………………………………………… D. Oyama, N. Tsuyuguchi, J. Hirama, Y. Adachi, and J. Kawai

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Copyright ©2023 by the Magnetics Society of Japan.
This article is licensed under the Creative Commons Attribution International License (CC BY 4.0)
http://creativecommons.org/licenses/by/4.0/

J. Magn. Soc. Jpn., 47, 84-89 (2023)<Review>

Dynamic magnetization process of magnetic nanoparticles for biomedical
applications
Yasushi Takemura, Suko Bagus Trisnanto, and Satoshi Ota*

Division of Electrical and Computer Engineering, Yokohama National University, Yokohama 240-8501, Japan*Department of Electrical and Electronic Engineering, Shizuoka University, Hamamatsu 432-8561, Japan

Magnetic nanoparticles have been used in various biomedical applications. Among these, magnetic particle imaging
and hyperthermia are considered clinically useful diagnostic and therapeutic methods, respectively. An alternating
magnetic field is applied to the magnetic nanoparticles in these methods. The magnetization response of a magnetic
nanoparticle is essential, and the dependence of its field intensity and frequency determines its diagnostic andtherapeutic performance. This article reviews the fundamental issues of the magnetization process and magnetization
relaxation of magnetic nanoparticles and presents our recent experimental results.
Keywords: magnetic nanoparticles, superparamagnetic nanoparticles, magnetization relaxation, Brownian relaxation,
Néel relaxation, hyperthermia, magnetic particle imaging.
1. Introduction

2. Magnetic nanoparticles for biomedical applications

This article introduces the dynamic magnetization
process of magnetic nanoparticles (MNPs) forbiomagnetic applications, which was a research subject of
MSJ Outstanding Research Award 2022.
The main subject in this article is the measurement
and analysis of dynamic magnetization in MNPs bycarrying out alternating current (AC) magnetization
hysteresis and magnetization measurements under apulsed magnetic field. Then, we elucidated the two-stepmagnetization process of the Néel and Brownian
relaxations from these measurements. Although this twostep process has not been conventionally discussed, it isimportant to understand the magnetization properties of
MNPs, particularly for biomedical applications such as
hyperthermia and magnetic particle imaging (MPI).
Hyperthermia is a therapeutic treatment for cancer,
wherein cancer cells are killed at temperatures above
42.5°C while normal cells remain undamaged1). Magnetic
hyperthermia is a proposed treatment that uses selfheating from a magnetic material that is autonomously
heated by its hysteresis and/or relaxation loss under anapplied AC magnetic field2-5). MNPs are promising for use
in hyperthermia, as they are easily delivered into thehuman body through blood vessels. After coating or
conjugating biofunctional materials, MNPs can beselectively delivered to specific tumors or cells.
MNPs collected at the tumor or cancer cells can be used
as "marker" in MPI6-8). The magnetization change of the
MNPs under an applied AC magnetic field is detected bya receiver coil located outside the human body. The
dynamic magnetization process essentially determines
the sensitivity and spatial resolution of imaging9-10).

Iron oxide nanoparticles are widely used in biomedical
applications as they are biocompatible and less toxic11).
They are clinically used as contrast agents in magnetic
resonance imaging (MRI). Particles exhibiting remanent
magnetization and coercive force agglomerate after
applying the magnetic field, causing occlusion of bloodvessels. Therefore, superparamagnetic nanoparticles of
Fe3O4 and γ-Fe2O312-16) are used as contrast agents in
MRI and for clinical testing of hyperthermia17).

Corresponding author:

Yasushi Takemura (e-mail: takemura@ynu.ac.jp).

84

3. Dynamic magnetization in magnetic nanoparticles
3.1 Brownian and Néel relaxations
MNPs with relatively small diameters, which typicallyexhibitsuperparamagnetic
properties,
areconventionally used in biomagnetic applications. In thissection, we discuss the magnetization relaxation of
MNPs with a single-domain structure. MNPs dispersedin solution are widely used owing to their chemical
synthesis and delivery through an injection needle andcatheter into the human body. These particles are
subject to Brownian motion. The magnetic moment ofeach particle is randomly oriented by the thermal energy
under an externally applied magnetic field, Hex=0. The
magnetic moment aligned in the direction of Hex>0 is
relaxed to a random orientation when Hex is turned to be
0. The time constant of this relaxation, the Brownian
relaxation time, τB, is given as18)

𝜏𝜏� �

����
�� �

,

(1)

where η, VH, kB, and T are the dynamic viscosity of the fluid,hydrodynamic volume, Boltzmann’s constant, andabsolute temperature, respectively. There are several
definitions of the diameter of MNPs. The primary andsecondary diameters are the diameters of a single-core
particle and the aggregated primary particles whose
behavior in solution is characterized by the

Journal of the Magnetics Society of Japan Vol.47, No.4, 2023

INDEX

hydrodynamic diameter, respectively. τB is determinedfrom the secondary diameter. τB is sufficiently longcompared to the observation time in the measurement
when the particles are dispersed in a high-viscosity
solution or when the hydrodynamic diameter is large.
Particles with a small diameter in a low-viscosity solution
exhibit superparamagnetic features owing to a short τB.
Superparamagnetic nanoparticles under an applied DC
or AC magnetic field with a frequency f << 1/(2πτB)
exhibit magnetization hysteresis curves with no area,
considering that the magnetic moment associated withthe magnetic easy axis of the nanoparticles follows thechange in the applied magnetic field owing to particle
rotation. In the case of f > 1/(2πτB), the particle rotation
is delayed against the change in the field direction.
The Néel relaxation denotes the rotation of themagnetic moment of the nanoparticles. This relaxation isallowed even when the nanoparticles are physically fixed.
The Néel relaxation time can be described as� �Fig. 1 Calculated Brownian, Néel, and effective
relaxation times of magnetic nanoparticles
depending on their core diameter, dcore21). Spherical
nanoparticles coated with 15–nm layer are dispersed
in water (η = 1.0×10-3 Ns/m2). Anisotropy constant,
Ku = 20 kJ/m3, is used.

(2)𝜏𝜏� � 𝜏𝜏� exp� � � �,�� �

where Ku, VM, and τ0 are the magnetic anisotropy
constant, the volume of the primary particle, and theattempt time, respectively. The details of theserelaxations are introduced in references18-20).
3.2 Effective relaxation time
The magnetization of MNPs dispersed in a liquid isaligned in the direction of the applied magnetic field andaccompanied by both Brownian relaxation and Néel
relaxation. The effective relaxation time τeff has been
widely discussed using the following equation18).

𝜏𝜏��� � 1�1�𝜏𝜏� � 1�𝜏𝜏� �(3)Figure 1 shows an example of the calculated relaxation
times depending on the core diameter dcore of thenanoparticle21). A particle monodispersed in water (η =1.0×10-3 N•s/m2) with a 15 nm thick coating layer was
assumed in this calculation. When dcore < 15 nm, τN < τB.
The effective relaxation time is useful for understanding
the relaxation process and estimating the self-heating
power of MNPs, as discussed in Section 4.3.
4. Measurement of dynamic magnetization in magnetic
nanoparticles
4.1
Linear/nonlinear
responses
indynamic
magnetization
The dynamic magnetization process of MNPs can bemeasured using a detection coil22-24). Figures 2(a) and 2(c)show the waveforms of the applied AC magnetic field H(t)and the magnetization of the MNPs M (t), typicallyobserved from superparamagnetic nanoparticles. If themagnetization rotation cannot follow the change in theapplied AC magnetic field, M (t) delays against H (t),thereby exhibiting a phase delay, as shown in Figs. 2(b)and 2(d). Here, Figs. 2(a)/2(b) and 2(c)/2(d) correspond tothe magnetization processes in the linear and nonlinear

Fig. 2 Waveforms of applied magnetic field H (t),magnetization of MNPs M (t), and magnetization
curves M (t)-H (t) for linear response (a) withoutphase difference and (b) with phase difference, andnonlinear response (c) without phase difference and(d) with phase difference25).
responses of the MNPs, respectively.
Figure 3 shows the DC and AC magnetization curves ofthe MNPs in the liquid and solid states25). A magnetic
field of up to 0.4, 4, and 16 kA/m of DC or AC at 1–100
kHz was applied. The material used in this measurement
was a water-based colloidal solution of γ-Fe2O3/Fe3O4
coated with carboxydextran supplied by Meito Sangyo Co.,
Ltd. The core diameter and hydrodynamic diameter were
21.6 nm and 35.8 nm, respectively. The MNPs wereprepared by magnetic separation of Ferucarbotran, which
is a source material for Resovist. Resovist is a contrast
agent used clinically for magnetic resonance imaging.
Details of the samples and measurements have beenpreviously reported26-28).
The liquid samples exhibited greater magnetization
than the solid samples owing to the magnetization
rotation of Brownian relaxation along with Néel
relaxation25,26). The remanent magnetization andcoercive force were almost zero for the DC magnetization
curves of both the liquid and solid samples, which
demonstrated the superparamagnetic nature of thesamples. The area of the AC magnetization curves

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85

INDEX

Fig. 3 DC and AC magnetization curves for liquid andsolid samples of γ-Fe2O3/Fe3O4 nanoparticles. Magnetic
fields of up to 0.4, 4, and 16 kA/m in DC or AC at 1–100
kHz are applied25).
increased as the field frequency increased. Similarly, themagnetization values in the AC magnetization curves
decreased as the field frequency increased. Thesefrequency dependences can be attributed to the delay inthe magnetization rotation against the change in theapplied magnetic field26). Additionally, we reported
measurements of AC magnetization under a DC bias
magnetic field, which clarified the dynamics of aligned
magnetization10).
4.2 Calculation of specific loss power
In magnetic hyperthermia, the specific loss power(SLP) or specific absorption rate is an essential
parameter, which is determined by measuring the selfheating temperature of the MNPs under an applied AC
magnetic field. Wildeboer et al. suggested the instabilityof this measurement method owing to the temperature
distribution in the samples and other factors29).
We proposed quantifying the SLP of MNPs bymeasuring the AC hysteresis curves30,31). As discussed in
the previous section, even a superparamagnetic magnetic
nanoparticle with no area in the static hysteresis curve
exhibits an area in the AC hysteresis curve, which isequivalent to the magnetization relaxation loss. Figure 4
summarizes the calculation of SLP and intrinsic loss
power (ILP) as well as the AC susceptibility of MNPs
under nonlinear response to the applied AC magnetic
field. SLP was calculated using the imaginary part of theAC susceptibility based on linear response approximation,
as indicated in Case 1 in Fig. 4. The SLP of the MNP
under a nonlinear response was calculated using the areaof the AC hysteresis curve (Case 2 in Fig. 4).
The advantage of the measurement of AC hysteresis
curves is that we can quantify the SLPs of liquid, solid,

86

Fig. 4. Imaginary part of AC susceptibility χ'', specificloss power (SLP), and intrinsic loss power (ILP) ofmagnetic nanoparticles under nonlinear response to
applied AC magnetic field. (a) Waveforms of appliedmagnetic field H (t) and magnetization M (t), (b) AC
hysteresis derived from H (t) and M (t), (c)magnetization assuming linear response M LR(t), and(d) magnetization curve25).
power, intracellular, and possibly other states of the MNPsamples. Conventional temperature measurement using
a sensor probe is not suitable for some of these samples,
especially for solid and intracellular MNP samples31).
Figure 5 shows the microscopic images of the detached
HeLa cells, which were collected and used as intracellular
samples. Figure 6 shows the SLPs of the liquid, solid(fixed), and intracellular MNP samples. The liquidsample exhibited the highest SLP owing to higher
magnetization caused by Brownian relaxation. The
MNPs in the intracellular sample locally aggregated in
the cells, which increased the dipole interaction of the
MNPs and reduced the magnetization rotation of the Néel
relaxation in the intracellular sample, resulting in asmaller SLP than that of the solid sample.
Furthermore, we measured the AC hysteresis curves ofthe MNPs with their oriented easy axes. The SLP of these
MNPs was greater than that of MNPs with non-oriented
easy axes26).
4.3 Two-step relaxation process
The power dissipation by magnetization relaxation of
the MNPs can also be derived as18)�� � ��� 𝜒𝜒� 𝐻𝐻��
𝑓𝑓�������

���������� ��,(4)

where μ0 and χ0 are the permeability of vacuum and static

Journal of the Magnetics Society of Japan Vol.47, No.4, 2023

INDEX

Fig. 5 Detached HeLa cells used for intracellular
sample. (a) Phase contrast, (b) fluorescence view of
microscopic images, and (c) illustration of
intracellular and extracellular MNPs31).

SLP [kW/kg-Fe]

60

LiquidFixed
Cellular

50
40
30
20
10
0

8 kA/m0100

200 300 400 500
Frequency [kHz]600

figure also shows the response of the particles, indicatedby the average angles of the easy axes. This particle
response of Brownian relaxation starts at 10-5 s andrelaxes at 10-3 s.
Two-step relaxation was clearly observed in our
measurements, as shown in Fig. 8 33). The measured M(t)exhibited Néel relaxation followed by Brownian
relaxation. The waveforms of both relaxations agree with
their relaxation times, depending on the diameter
described by Eqs. (1) and (2), respectively. The details of
the calculations and experiments are reported in Refs. 33
and 34. Recently, Bui et al. reported an analysis ofmagnetic susceptibility based on distinguished Brownian
and Néel relaxations35).
4.4 Dynamics of magnetization easy axis
As discussed in the previous section, we observed thetemporal magnetization of the easy axis of MNPs.
Furthermore, we clarified the effect of dipole interactions
in multi-core MNPs on the magnetization response bypulse excitation.
The time evolution of the magnetic moment and easy
axis in an individual magnetic nanoparticle dispersed inFig. 6 Frequency dependence of specific loss powersof liquid, solid (fixed), and intracellular MNP
samples31).
susceptibility, respectively. As discussed in Section 3.2,
the effective relaxation time τeff, shown in Eq. (3) is usefulfor estimating the self-heating power of the MNPs. Eq. (4)shows that the SLP of the MNP is dominantly dependent
on the faster relaxation process of the Brownian and Néel
relaxations.
MNPs with core diameters less than 10 nm exhibited
relaxation times τN < τB. τeff essentially equals τN, and thepower dissipation is dominantly determined by Néel
relaxation, thereby indicating that the SLPs of the liquidand solid samples are equivalent. Nevertheless, we foundthat the SLP of the liquid sample was greater than thatof the solid sample, which agrees with the difference in
the AC hysteresis curves of the liquid and solid samples,as shown in Fig. 325,32). These experimental results cannot
be explained by the effective relaxation time τeff andfurther measurements of pulse excitation have been
initiated.
Figure 7 shows the calculated responses of themagnetization and easy axis of MNPs33). The core andhydrodynamic diameters of dc= 10 nm and dh = 40 nm,
and anisotropy constant of Ku =10 kJ/m3 are summed,
respectively. The upper figure shows the waveform of theapplied pulsed magnetic field H (t), which simulates theactual pulse signal of our experimental setup. The
magnetization M (t) shown in the lower figure
corresponds to H (t) without a time delay, as τN is
sufficiently small. This magnetization response from 10-7
to 10-5 s is responsible for Néel relaxation. The lower

Fig. 7 Calculated magnetization response of magnetic
nanoparticles. (a) Waveform of applied 100-Oe pulsed
magnetic field H (t) close to experimental conditionsand (b) average responses of temporal magnetization
M (t) and field-relative easy-axis angle ψ (t)33).

Fig. 8 Temporal magnetization responses of liquidsamples of γ-Fe2O3 nanoparticles with different core
diameters (13, 6, and 4 nm)33).

Journal of the Magnetics Society of Japan Vol.47, No.4, 2023

87

INDEXa fluid was numerically simulated by the Landau-LifshizGilbert (LLG) equation36,37) as
𝛾𝛾
𝝎𝝎
𝑑𝑑𝑑𝑑
� 𝝎𝝎 � 𝑑𝑑 ��𝑑𝑑 � ����� � �
1 � ��
𝛾𝛾
𝑑𝑑𝑑𝑑

� �𝑑𝑑 � �𝑑𝑑 � ����� �

𝝎𝝎
���,
𝛾𝛾

�5�

where α is the damping parameter (α = 0.1) and γ isestimated as γ = μ0MsVM(1+α2)/(2ατNkBT ). m is themagnetic moment normalized by the saturation magnetic
moment, Ms. Heff is an effective field comprising
excitation field, an anisotropy field, and thermallyfluctuating field. The anisotropy field was estimated as
Han= 2Ku(m·n)n /(μ0Ms). The orientation of the easy axis
is calculated using the unit vector and angular velocity ofthe easy axis, n and ω, respectively, given as: dn/dt = ω ×
n. The random torque due to thermal disturbance isconsidered in ω.
The angle between the magnetization and easy axis ψ
was evaluated for individual particles depending on theanisotropy energy27). ψ was calculated from the vector
product of the unit vector of the magnetization and easy
axis, |m × n|. The original symmetry can be applied tothe easy axis. The averaged value of ψ in Fig. 9 indicatesthat ψ decreased with large anisotropy energy as both Ku
and the core diameter dc increased. The anisotropy energybinds the magnetization to the rotatable easy axis. The
increase in ψ owing to the effect of thermal fluctuation
illustrates the superparamagnetic regime.
The effects of orientation and oscillation on the easy
axis were empirically evaluated under an AC magnetic
field. The AC magnetization curves of the solid sample
subtracted from those of the liquid sample were
evaluated38). Moreover, we prepared the mixture
containing MNPs and epoxy resin cured under AC
magnetic fields with frequencies between 0.2–100 kHz at
an intensity of 8 kA/m39). This approach was used toensure that the easy axis had a fixed orientation whenmeasurements were conducted in the AC magnetic field,
thereby indicating that the coercivities of the AC
magnetization curves in the liquid sample increased for along τB compared to the applied field frequency,
considering the easy axis orientation toward the direction
/4

d = 11 nm

3

K = 12 kJ/m

 [rad]c

The dynamic magnetization process of MNPs isessential for determining various properties ofhyperthermia and MPI, which are major medical
applications of MNPs. The measurements of the staticand dynamic magnetization curves of MNP samples,
including liquid, solid, and intracellular states, conductedin this study clarified the distinguished Brownian and
Néel relaxations depending on the applied magnetic field
intensity and frequency. The Brownian relaxation isaccompanied by particle rotation and can be magneticallymeasured as the response of the magnetization easy axesof MNPs. Furthermore, we observed the dynamics of theeasy axes in the measurements using both the AC andpulsed magnetic fields. These experimental results of our
study
are
significant
forunderstandingthemagnetization dynamics of MNPs, which have not beenpreviously considered.
Acknowledgements The experiments were performed incollaboration with our lab team coauthors in thereferences below. The authors wish to express their
gratitude for the advice and support from Profs Keiji
Enpuku and Takashi Yoshida from Kyushu University.
This study was partially supported by JSPS KAKENHI
JP20H05652, JP20H02163, JP22K14268, JP17K14693,
JP17H03275, and JP15H05764.
1)
2)
3)
4)
5)
6)
7)
8)
9)

/12

8

10 12 143 16 18
K [kJ/m ]
u

9

10

11 12
d [nm]

13cFig. 9 Angle between magnetization and easy axis ψ
depending on anisotropy energy determined byvalues of Ku and dc. Easy axis is rotatable. ψ ism × n|. Statistical
calculated using expression |manalysis is conducted in one cycle of applied field witha time interval of 100 ns (N= 100)27).

88

5. Summary

u

/6

0

of the applied magnetic field effectively increased theanisotropy energy. Conversely, the orientation of the easy
axis decreased significantly for a long τN compared to theapplied field frequency owing to the small magnetic
torque caused by small magnetization.

10)
11)
12)
13)
14)

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Received Feb. 23, 2023; Accepted Mar. 19, 2023.

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Copyright ©2023 by the Magnetics Society of Japan.
This article is licensed under the Creative Commons Attribution International License (CC BY 4.0)
http://creativecommons.org/licenses/by/4.0/

J. Magn. Soc. Jpn., 47, 90-102 (2023)<Review>

First-principles Studies on Spin-dependent Transport of Magnetic
Junctions with Half-metallic Heusler Compounds
Y. Miura*,***Research Center for Magnetic and Spintronic Materials (CMSM), National Institute for Materials Science (NIMS),

1-2-1 Sengen, Tsukuba, Ibaraki 305-0032, Japan**

Center for Spintronics Research Network (CSRN), Graduate School of Engineering Science, Osaka University,

Machikaneyama 1-3, Toyonaka, Osaka 560-8531, Japan

Two types of magnetoresistance (MR), i.e., tunnel magnetoresistance (TMR) and current perpendicular toplane giant magnetoresistance (CPP-GMR), are theoretically discussed for systems with half-metallic (HFM)
Co-based full Heusler compounds. In TMR, the non-collinear spin structure at the Co2MnSi(CMS)/MgO(001)interface that results from thermal spin fluctuations significantly reduced the TMR ratio at room temperature (RT).
Enhancement of the exchange stiffness of CMS/MgO was essential to suppress the reduction in TMR at RT.
Furthermore, it is proposed that inserting of a B2-CoFe layer between CMS and MgO is a promising way to enhance
the interface exchange stiffness constant. In CPP-GMR, the interface spin asymmetry γ in the Valet-Fert model wasessential to enhance GMR at RT, because the temperature dependence of γ in experiments was much larger thanthat of the bulk spin asymmetry β. I showed that the experimental CPP-GMR ratio increases with the decrease in
the theoretical resistance-area product RPA, which is roughly consistent with the RP dependence of γ. This meansthat matching of the conductive channel between HMF and a non-magnetic metallic spacer is a key parameter toenhance γ. These findings will be very important for room temperature spintronics devices applied in future artificial
intelligence hardware.
Key words: magnetoresistance, first-principles calculation, Heusler compound, TMR, CPP-GMR, ballistic transport,
exchange stiffness
1. In troduction
I introduce ”Theoretical Study on Spin-dependent
Transport Properties in Magnetic Junctions” in thisreview paper, which was a research subject of MSJ
Outstanding Research Award 2022.
The
spin-dependent
tunneling
betweentwo
ferromagnetic (FM) electrodes separated by anon-magnetic (NM) layer provides magnetoresistance(MR) that depends on the relative magnetization
directions of the ferromagnetic electrodes.1–3) The effectis applied in magnetoresistive random access memory(MRAM) and ultra-sensitive magnetoresistive sensors,which are essential to realize artificial intelligence (AI)
hardwareandneuromorphic
devicesinthenext-generation information society.4,5) There are two
types of MR devices according to the type ofnonmagnetic
layer,
whicharetunnelingmagnetoresistance (TMR) devices with an insulating
barrier layer, and current-perpendicular-to-plane giant
magnetoresistance (CPP-GMR) devices with a NM
metal spacer. To realize AI-dedicated and neuromorphic
spintronics devices, a large MR ratio and low resistance
are required.
High TMR ratios over 300% at room temperature havebeen realized in magnetic tunnel junctions (MTJs) withsingle-crystalline MgO and bcc-FeCo6–8) from coherent

Corresponding author: Y. Miura(e-mail: MIURA.Yoshio@nims.go.jp)

90tunneling through the Δ1 evanescent state in MgO andthe highly spin-polarized Δ1 band around the Fermi
level in bcc-FeCo9,10). This means that in TMR devices,
the spin dependence of the current can be characterized
by the spin polarization of the Δ1 state of theferromagnetic electrodes at in-plane wave vector k║ = 0
rather than that of the total density of states (DOSs)
around the Fermi level. In MgO-based MTJs, it isdifficult to reduce the resistance while maintaining high
TMR. Reducing the barrier thickness of MTJs decreases
the TMR as well as the resistance, because thetunneling of non-spin-polarized Δ5 and Δ2 states is not
negligible in a MgO layer with a thickness of a few
monolayers. Thus, half-metallic ferromagnets (HMFs),
which are metallic for the majority-spin band andinsulating for the minority-spin band with complete(100%) spin polarization at the Fermi level, will be
important to realize both high TMR and low resistancefor MTJs with few-monolayer MgO thickness.
CPP-GMR devices composed of all-metallic layers havelower resistance than TMR devices, but their MR ratios
are also typically more than an order of magnitude
smaller. This is due to the presence of many scattering
processes in all-metallic systems, because in a metallic
system, not only electrons with k║ = 0 but also thosewith k║ ≠ 0 contribute equally to the current. Thus, thespin-dependent transport in GMR devices can becharacterized by the spin polarization of the total DOSsof the ferromagnetic electrodes rather than the spinpolarization at the specific k║, and HMFs again are

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Table 1 Summary of experimental results on TMR ratio [%] at room temperature (RT) and low temperature (LT)for MTJs with Co-based full Heusler compounds Co2YZ (exact temperatures differ between studies).
Bottom electrode

BarrierUpper electrode

TMR %

TMR %

Year

@ LT

@ RT

[Reference]

Co2(Cr0.6Fe0.4)Al

Al-O

Co2(Cr0.6Fe0.4)Al

26.5

16

200326)

Co2MnAl

Al-O

Co0.5Fe0.5

40

27

200427)

Co2FeAl

Al-O

Co0.75Fe0.25

47.3

200528)

Co2MnSi

Al-O

Co2MnSi

570

67

200629)Co2Fe(Al0.5Si0.5)

Al-O

Co0.75Fe0.25

106

76

200630)Co2(Cr0.6Fe0.4)Al

MgO

Co0.5Fe0.5

240

90

200731)

Co2MnSi

MgO

Co0.5Fe0.5

753

217

200832)

Co2MnSi

MgO

Co2MnSi

700

180

200933)

Co2Fe(Al0.5Si0.5)

MgO

Co2Fe(Al0.5Si0.5)

832

386

200934)

Co2FeAl

MgO

Co2FeAl308

130

200935)

Co2FeAl

MgO

CoFe

700

330

201036)

Co2Mn1.29Si

MgO

Co2Mn1.29Si

1995

354

201237)Co2(Fe0.5Mn0.5)Si

MgO

Co2(Fe0.5Mn0.5)Si

2610

429

201538)

Co2FeAl

MgAl2O4

Co2Fe(Al0.5Si0.5)

616

342

201639)

Co2Mn1.3Si0.84

MgO

Co2Mn1.3Si0.84

2010

335

201640)Co2Fe(Ga0.5Ge0.5)

Cu(In0.8Ga0.2)Se2

Co2Fe(Ga0.5Ge0.5)

100

40

201641)

Co2Fe(Ga0.5Ge0.5)

CuGaSe2

Co2FeGa(0.5Ge0.5)

250

100

201942)

important for obtaining large GMR.
Among the many theoretically predicted HMFs,11–16)
the Co-based full Heusler compounds Co2YZ (Y = Cr,
Mn, Fe, Z = Al, Si, Ga, Ge) are the most promising
candidates for use in spintronics devices because of
their high Curie temperatures above room temperature(RT). A characteristic feature of Co-based full Heusler
compounds is that their electronic structure hardly
changes with respect to the specific atomic disorder,
such as B2-type disorder, where Y and Z atom sites are
randomly occupied.17–19) The robustness of high spinpolarization against the atomic disorder of Co-based
Heusler compounds is important in terms of therelaxation of experimental requirements, because it isexpected that some degree of atomic disorder will occur
during thin-film fabrication. The valence-band
electronic structures of typical halfmetallic Co-based
full Heusler compounds Co2MnSi (CMS) were
investigated by photoelectron spectroscopy to confirm
the temperature dependence of the electronic
structures.20)
Theexperimental
valenceband
photoemission spectra at 30 K were in good agreementwith density functional theory (DFT) calculations atzero temperature, and no distinct temperaturedependence was observed in the experimental valenceband
spectra.
Furthermore,thetemperaturedependence of the spin-polarization of CMS was shown
to be small by spin-resolved hard x-ray photoelectron
spectroscopy.21) Recently, we calculated the temperaturedependence of the bulk electronic structures ofhalf-metallic Co-based Heusler compounds using thedisordered local moment (DLM) method,22) and foundthatthetemperaturedependenceofthespin-polarization of the sp density of states (DOS) of
Co2FeGa0.5Ge0.5 (CFGG) is weaker than that of
CMS.23,24) Furthermore, several new Co-based Heusler
compounds such as Co2MnGa1−xAsx and Co2FeAl1−xSnx
were proposed by the machine learning method withfinite temperature first-principles calculations using theDLM.25)
Table 1 summarizes experimental studies on TMR
ratios at low temperature (LT) and RT for Co-based fullHeusler MTJs26-42). Half-metallic Co2YZ compounds
have been applied in TMR devices with an amorphousalumina barrier26–30) and then in MTJs with a MgObarrier,
and
large
TMR
ratiosweredemonstrated.31–38,40)
Furthermore,newbarriermaterials such as MgAl2O439) and Cu(In1−xGax)Se241,42)
have been applied as the barrier layer in Heusler-based
MTJs. Particularly, MTJs with Mn-rich CMS andCo2(Mn,Fe)αSi with MgO barriers provided huge TMR
exceeding 2000% at very low temperature,38,40)
indicating the potential of the halfmetallic electronic
structures. However, the TMR also rapidly decreases
with increasing temperature.
As is shown in Table 1, experiments on the TMR effectof MTJs with half-metallic Co-based full Heusler
compounds have not been reported after 2019. There are
two reasons for the decrease in experimental studies on
TMR in Heusler-based MTJs. One is the large
temperature dependence of the TMR ratios of MTJs
with half-metallic Co-based full Heusler compounds.

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Table 2 Summary of experimental results on GMR ratio % and ΔRA mΩ· μm2 at room temperature (RT) and low
temperature (LT) for CPP-GMR devices with Co2YZ (exact temperatures differ between studies).
System

GMR % @ LT

GMR % @ RT

Year

(ΔRA mΩ· μm2 )(ΔRA mΩ· μm2 )[Reference]

Co2MnSi/Cr/Co2MnSi(001)

2.4 (19)200649)

Co2MnSi/Cu/Co2MnSi(001)9200850)6.9 (7.4)

200851)

Co2MnSi/Cr/Co2MnSi(001)

5.2 (6.5)

200952)

Co2MnSi/Ag/Co2MnSi(001)28.8 (8.92)

200953)

Co2Fe(Al0.5Si0.5)/Ag/Co2Fe(Al0.5Si0.5)(001)

Co2Fe(Al0.5Si0.5)/Ag/Co2Fe(Al0.5Si0.5)(001)80 (17)34 (8)

201054)

Co2Mn(Ga0.5Sn0.5)/Ag/Co2Mn(Ga0.5Sn0.5)(001)17.2 (6.5)

8.8 (4)201055)

Co2MnSi/Ag/Co2MnSi(001)67.2

36.4 (11.5)

201056)

Co2Fe(Ga0.5Ge0.5)/Ag/Co2Fe(Ga0.5Ge0.5)(001)129.1 (26.4)

41.7 (9.5)

201157)

Co2MnGe/Cu/Co2MnGe(001)9 (6)201158)Co2(Fe0.4Mn0.6)Si/Ag/Co2(Fe0.4Mn0.6)Si(001)74.8

201159)Co2(Fe0.4Mn0.6)Si/Ag/Co2(Fe0.4Mn0.6)Si(001)184

58 (11)

201260)Co2Fe(Ga0.5Ge0.5)/Ag/Co2Fe(Ga0.5Ge0.5)(001)183 (33)

57 (12)

201361)

Co2Fe(Ga0.5Ge0.5)/NiAl/Ag/NiAl /Co2Fe(Ga0.5Ge0.5)(001)285 (78)

82 (31)

201662)

Co2Mn1.45Si0.82/CoFe/Ag/CoFe/Co2Mn1.45Si0.82(001)20.7 (3.1)

201763)Co2(Fe0.4Mn0.6)Si/Ag3Mg/Co2(Fe0.4Mn0.6)Si(001)63 (25)201764)Co2(Fe0.4Mn0.6)Ge/AgSn/Co2(Fe0.4Mn0.6)Ge(001)

25 (7.5)

201865)30

201966)

Co2Fe(Ga0.5Ge0.5)/Ni/Ag/Ni/Co2Fe(Ga0.5Ge0.5)(001)32.5

202167)

CoFe/Co2(Fe0.4Mn0.6)Si/Ag/Co2(Fe0.4Mn0.6)Si/CoFe(001)50 (19.1)

202168)Co2(Fe0.4Mn0.6)Si/Ag3Mg/Co2(Fe0.4Mn0.6)Si(001)

The TMR ratio of Heusler-based MTJs at RT is still
smaller than that of CoFe-based MTJs. Recently, a
breakthrough in the RT TMR of CoFe-based MTJs wasachieved by Scheike et al., where a 631% TMR ratio at
RT and 1143% TMR ratio at LT were observed for
CoFe/MgO/CoFe(001) MTJs.43) To demonstrate thepotential of half-metallic Heusler compounds, it isimportant to achieve a larger TMR ratio at RT than thatof CoFe-based MTJs. The other reason for the decreasein studies is requirement of MTJs with theperpendicularmagnetic
anisotropy(PMA).
In
spin-transfer torque switching of the magnetization
direction in MTJs, PMA is required in order to reduce
the effective anisotropy field of MTJs. Since theCo-based full Heusler compounds show basically cubic
symmetry, the magneto-crystalline anisotropy (MCA) of
Co2YZ is zero. Thus, the magnetic anisotropy of
Co2YZ(001) thin films tends to have an in-plane easy
axis due to the shape anisotropy. Some Mn-based
Heusler compounds such as Mn3Ga and Mn3Ge with
D022 structure have tetragonal structures, showing
perpendicular MCA in the bulk.44–47) However, theexperimental results for the TMR effects of
Mn3Ga/MgO- and Mn3Ge/MgO-based MTJs44,48) are verysmall compared with those of Co2YZ/MgO-based MTJs
because of the large lattice mismatch of Mn3Ga and
Mn3Ge with MgO47) and the non-half-metallic behaviorof the Δ1 states of Mn3Ga.44) Therefore, achieving92

14 (12.4)100

perpendicular MCA in Heusler-based MTJs will be also
a future task.
Table 2 summarizes experimental studies on GMR
ratios and the difference in resistance-area productbetween parallel and antiparallel magnetizations ΔRA
at LT and RT for various CPP-GMR systems with
Co-based full Heusler compounds.49-68) Half-metallic
Co2YZ have also been applied in CPP-GMR devices, andrelatively large GMR ratios have been observed for
Heusler-based magnetic junctions with a Cr spacer,49,52)
Cu spacer,50,58) Ag spacer,51,53–57,59–61) Ag3Mg spacer64,66)
and AgSn spacer.65) Furthermore, insertions of anadditional layer were attempted to enhance thematching of conductive channels between Co-based fullHeusler compounds and NM spacers, such as NiAl
insertion in the CFGG/Ag(001) interface,62) Ni insertionin the CFGG/Ag(001) interface,67) CoFe insertion in the
CMS/Ag(001) interface63) and Co2(Fe0.4Mn0.6)Si insertionin the CoFe/Ag(001) interface,68) which led to anincrease in the CPP-GMR ratios.
In this review, I discuss the spin-dependent transport
properties of TMR and CPP-GMR devices withhalf-metallic Co2YZ based on first-principles electronic
structureandballistictransport
calculations.
Particularly, I focus on the spin-dependent transport ofmagnetic junctions with half-metallic Co2YZ. First, I
discuss the origin of the temperature dependence of the
TMR ratios in MTJs. The spin-dependent conductance

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INDEXof MTJs with CMS (or Fe) and MgO was investigatedbased on first-principles calculations in a noncollinear
spin system. Noncollinear magnetic structures areformed as a result of spin fluctuation at finite
temperatures. I focus on the spin-flip scattering ofconducting electrons caused by the noncollinearity of
local spin moments in various interfacial layers, and I
discuss the electronic states at the interfaces that
contribute to the spin-flip conductance. Our theoreticalanalysis confirmed the crucial contribution of thespin-flip process at the interface, which leads to asignificant reduction in the MR ratio at RT. Then, I
discuss the interface spin-asymmetry in CPP-GMR
devices. I argue that the matching of the Fermi surface
projected to the two-dimensional Brillouin zone inin-plane wave vector k║ between the CMS and NM
spacers is important to enhance the interface spin
asymmetry. Furthermore, I clarify the correlation
between experimental CPP-GMR ratios and thetheoreticalinterfaceresistanceinparallelmagnetization in CPP-GMR.
2. Computational Method
I performed first-principles calculations for supercells
consisting of Co-based Heusler compounds Co2YZ (Y =Mn or Fe, Z = Si, Ga or Ge) and various nonmagnetic (NM) layers X such as X = MgO, Ag, Cr, V, Al
and Au using the DFT within the generalized-gradientapproximation for the exchange-correlation energy.69) In
order to facilitate the optimization of atomic positions,which is important for determining the interface
structure, I adopted plane-wave basis sets along withthe ultra-soft pseudopotential method by using thequantum code ESPRESSO.70) The number of k points istaken to be 15×15×1 for all cases, and MethfesselPaxton smearing with a broadening parameter of 0.01
Ry is used. The cutoff energy for the wavefunction andcharge density is set to 30 Ry and 300 Ry, respectively.
These values are large enough to deal with all theelements considered here within the ultra-soft
pseudopotential method. Co2YZ/X/Co2YZ(001) magnetic
junctions with Co (YZ ) termination were constructed ina multilayer structure containing seventeen (fifteen)
atomic layers of Co2YZ and seven or nine atomic layersof NM. The in-plane lattice parameter of the supercell isfixed to that of Co2YZ. These values correspond to a0/√2,
where a0 is the lattice constant of the bulk Co2MnSi(5.65 Å). Since the lattice constant of the NM layer X isdifferent from that of Co2YZ, the lattice mismatches
between Co2YZ and X on the 45◦ in-plane rotation at the(001) face are considered, leading to tetragonal
distortion in the NM layer (X ).
For transport calculations, I calculated the ballistic
conductance of the magnetic junctions based on theLandauer formula.71) I considered an open quantum
system consisting of a scattering region corresponding
to NM spacer X and a junction with Co2YZ attached toleft and right semi-infinite electrodes corresponding to

Fig. 1 Local density of states (LDOS) at Fermi level(EF) projected onto each atomic sphere as a functionof the distance from interface for Co2MnSi(CMS)/MgO(001) with MnSi termination. Positive(negative) sign of y-axis indicates majority-spin(minority-spin) LDOS. Schematic figures of supercellof CMS/MgO/CMS(001) MTJ are shown above theLDOS. (b) The solid lines show LDOS of Mn d at
MnSi-terminated CMS/MgO(001) interface as afunction of energy relative to EF. LDOS in bulk
(electrode) region is also shown by dashed line as areference. ref.[74]bulk Co2YZ. The transmittance can be obtained bysolving the scattering equation with infinite boundary
conditions, in which the wavefunction of the scattering
region and its derivative are connected to the Blochstates of each electrode.72) The potential in the
scattering equation can be obtained from self-consistent
filed electronic structure calculations for the supercell
containing a left electrode and a scattering region. It
was confirmed that five atomic layers of Co2YZ between
the right edge of the electrode region and the left-handside of the Co2YZ/X interface are sufficient to represent
the shape of the local potential of bulk Co2YZ in theelectrode region.
Since our system is repeated periodically in the xy
plane and propagating states can be assigned by anin-plane wave vector k║ = (kx, ky) index, different k║ do
not mix and can be treated separately. Furthermore,
our approach neglects the spin-orbit interaction andnoncollinear spin configuration. Thus, I solved
scattering equations for some fixed k║ and spin index
using Choi and Ihm’s method.72, 73)
3. Spin-dependent transport in TMR devices
3. 1 Interf ace el ectronic structure s
Figure 1(a) shows the majority- and minority-spin
local density of states (LDOS) at the Fermi levelprojected onto each atomic sphere as a function of the
distance from the Co2MnSi(CMS)/MgO(001) junction.74)
It is found that in the case of MnSi termination,interface states appear in the minority-spin state at the
Fermi level, reducing the half-metallicity of CMS.
Similar results have been obtained in the Co
termination
ofthe
CMS/MgO(001)junction.75)
Examining the electronic structure at the interface in

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Fig. 2 (a) Schematic figure of CMS/MgO/CMS MTJs
with MnSi termination and local spin moments foreach layer, with a noncollinear magnetic structure
on both sides of junction. (b) Parallel andantiparallel conductance of CMS/MgO/CMS MTJ as
a function of the angle of interfacial local spin
moments θ. (c) In-plane wave-vector (kk║) dependenceof antiparallel conductance of CMS/MgO/CMS MTJ
with θ = 15◦ for MgO thickness ~ 2.0 nm (nine atomic
layers of MgO). ref. [81]more detail, Fig. 1(b) presents the majority- andminority-spin LDOS of each atom and atomic orbital in
the MnSi-terminated CMS/MgO(001). The LDOS in thebulk (electrode) region is also shown as a reference. In
Fig. 1(b), it is found that the spin moment of theinterfacial Mn (4.06 μB) is larger than those of the bulk
CMS (3.31 μB) due to the charge transfer from theminority-spin to the majority-spin states. I consideredthat the relaxation of the atomic positions and the
reduced symmetry at the interface cause chargetransfer from the minority-spin to the majority-spin 3d
states owing to the localization effect of 3d electrons.
Furthermore, in Fig. 1(b), minority-spin states areobserved around the Fermi level in the LDOS of theinterfacial Mn and Si atoms. The spin polarizations ofinterface Mn and Si are -0.4 and 0.01, respectively. At
the interface, the Mn atom loses half of its first nearest
neighbor Co atoms, and non-bonding Mn d states(possibly dyz, dzx and d3z2−r2) can appear around the
Fermi level. Since the Mn d3z2−r2 orbital hybridizes with
the O pz orbital at the interface, the LDOS of theinterfacial Mn dγ states maintain a half-metallic
character. Contrary to this, the interfacial Mn dεorbitals (dyz and dzx) become nonbonding in the O-top
configuration, reducing the spin polarization at the
MnSi termination. Mavropoulos, et al. suggested thatthe interface states that appear in the minority-spin gap
at the junctions of MTJs can also contribute to thetunneling conductance in anti-parallel magnetization,
through spin mixing processes such as magnon
excitations and inelastic scattering at RT.76-78)
3.2 Spin-flip scattering at interfaces
Since the CMS/MgO(001) interface is not half-metallic

94

Fig. 3 Schematic images of LDOS for interface Co or
Mn atoms of CMS in (a) collinear spin system (θ = 0)
and (b) noncollinear spin system (θ ≠ 0), respectively.
Gray areas and cross-hatched black areas indicate
the interface d-states and interface s-states,
respectively. ref. [81]due to the appearance of non-bonding states in theminority-spin states around the Fermi level, thespin-flip scattering can be enhanced at finite
temperature through the interface states as a result of
the thermal fluctuation of magnetic spin moments.79)
Thus, the effects of thermal fluctuation and thenoncollinear magnetic structure at the interface of MTJ
on the spin-dependent transport are considered. The
potential for a noncollinear-spin system was obtained byrotating the density matrix of a collinear-spin systemwith a spin-1/2 rotation matrix. According to Kübler’s
formulation,79,80) off-diagonal elements of the effective
potential that provide spin-mixing in the ballistic
conductance are given by(δExc/δn↑ – δExc/δn↓)(sinθ cosφ ± i sinθ sinφ)/2, (1)where δExc/δns (s =↑, ↓) is the exchange and correlation
potential in a collinear-spin system and θ and φ are thepolar and azimuthal angles of a local spin moment withrespect to the global spin-quantum axis, respectively.
Since our calculations neglected spin-orbit interaction,
the azimuthal angle φ did not affect the calculation
results and was set to zero. The off-diagonal part of thelocal potential expressed by equation (1) is given at
real-space positions of the supercell within each atomic
sphere of interfacial atoms having a noncollinear spin
moment.
Fig. 2 (a) shows the model system used for
CMS/MgO/CMS MTJs with MnSi termination in theanti-parallel magnetization, where the interface Mn and
sub-interface Co spin moments on both sides of thejunction were canted by an angle θ in order to provide
interfacial spin-flip scattering.81) Figure 2(b) shows the
conductance of a CMS/MgO/CMS MTJ with MnSi
termination in parallel or anti-parallel magnetization as
a function of the angle of the interface spin moments.
zero conductance was obtained at θ = 0◦ for anti-parallel
magnetization because of the half-metallic character of
CMS. On the other hand, the anti-parallel conductanceincreased with increasing θ, while the parallel
conductance decreased. This behavior can be attributed
to spin-flip scattering because of the noncollinear
interfacial magnetic structures. Fig. 2(c) shows thek║) dependence of the tunnelingin-plane wave-vector (kconductance of the MTJ in anti-parallel magnetization
with the interfacial Mn spin moment θ = 5◦. It was
already shown in ref. [74,75] that bulk CMS has a Δ1band at the Fermi level in the majority-spin states, andJournal of the Magnetics Society of Japan Vol.47, No.4, 2023

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Fig. 4 Logarithmic plots of TMR ratios as a functionof angle of local spin moment θ for noncollinear
magnetic structures of various interfacial layers in
CMS/MgO/CMS MTJs and Fe/MgO/Fe MTJs. ref.
[81]
thek║-dependenceoftheconductanceof
CMS/MgO/CMS MTJs in parallel magnetization has abroad peak at k║ = (0,0) because of the slow decay of Δ1states in the MgO barrier.9) As can be seen in Fig. 2(c),the k║-dependence of the conductance in anti-parallel
magnetization also shows a broad peak at k║ = (0,0),
indicating that the spin-flip conductance is dominatedby the Δ1 channel of the conducting electrons.
Fig. 3 shows schematic images of the LDOS of interface
Mn and sub-interface Co atoms in collinear spin (θ = 0◦)
and noncollinear spin (θ ≠ 0◦) cases.81) In the case of acollinear spin system, the CMS/MgO interface is not
half-metallic and has interface states in thehalf-metallic gap of minority-spin states originatingfrom the non-bonding Mn d orbital (see also Fig. 3 in ref.
[75]). Then, the noncollinear spin moments of interface
Mn and Co generate spin-mixing in the LDOS of
CMS/MgO/CMS(001). At the Fermi level, as shown in
Fig. 3(b), both bulk s-states and interfacial Mn d-states
are projected on the majority-spin and minority-spinstates of the global spin-quantum axis, providing
spin-flip scattering of the Ballistic conductance. The
broad peak at k║ = (0,0) in Fig. 3(c) indicates that the
projected minority-spin Δ1 states mainly contribute to
the conductance in anti-parallel magnetization. Thismeans that the contribution of the interfacial d-statesthat appeared at the MnSi termination of CMS/MgO
junctions in the collinear-spin system (cross-hatchedblack areas in Fig. 3(a) and (b)) was rather small
compared to that of the s-states caused by thenoncollinearity of interfacial Mn and Co spin moments(light-gray areas in Fig. 3(b)). Since the interface states
were mainly composed of dxy and dx2−y2 orbitals ofinterfacial Mn and Co atoms, they show fast decay in
the MgO barrier.
3.3 Effects of noncollinear magnetism on TMR
To examine the interfacial structure dependence ofthe spin-flip conductance, Fig. 4 shows logarithmic plotsof TMR ratios as a function of the angle of the local spin
moment θ in various interfacial layers of CMS/MgO/
CMS. First, I can confirm that the TMR ratios of the

MTJs decreased with increasing θ due to the spin-flip
conductance in the interfacial region. In particular, theTMR ratios for CMS/MgO/CMS MTJs with noncollinear
first and second interface Co spin moments had values
similar to that of Fe/MgO/Fe MTJs for θ > 5◦. This
indicates that the advantage of half-metallic electrodes
is valid only for small θ if the noncollinearity arises atinterfacial Co spin moments. On the other hand, thedecrease in the TMR ratio with increasing θ was rather
gradual for MTJs with noncollinearity in the firstinterface Mn spin moment at the MnSi termination andthe third interface Co spin moment, compared to that in
the first and second Co layers, indicating that the
spin-flip conductance was suppressed at the interfacial
MnSi-layers and that spin-flip scattering mainly
occurred in the first and second Co layers. Since the Siatom is nonmagnetic, the off-diagonal part of theeffective potential expressed by (δExc/δn↑ – δExc/δn↓) was
rather small, which led to a suppression of the spin-flip
probability at the MnSi-layer. In the calculations, theangle dependence of the size of the Co and Mn spin
moments was neglected. This is a reasonableapproximation for Mn spin moments in view of theirlocalized
characterinbulk
CMS82,83)
and
MnSi-terminated interfaces.84) For Co-terminatedinterfaces, the strong hybridization between Co and O
atoms can cause angular dependence for the interfacial
Co spin moments. As discussed for Ni spin moments in
NiMnSb,85) longitudinal fluctuations will increase thelength of the local spin moments with increasing angle.
This will enhance spin-flip scattering in interfacial
regions, resulting in further decrease in the TMR ratio.
3.4 Exchange stiffness at interfaces
To estimate the exchange stiffness of the interfacial
spin moments, The increase in the one-electron band
energy E(θ) relative to the collinear-spin system (θ = 0◦)
was calculated. Fig. 5(a) shows E(θ) as a function of theangle of local moments θ for various interfacial layers in
CMS/MgO(001) and Fe/MgO(001) junctions.81) Then, theresults were fitted using E(θ) = B (1–cosθ). Here, B is
the inter-atomic-layer exchange stiffness constant; thevalue in Table 3 for each layer in the interfacial andbulk regions is shown in Table 3. This estimation
corresponds to the magnetic force theorem method.86,87)
It was confirmed that the increase in the band energy
as a function of the canting angle shown in Fig. 5(a) can
be fitted by ~ θ2 up to θ = 30◦. This means that the error
in the estimation of the exchange stiffness constant by
the magnetic force theorem is very small in the present
system.88) First, it can be found that the exchange
stiffness of the interfacial Co layer at the Co
termination was much smaller than that of theinterfacial MnSi-layer at the MnSi termination and thatof bulk CMS. These results are consistent with theresults of recent first-principles calculations of theexchange constant of CMS/MgO(001).89)
Furthermore, the exchange stiffness of the

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Fig. 5 (a) Increase in band energy relative to that ofcollinear-spin system E(θ) as a function of angle oflocal spin moments θ for first-layer Co spin momentat Co termination, first-layer Mn spin moment andsecond-layer Co spin moment of CMS/MgO(001), andfirst-layer Fe spin moment of Fe/MgO(001)junctions. ref. [81] (b) Temperature dependence ofTMR
ratiosof
CMS/MgO/CMS(001)andFe/MgO/Fe(001) calculated by Eq. (2) including
noncollinear spin structure of various spin moments.
sub-interfacial Co-layer at the MnSi termination was
smaller than that of the interfacial MnSi-layer. Thismeans that at the MnSi termination, the sub-interfacial
Co spin moments fluctuate more easily than interfacial
Mn spin moments. On the other hand, a very highexchange stiffness was found for the interfacial Fe-layer
at Fe/MgO junctions compared to those of CMS/MgO
junctions, indicating the robustness of interfacial Fe
spin moments against thermal fluctuation. One possible
reason for this behavior of the exchange stiffness ininterfacial regions compared to that of bulk CMS isrelated to the change in the interfacial spin moments.
As is discussed in ref. [75,84] the majority-spin chargeof interfacial Co atoms transfers to the MgO side
because of the strong bonding between Co and O atoms.
On the other hand, the interfacial Mn spin moments of
the CMS/MgO junction74,84) and interfacial Fe spin
moments of the Fe/MgO junction9,81) increase incomparison with those of the bulk because of thelocalization effect (and band-narrowing effect) of the
non-bonding d-orbitals in the interfacial regions. Since
E(θ) can be characterized by the off-diagonal elementsof the local potential expressed by equation (1), thedecrease (increase) of local spin moments reduced(enhanced) the off-diagonal terms, leading to the low(high) exchange stiffness.
3.5 Temperature dependence of TMR
Finally, I discuss the effect of interfacial spin-flip
scattering on the TMR ratios at finite temperatures. To
estimate the TMR ratio at a finite temperature, theBoltzmann average of the tunneling conductance wascalculated using the following equation,
GP(AP)(θ) = ∫ gP(AP)(θ) exp(–2E(θ) / kBT ) sinθ dθ/ ∫ exp(–2E(θ) / kBT ) sinθ dθ,(2)where gP(AP)(θ) is the θ-dependence of the tunnelingconductance in parallel (P) and anti-parallel (AP)96

magnetization, as shown in Fig. 2(b). E(θ) is theincrease in the band energy caused by thenoncollinearity of the local spin moments at eachinterfacial layer, as discussed in the previous paragraph.
The factor of 2 for E(θ) indicates contribution from bothsides of the MTJs.
Fig. 5(b) shows the calculated temperature dependenceof the TMR ratio for the MTJs of CMS/MgO/CMS and
Fe/MgO/Fe MTJs with 2 nm MgO thickness. As can beseen here, the reduction in the TMR ratios of
CMS/MgO/CMS MTJs with the 1st layer Co spin
fluctuation at Co termination and the 2nd layer Co spin
fluctuation at MnSi termination are much faster thanthat of Fe/MgO/Fe MTJs with 1st layer Fe spin
fluctuation. This means that the interfacial spin-flip
scattering significantly reduces the TMR ratio at RT.
This result qualitatively agrees with the results of thetemperature dependence of the TMR ratio. The
temperature dependence of the TMR ratios of
CMS/MgO/CMS MTJs with the 1st layer Mn spin
fluctuation at the MnSi termination is also significant,but the TMR ratio maintains a large value at RT,
indicating that the large exchange stiffness constant at
the interface improves the TMR ratio at RT. The
tunneling conductance evaluated at finite temperatureusing equation (2) is 700% at RT for CMS/MgO/CMS
MTJs with the thermal fluctuation of the first layer Co
spin moment at the Co termination, and 1500% at RTwith the thermal fluctuation of the 2nd Co spin momentat the MnSi termination. These TMR ratios are smaller
than the TMR ratio of 2500% at 300 K for Fe/MgO/Fe
MTJs with thermal fluctuation of the 1st layer Fe spin
moment.
From these results, I can conclude that theexperimentally observed low TMR ratio of the MTJs at
RT can be attributed to the spin-flip conductance causedby thermal fluctuation of the interfacial spin moments.
Therefore, to suppress the reduction of the TMR ratios
at finite temperature in CMS/MgO/CMS MTJs, theexchange stiffness of Co spin moments at the
CMS/MgO(001) interface must be enhanced. In
estimating the thermal average of the tunnelingconductance, E(θ) was treated as the thermal excitationenergy of the local spin moments per in-plane unit cellarea, which corresponds to the replacement of various
Table 3 Inter-layer exchange stiffness constant B
meV/u.c.a. fitted to increase in band energies
E(θ)=B(1–cosθ) due to noncollinearity of local spin
moments for CMS/MgO(001) and Fe/MgO(001)junctions. 1st and 2nd indicate first and second layer
at the interface with MgO, respectively. u.c.a. isunit-cell area ~32 Å2. Ref.[81]B meV/u.c.a.

Co1st

Bulk (CMS or Fe)

414

414

565

600

MgO interface

145

347

529

753

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Co2nd

Mn1st

Fe1st

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MgO, CFS and CFA are better than CMS and CMA. It
was considered that the behavior of the exchange
stiffness in the interfacial region is related to the
behavior of the interfacial spin moments, because theexchange stiffness constant is proportional to the squareof the local spin moments. In fact, as can be seen here,
the behavior of the interfacial Co spin moments is
consistent with the behavior of the interfacial exchange
stiffness constant. This means that the enhancement of
the interfacial Co spin moment is effective to obtain alarge exchange stiffness constant and suppress thethermal fluctuation of Co spin moments at the MgOjunction.
Fig. 6 (a) Exchange stiffness constant B of Co atom
at Co termination of various MgO interfaces with
Co-based Heusler compounds and B2-CoFe.
Estimation of exchange stiffness constant B is sameas in Fig. 5(a). (b) Interfacial Co spin moments at Co
terminations of various MgO interfaces with
Co-based Heusler compounds and B2-CoFe.
magnetic excitation modes at interfacial regions by asingle excitation mode of interfacial spin moments givenby the in-plane unit cell E(θ). If other magnon excitation
modes are considered, the temperature dependence of
TMR shown in Fig. 5(b) will change. However, theinclusion of the other excitation modes in equation (2)will lead to a further decrease in the TMR ratio at RT,
and the chemical trend of the exchange stiffness at theinterface has little dependence on the excitation modes.
Therefore, our conclusion that the significant reductionof the TMR ratio of CMS/MgO/CMS MTJs at RT can be
attributed to the interfacial spin-flip conductance does
not change with a more accurate estimation of thethermally averaged tunneling conductance.
3.6 Enhancement of interface exchange stiffness
It was concluded that the reduction in the TMR ratioin CMS/MgO/CMS MTJs at RT can be attributed tospin-flip scattering in the interfacial region caused bythermal fluctuation of interfacial and sub-interfacial Co
layers, and to suppress reduction in the TMR ratio at
RT, it is important to enhance the exchange stiffness of
Co layers at CMS/MgO junctions. Thus, I calculated theexchange stiffness constant at the interface of MgO for
the other Heusler compounds and B2-CoFe. Fig. 6
shows a bar graph of the inter-atomic layer exchange
stiffness constant at each interface. As shown in Fig. 6,very large exchange stiffness constants were obtained
for the Co-terminated B2-CoFe/MgO interface,indicating that the B2-CoFe/MgO interface is very
robust against thermal fluctuation.
Furthermore, the exchange stiffness of the
Co-terminated Co2FeSi(CFS)/MgO and Co2FeAl(CFA)/
MgO interfaces is larger than that of CMS/MgO and
Co2MnAl(CMA)/MgO interfaces. Thus, in order tosuppress the thermal fluctuation at the interface with

3.7 New physical property for temperature dependenceof TMR
Recently, a new physical property characterizing thetemperature dependence of TMR in MTJs was proposedin ref. [90] It was found that the intra-atomic s−dexchange coupling Jsd at the interface was also a key
parameter in the reduction of TMR at RT. Masuda
described the temperature dependent spin-flip
Hamiltonian including Jsd at the interface Fe of
Fe/MgO/Fe(001) MTJs by the coherent potential
approximation of various magnetization directions
according to the temperature dependence of themagnetization up to the Curie temperature. A smaller
Jsd can disconnect the coupling between conductive selectrons and localized d electrons, leading tosuppression of the spin-flip scattering at the interface.
Therefore, ferromagnetic materials with smaller Jsd will
be preferable to obtain larger TMR at RT. This new
physical parameter Jsd will also be important for
improving the large temperature dependence of the
TMR of Heusler based-MTJs.
4. Spin-dependent transport in CPP-GMR devices
4.1 Valet-Fert model
According to Valet and Fert’s two-current model,91)
the resistance change-area product between parallel
and antiparallel magnetization congurations (∆RA =RAPA – RPA) can be expressed by two intrinsic factors in
spin-dependent electron scattering. They are the bulk
spin-asymmetry coefficient (β) in ferromagnetic (FM)layers and the interfacial spin-asymmetry coefficient (γ),
which are included in the following equation,∆RA = (β ρ*F + 2 γ ρ*N r*b)/( ρ*F tF + ρ*N tN + 2 r*b) (3)where ρ*F and ρ*N are the resistivity of theferromagnetic electrode and the non-magnetic (NM)spacer layer in the bulk, and the tF and tN are thethickness of the FM and NM layers, respectively. The
r*b is the spin-independent interface resistance. The β isenhanced by using the HMF in the FM layer, while
enhancement of the γ is accomplished by reduction of
the interface resistance RFM/NM through the choice of
non-ferromagnetic (NM) spacers. Here, I mainly discuss
the γ in HFM/NM interface, because the temperaturedependence of is much larger than that of the bulk spin

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Fig. 7 (a) Bar graph comparing transmittance of
CMS/X/CMS(001) for X = Au, Ag, Al, V and Cr with
MnSi and Co termination. (b) LDOS of interfacial
Co-d at Co termination and interfacial Mn-d at MnSi
termination in CMS/Ag/CMS(001), together withtransmittance averaged over the whole k║ region asfunction of energy relative to Fermi energy. ref. [92].
asymmetry β.
The γ is expressed by the majority-spin resistance (RP↑)
and minority-spin interface resistance (RP↓) in theparallel magnetization conguration as follows,γ = (RP↓ – RP↑)/(RP↓ + RP↑)
(4)↓
The RP at the HMF/NM interface is determined by theinterface state-mediated spin-ip scattering, as
discussed in the previous section, because there are nostates around the Fermi level of HMF minority-spinstates in the bulk. In HMF/NM junctions, there aremany scattering processes, making them complicatedcompared with HMF/insulator junctions such as
Heusler/MgO. This results in a nite value for RP↓ in the
HMF/NM junctions, which will be difficult to control
experimentally. On the other hand, the RP↑ will be
determined by the matching of the conductive channel
between the majority-spin states of HMF and NM. Thus,in CPP-GMR devices with HMFs, matching of the
majority-spin band dispersions with the NM spacer isimportant to reduce the RP↑ of HMF/NM interfaces. As
shown in the inset of Fig. 7(a), γ will rapidly increase
with decreasing RP↑ under xed RP↓. This means thatthe choice of NM spacer layer is very important toenhance the CPP-GMR with HFM Heusler compounds.
4.2 Comparison of the transmittance for CMS/X/CMSAs discussed in ref., [56] the transport properties
obtained from the Landauer formula do not give the real
conductance and resistance for a three-dimensional
metallic multilayer. However, our aim in this paper is
not to obtain the quantitatively correct conductance andresistance of HFM/NM/HFM junctions, but to clarify thedifferences in the conductance and resistance thorough
HFM/NM junctions depending on the NM spacer andthe interfacial termination. If the electrode region(ferromagnetic layer) consists of Co2MnSi (CMS) for allcases, the difference in resistance between HFM/NM/
HMF and HFM/NM’/HFM junctions indicates thedifference in the interfacial resistance between the98

HFM/NM and HFM/NM’ junctions, which can originate
from electron scattering due to changes in the local
potential and band structures at the interfacial region.
Furthermore, a completely epitaxial multi-layer was
assumed, where the crystal momentum parallel to thelayer (or k║) is conserved because of thetwo-dimensional periodicity of the system, and thenumber of conductive channels perpendicular to theplane is less than about ve or six per k║. Therefore, theballistic transport calculations from the Landauer
formula can be applied to evaluate the difference in theinterfacial resistance depending on the band structuresof the materials on both sides of the interface. This
point has already been confirmed in our previous workin ref. [56] where the difference in the resistance-area
products in the ballistic transport calculation between
CMS/Cr/CMS(001) and CMS/Ag/CMS(001) is roughly
comparable to that obtained experimentally. It isconsidered that this justies the use of the Landauer
formula for the investigation of the interfacial
resistance of all metallic multilayers depending on the
non-ferromagnetic
spacerandtheinterfacial
termination.
Figure 7 shows the majority-spin resistance-area
product of CMS/X/CMS(001) with MnSi termination andCo termination for NM spacer X = fcc-Au, fcc-Ag, fcc-Al,
bcc-V, and anti-ferromagnetic bcc-Cr in the parallel
magnetization conguration.92) First, Fig. 7 shows thatthe majority-spin resistance-area product RP↑A of thejunctions with X = Au, Ag, Al, and V is about 3~5mΩµm2, which corresponds to a conductance of 0.6~1.0
G0, where G0 = e2/h is the ballistic conductance without
scattering in the Landauer formula. On the other hand,the junctions with anti-ferromagnetic bcc-Cr spacer areabout 13~16 mΩµm2, which is 3~5 larger than thatwith the other spacer. These results qualitatively agreewith recent experimental results on CPP-GMR devices
incorporating epitaxial CMS/Ag/CMS and CMS/Cr/CMS,
where a smaller resistance-area product has beenobtained for the CMS/Ag(001) interface than for
CMS/Cr(001).
The other feature of the transmittance of
CMS/X/CMS(001)
shown
in
Fig.
7
is
the
interface-structure dependence, i.e., the resistance-area
product with Co termination is larger than that with
MnSi termination except for the anti-ferromagnetic
bcc-Cr spacer. Analyzing the k║-dependence of the
majority-spin transmittance at E = EF for CMS/X/CMS
with Co and MnSi termination, I found that thedifference in transmittance between the twoterminations is significant at kx ≠ 0, especially for X =Ag, Au, Al and V. This means that the transmittance in
the
whole
k║
regioncontributes
totheinterface-structure dependence. To understand this, I
show in Fig. 7(b) the local density of states (LDOS) ofinterfacial Co-d at the Co-terminated interface andinterfacial Mn-3d at the MnSi-terminated interface in
CMS/Ag(001), together with the transmittance averaged

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Fig. 8 Majority-spin conductance in parallel
magnetization configuration calculated for (a)CMS/Ag/CMS and (b) CMS/Cr/CMS as function of k║= (kx, ky). Fermi surfaces in Brillouin zone
corresponding to tetragonal unit cell of (c) L21-CMS,(d) fcc-Ag, and (e) anti-ferromagnetic (AFM) bcc-Cr
plotted by XCRYSDEN.93) ref.[56]over the whole k║ region as a function of the energy
relative to the Fermi energy. It is evident that thetransmittance increases with the decrease in the dcomponent of the LDOS of interfacial atoms, indicatingthat the interfacial d-orbitals act as a scatterer ofelectrons. Furthermore, I found that the LDOS of Co-dat the Co termination shows large components at the
Fermi level compared with those of Mn at the MnSi
termination. The large d-components at the interfacial
regions cause additional reection of propagating
electrons, leading to the large interfacial resistance inmetallic multilayer. These features can be observed also
in the LDOS of CMS/Au, CMS/Al and CMS/V interfaces.
4.3 Fermi surface matching at HFM/NM interface
Figures 8(a) and (b) show the k║-dependence of the
majority-spin conductance in the parallel magnetizationconguration of CMS/Ag/CMS and CMS/Cr/CMS. It isclearly seen that the conducting channels of
CMS/Cr/CMS are restricted to a small region around k║= (0,0). On the other hand, highly conducting channels
spread over almost the entire region in the k║ plane for
CMS/Ag/CMS. The highly conducting region in the k║plane can be understood qualitatively by considering thematching of the Fermi surface over the k║-plane
between CMS and Ag.
Figures 8(c)-(e) show the Fermi surfaces in the
Brillouin zones of L21-CMS, fcc-Ag, and AFM bcc-Cr
with a tetragonal unit cell. A large overlapping area of
the Fermi surface can be seen on the k║-plane between
CMS and Ag, resulting in the small resistance-area
product (2RCMS/AgA = 3.21 mΩ·µm2) for CMS/Ag/CMS,
while the mismatch of the Fermi surface between CMS
and Cr causes the large resistance-area productFig. 9 Correlation between experimental CPP-GMR
ratios at room temperature vs. theoreticalresistance-area product RP for various CPP-GMR
devices in experiments. Broken line indicatesinterface spin asymmetry γ as function ofmajority-spin interface resistance in parallel
magnetization RP↑.
(2RCMS/CrA = 16.1 mΩ·µm2) of CMS/Cr/CMS. Although
no conductance (innite resistance) is expected in theminority-spin channel in ideal half-metals, a nite
resistance-area product could appear in theminority-spin channel in real half-metals owing to suchreasons such as atomic disorder, thermal uctuation ofmagnetic moments, spin-orbit coupling, and so on. The
minority-spin resistance-area product causes a
reduction in both β and γ. Thus, one can expect a larger
value of γ for CMS/Ag/CMS compared to CMS/Cr/CMS,
since the majority-spin resistance-area product of
CMS/Ag/CMS is much smaller than that of
CMS/Cr/CMS.
Experimentally, the CMS/Ag/CMS and CMS/Cr/CMS
junctions with the same annealing temperature (350◦C)and exactly the same stacking structure except for the
spacer layer showed RA of 51.4 and 66.9 mΩ·µm2,
respectively.56) Here, the difference of RA (~ 15.5mΩ·µm2) between them is mainly caused by thedifference in interface resistances, i.e., RCMS/AgA andRCMS/CrA, because the contribution of the bulk resistancein Ag and Cr spacers is negligibly small. Although theexperimental RA is much higher than the calculated
2RCMS/NMA (NM = Ag or Cr) since it includes all ofresistances in the CPP-pillar, the difference in RA, i.e.,
2RCMS/CrA − 2RCMS/AgA of 15.5 mΩ·µm2 is roughly
comparable to the calculated one (~ 12.9 mΩ·µm2). Thisagreement is evidence of a small interface resistanceand large γ between CMS and Ag due to good
Fermi-surface matching, as predicted in our
calculations.
4.4
Correlation
betweentheoretical
RP andexperi mental CPP-GMR
Fig. 9 shows the experimental CPP-GMR in various
systems as a function of the calculated majority-spin
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experimental CPP-GMR ratio increases with thedecrease in the theoretical RPA, which is roughly
consistent with the RP↑ dependence of the interface spin
asymmetry γ as shown in the inset of Fig. 7. This meansthat the enhancement of γ by the matching of the
conductive channel between HFM and NM throughFermi surface matching is very important to obtainlarge CPP-GMR. In experiments, insertion of B2-type
NiAl between Co2FeGa0.5Ge0.5 (CFGG) and the Ag
spacer dramatically enhanced the CPP-GMR and ∆RAboth at LT and RT62). This modication was motivatedby a theoretical calculation showing that the Fermi
surface matching between CFGG and B2-type NiAl ismuch better than that of CFGG and Ag. Furthermore,
the experimental results showed that not only NiAl but
also Ni insertion between CFGG and the Ag spacerenhanced the CPP-GMR67). This result is also conrmedbytheoretical
calculations
showingthat
CFGG/Ni/Ag/Ni/CFGG exhibits smaller RP↑ than
CFGG/Ag/CFGG.
More
recently,
half-metallic
Co2FeMnSi (CFMS) was inserted between A2-CoFe andAg spacer, and the CPP-GMR was maximized when the
thickness of CFMS was around 7 nm68). One possible
reason for the large CPP-GMR was attributed to thebetter Fermi surface matching of CFMS/CoFe as
compared with CoFe/Ag. All these results indicate thatFermi surface matching between HFM and the NM
spacer layer is a key factor in enhancing the CPP-GMR
for future ultra-sensitive magneto-resistive sensors.
5. Summary
In this paper, rst-principles studies on electronic
structures and ballistic transport properties of HMF
Co-based Heusler compound-based magneto-resistive
devices were reviewed.
The effects of spin-ip scattering by interfacial
noncollinear magnetic structures on the TMR ratios of
MTJs with Co2MnSi(CMS) and MgO were investigatedusing rst-principles calculations. It was found that theeffects of the noncollinearity of interfacial Co spin
moments on the TMR are signicant in determining thespin-flip conductance. Furthermore, the inter-atomic
layer exchange stiffness constant of interfacial andsub-interfacial Co spin moments at CMS/MgO junctions
is much smaller than that in bulk regions. From theseresults, I conclude that the low TMR ratio at room
temperature in MTJs with half-metallic Co-based fullHeusler compounds can be attributed to spin-flip
scattering by the noncollinear magnetic structures ofinterfacial Co as a result of thermal uctuations. These
results are validated by recent experimental results, i.e.,the signicant reduction in the TMR ratios of
CMS/MgO/CMS MTJs at RT compared to those of
Fe/MgO/Fe MTJs. This means that the spin-flip
scattering at the interface is at least as important as
any other effect. I showed that the interfacial exchange
stiffness can be strongly enhanced by inserting an
ultrathin B2-CoFe layer in CMS/MgO junctions, leading100

to a larger TMR ratio at room temperature.
For CPP-GMR, the ballistic conductance of HFM/NM/
HFM was calculated in order to clarify the origin ofinterfacial resistance. The majority-spin transmittanceof CMS/X/CMS(001) in the parallel magnetizationconguration was calculated by the Landauer formula,and it was found that the matching of the Fermi surface
projected to the two-dimensional Brillouin zone inin-plane wave vector k║ between CMS and NM spacers
is a main contributing factor to the interfacial
resistance among spacers. The experimental CPP-GMR
was well reproduced as a function of the theoreticalresistance-area product in parallel magnetization
through the equation of interface spin asymmetry γ.
All these ndings suggest that the TMR ratios of MTJs
and CPP-GMR with half-metallic Co-based full Heusler
compounds can be designed by controlling theirinterfaces, which is worth further investigation.
Acknowledgements I am grateful to M. Shirai and K.
Abe of Tohoku University, K. Hono, S. Mitani, Y.
Sakuraba, H. Sukegawa, S. Kasai, K. Masuda and I.
Kurniawan of the Na-tional Institute for Materials
Science, and K. Nawa of Mie University for valuable
discussions on this work. This work was partly
supported by Grants-in-Aid for Scientic Research(Grant Nos. 17H06152, 20H00299, 20H02190,
20H02186, 21H01750 and 22H04966) from the Japan
Society for the Pro-motion of Science, Center for
Spintronics Research Network (CSRN) of Osaka
University, and the Cooperative Research Project
Program of the Research Institute of ElectricalCommunication in Tohoku University.
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Received Mar. 31, 2023; A ccepted Apr. 19, 202 3

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Copyright ©2023 by the Magnetics Society of Japan.
This article is licensed under the Creative Commons Attribution International License (CC BY 4.0)
http://creativecommons.org/licenses/by/4.0/

J. Magn. Soc. Jpn., 47, 103-107 (2023)<Paper>I n c r e a s e in c o e r c iv it y o f S m (F e - C o )- B t h in f ilm s d u e t od iffu s io n o f A l e le m e n t fr o m c a p la y e r
Y. Mori†, S. Hatanaka, M. Kambayashi, S. Nakatsuka*, K. Hirayama*,
M. Doi, and T. Shima
Graduate School of Engineering, Tohoku Gakuin Univ., 1-13-1 Tagajo, 985-8537, Japan*Department of Engineering, Tohoku Gakuin Univ., 1-13-1 Tagajo, 985-8537, JapanThe effects of Al diffusion and heat treatment on the structure and magnetic properties for Sm(Fe-Co)-B thin film
have been investigated. In the X-ray diffraction patterns, peaks of (002) and (004) from ThMn12-type compounds wereclearly observed for all the samples. The coercivity µ0Hc was improved by introducing an Al cap layer and it was
further increased by heat treatment. A high µ0Hc of 1.78 T was obtained at 400 ºC by increasing the annealing time to
4 hours. It was considered that infiltration of Al into the Sm(Fe-Co)-B layer contributed to the improvement ofmagnetic properties.
Keywords: coercivity, ThMn12 compound, Sm(Fe-Co)-B film, grain boundary diffusion, Al cap layer

Corresponding author: Y. Mori(e-mail: mori.tohokugakuin.mml@gmail.com).

2.

Experimental procedure

The samples were prepared by using an ultra-highvacuum magnetron sputtering system with base(a) w/o Al(b) tAl = 1.0 nm(c) 3.0 nm(d) 4.7 nm(e) 9.4 nm(f) 15.0 nm(g) 18.0 nm(h) 20.0 nm

20

30

(a)

(a)

(b)

(b)

(c)

(c)

(d)

(d)

(e)

(e)

(f)

(f)

(g)

(g)

(h)

40

50

60

2 theta (deg.)

70

80

(004)

(002)

V (200)(004)

Main-phase (1-12)
Sub-phase (α-FeCo)

MgO (200)

RFe12 (R: Rare earth element) compounds withtetragonal ThMn12-type crystal structure are expected
to be new high-performance permanent magnetic
materials
because
of
their
high
saturation
magnetization due to composition with high Fe content.
Among these compounds, SmFe12 based compounds
exhibits high intrinsic magnetic properties1)-7). For
example, Hirayama et al. reported that high saturation
magnetization (µ0Ms = 1.78 T), high anisotropy field(µ0HA = 12 T) at room temperature and high Curie
temperature (TC = 879 K) were obtained in theSm(Fe0.8Co0.2)12 epitaxial film with V buffer layer2),
which were higher than those of Nd2Fe14B sinteredmagnet, however obtained µ0Hc was less than 0.1 T.
Since the RFe12 compounds are well known to exhibit
thermo-dynamical instability in the bulk form, amethod of substituting a part of Fe with stabilizing
elements such as Al, Si, Ti, V, Co, W and Zr was used tocontrol the microstructure, but as a result, a large
decrease in saturation magnetization could not be
avoided.
Recently, it was reported that a high µ0Hc above 1.1 T
was successfully obtained for the Sm(Fe0.8Co0.2)12B0.5
thin film11)-12). From the result of the microstructural
analysis, it was confirmed that the SmFe12 (1:12) grains
exhibiting a columnar structure were enveloped by a Brich amorphous grain boundary (GB) phase consisting of
80 at.% of Fe and Co. Therefore, controlling thecomposition and increasing the number of pining sites
in the GB phase play a very important role and will leadto further improvement of magnetic properties. The GB
diffusion using non-magnetic elements is expected to
improve magnetic properties, and many achievements
have been made to improve magnetic properties 13)-16).
Bolyachkin et al. reported that µ0Hc of Sm(Fe0.8Co0.2)12B0.5 (100 nm) thin film was improved by Si diffusion into
GB phase and based on the results of STEM-EDS
observation, micromagnetic simulation was performed
to predict the optimum microstructure. Then, it was

confirmed that the Si deposited as the cap layer isdiffused into the Sm(Fe0.8Co0.2)12B0.5 layer by heat
treatment. Most of the Si diffused into the GB phase
was found to be in the region of about 25 nm from the
top surface of the Sm(Fe0.8Co0.2)12B0.5 layer. Therefore,
according to the micromagnetic simulations, it waspredicted that µ0Hc of 1.9 T will be obtained when thepenetration depth of Si is 90 nm15). Thus, increasing theregion of non-magnetic elements diffused into the GB
phase plays an important role for achieving large µ0Hc.
The optimum cap layer material for diffusing into grainboundary phase should be the one that forms a solid
solution with Fe in the liquid phase at relatively low
annealing temperature. In this study, in order toinvestigate the effect of Al diffusion and heat treatment
on the crystal structure and magnetic properties for
Sm(Fe-Co)-B thin film, different heat treatments havebeen performed to Sm(Fe-Co)-B (100 nm)/ Al (tAl nm)
thin films and their magnetic properties and crystal
structures have been investigated.

(002)

Introduction

Intensity (log. scale)

1.

36

(h)

38

80

82

Fig. 1. XRD patterns for Sm(Fe-Co)-B/ Al thin films withdifferent Al cap layer thicknesses between 0 (w/o Al) and20 nm. Enlarged view of the (002) and (004) peaks from
ThMn12 phase are also shown.

Journal of the Magnetics Society of Japan Vol.47, No.4, 2023

103

Magnetization, µ0M (T)2.87 MJ/m

0.0

1.49 T
1.22 T
71.0 %-1.0-2.0
2.0 (c) 3.0 nm

3.25 MJ/m

1.0

3(f) 15.0 nm

3.36 MJ/m

1.40 T
1.41 T
72.4 %(g) 18.0 nm

3.35 MJ/m

1.41 T
1.31 T
73.3 %-1.0-2.0
2.0 (d) 4.7 nm

3

3.11 MJ/m

1.0

3

3

(a) w/o Al(b) tAl = 10 nm(c) 18 nm(d) 25 nm(e) 30 nm

1.31 T
1.50 T
77.3 %(h) 20.0 nm

3.19 MJ/m(g) 50 nm(h) 100 nm

-1.0
-6

-4

-2

0

2

1.49 T
1.30 T
69.6 %

4

6

-6

-4

Magnetic ﬁeld, µ0M (T)

-2

0

2

1.27 T
1.42 T
74.5 %

4

6

Fig. 2. Magnetization curves for Sm(Fe-Co)-B/ Al thinfilms with different Al layer thicknesses between 0 (w/oAl) and 20 nm.

pressure of less than 4.0 × 10-8 Pa. First of all, a V
buffer layer of 20 nm was deposited onto MgO (100)single crystal substrate at substrate temperature Ts of
400 ºC. Then, the Sm(Fe-Co)-B layer of 100 nm wasdeposited at Ts of 400 ºC by co-sputtering with Fe,
Fe50Co50, Fe80B20, and Sm targets. The composition of
the film was determined to be Sm7.3Fe74.0Co18.7Bx (at.%)by Energy dispersive X-ray analysis (EDX). However, it
is noted that due to the detection limit of light elements,
the composition of B cannot be determined by EDX.
Subsequently, an Al cap layer was deposited at Ts of 400ºC onto Sm(Fe-Co)-B layer and the thickness tAl waschanged between 0 and 100 nm. Moreover, heat
treatment was adjusted by annealing temperature Ta
between 400 and 450 ºC and annealing time ta from 0 to
5 hours. Finally, V layer of 10 nm was deposited as aprotective layer for preventing of oxidation. The
analysis of crystal structures was performed by X-ray
diffraction (XRD) with Cu-Kα radiation from the out-ofplane configuration. The magnetic properties were
evaluated by using a superconducting quantum
interfacedevice(SQUID)
magnetometer.
Allmeasurements were performed at room temperature.
3.

Results and discussion

X-ray diffraction patterns for Sm(Fe-Co)-B (100 nm)/
Al (tAl nm) thin films with different Al cap layer
thicknesses are shown in Fig. 1. The thickness of Al cap
layer was changed in a range between 0 (w/o Al) and 20
nm. The enlarged view of the (002) and (004) peaks from
ThMn12 phase are also shown. The peaks from ThMn12type compound were clearly observed for all the films,
and their position were shifted to lower angle withincreasing the Al cap layer thickness up to 9.4 nm (e),showing that c-axis elongated by substituting a part of
Fe-Co site with Al element which diffused into 1:12
phase in the Sm(Fe-Co)-B layer. No remarkable change
in peak position of the 1:12 phase was observed abovetAl = 9.4 nm, and the intensity was almost the same,
indicating that the c-axis elongation was saturated.

30

(002)
(a)

(a)

(b)

(b)

(c)

(c)

(d)

(d)

(e)

(e)

(f)

(f)

(g)

(g)
(h)

(h)

3

20

0.0

104

Main-phase (1-12)
Sub-phase (α-FeCo)
Fe3Al phase(004)

1.42 T
1.37 T
73.4 %

3(f) 35 nm

0.0

-2.0

3

3.20 MJ/m

V (200)µ0Ms = 1.58 Tµ0Hc = 1.11 T
Mr/ Ms = 67.6 %-2.0
2.0 (b) t = 1.0 nm
Al1.0(e) 9.4 nm

MgO (200)µ0HA ≈ 12 T

3

(200)

0.0
-1.0

Ku = 3.22 MJ/m

:
:

(002)

1.0

Intensity (log. scale)

2.0 (a) w/o Al

40

50

60

2 theta (deg.)

70

80

(004)

INDEX

36

38

80

82

Fig. 3. XRD patterns of Sm(Fe-Co)-B/ Al thin films withdifferent Al layer thicknesses between 0 (w/o Al) and 100
nm at annealing temperature of 450 ºC for 0.5 hours.

Magnetization curves for Sm(Fe-Co)-B (100 nm)/ Al(tAl nm) thin films with different Al layer thicknesses
are shown in Fig. 2. The filled circles and open ones aredenoted the curves measured in the perpendicular andin the parallel directions to the film plane, respectively.
The high µ0Hc of 1.11 T was obtained from the film
without Al cap layer (a) and then it was increased withincreasing the thickness of Al cap layer. The high µ0Ms
of 1.31 T, high µ0Hc of 1.50 T, and moderate uniaxial
magnetic anisotropy Ku of 3.35 MJ/m3 were obtained forthe film with tAl of 18 nm (g). With further increase of tAl
to 20 nm, the µ0Hc was slightly decreased to 1.42 T (h).
From these results, it was confirmed that the depositionof the Al layer was contributed to increase the coercivityof Sm(Fe-Co)-B thin films. The amount of Al diffused
into the 1:12 phase is expected to increase since µ0Ms
decreased above tAl = 9.4 nm, which is thought to be dueto the elongation of the a-axis, since the XRD results
show no change in the c-axis.
In order to further improve the µ0Hc, a heat treatment
was adopted and the effect of Al cap layer thickness on
the crystal structures for Sm(Fe-Co)-B thin film wasinvestigated. XRD patterns of Sm(Fe-Co)-B (100 nm)/ Al(tAl nm) thin films with different Al layer thicknesses atannealing temperature of 450 ºC for 0.5 hours areshown in Fig. 3. The thickness was changed between 0(w/o Al) and 100 nm. The peaks of (002) and (004) from
1:12 phase were observed for all the films. The positionof these peaks was shifted to lower angle withincreasing tAl. However, intensity of the peaks was
slightly decreased with increasing tAl. In addition, it
was confirmed that the peak from 31.1º was determined
to be from Fe3Al (200), intensity of the peak wasincreased with increasing tAl up to 35 nm (f) and thenwas decreased above 35 nm. Thus, formation of the
Fe3Al phase is observed with increasing the thickness of
Al layer, but it was decreased above 50 nm, which isthought to be due to the decrease in the amount of Fe
diffusing into the Al layer as the Al content increases.
Magnetization curves for Sm(Fe-Co)-B (100 nm)/ Al(tAl nm) films with different Al cap layer thicknesses atannealing temperature of 450 ºC for 0.5 hours areshown in Fig. 4. The Al layer thickness was changed

Journal of the Magnetics Society of Japan Vol.47, No.4, 2023

Magnetization, µ0M (T)4.33 MJ/m

0.01.37 T
1.40 T
78.1 %-1.0-2.0
2.0 (c) 18 nm

4.68 MJ/m

1.0
0.0

3

(f) 35 nm

3.83 MJ/m-2.0
2.0 (d) 25 nm

31.16 T
1.71 T
73.8 %(g) 50 nm

3.94 MJ/m

33(h) 100 nm

2.16 MJ/m(a) w/o ann.

-1.0
-6

-4

-2

0

2

1.20 T
1.66 T
75.3 %

4
6 -6 -4 -2Magnetic ﬁeld, µ0M (T)020.89 T
1.41 T
51.9 %

4(002)(b) ta = 0.5 hours(c) 1.0(d) 3.0(e) 4.0(f) 5.0

6

Fig. 4. Magnetization curves for Sm(Fe-Co)-B/ Al thinfilms with different Al cap layer thicknesses between 0(w/o Al layer) and 100 nm at annealing temperature of
450 ºC for 0.5 hours.

between 0 (w/o Al) and 100 nm. The µ0Hc of 1.18 T was
obtained for the film without Al cap layer (a). Then, theµ0Hc was increased with further increasing Al cap layer
thickness and the high µ0Hc of 1.71 T was obtained forthe films with the thickness of Al cap layer of 30 (e) and35 nm (f). Compared to the results of the optimum film
thickness without heat treatment, the optimum
thickness of Al layer was found to increase by additionof the heat treatment.
In order to sufficiently diffuse Al into the Sm(Fe-Co)-B
layer, the optimum annealing temperature andannealing time must be determined. XRD patterns for
Sm(Fe-Co)-B (100 nm)/ Al (35 nm) thin films with heat
treatments at 450 ºC for ta hours are shown in Fig. 5.
The annealing time ta was changed between 0 (w/o ann.)
and 5 hours. The enlarged view of the (002) and (004)peaks from ThMn12 phase are also shown. The positionof these peaks was shifted to lower angle by increasing
the annealing time from 0.5 (b) to 3.0 hours (d). Then,the peaks were shifted to higher angle when ta wasincreased above 4.0 hours (e), indicating that theamount of Al element into the Sm(Fe-Co)-B layer wasincreased by increasing annealing time and in the caseof extended heat treatment above 4.0 hours, c-axis wasshrank. In addition, since intensity of the peak from
Fe3Al (200) was increased remarkably by increasing ta
and almost no change in the intensity was observed, it
was considered that amount of Fe3Al compound
precipitation is increased by increase ta.
Magnetization curves for Sm(Fe-Co)-B (100 nm)/ Al(35 nm) thin films with different annealing time areshown in Fig. 6. The large µ0Hc of 1.71 T was obtained
at ta of 0.5 hours (b). However, the µ0Hc was remarkably
decreased with increasing ta and it was decreased to1.41 T above 4.0 hours (e). From this result, it was
confirmed that the µ0Hc takes a maximum value atannealing temperature of 450 ºC for a very shortannealing time of 0.5 hours. Furthermore, since the
Fe3Al phase is known to be ferromagnetic18), it is

(a)

(a)

(b)

(b)

(c)

(c)

(d)

(d)

(e)

(e)

(f)

3

20

0.0

(004)

Main-phase (1-12)
Sub-phase (α-FeCo)
Fe3Al phase

1.16 T
1.65 T
70.7 %

4.01 MJ/m

1.0

3

V (200)1.23 T
1.71 T
73.2 %

1.27 T
1.55 T
80.3 %

-1.0

-2.0

3

4.46 MJ/m

MgO (200)µ0Ms = 1.51 Tµ0Hc = 1.18 T
Mr/ Ms = 77.2 %-2.0
2.0 (b) t = 10 nm
Al1.0(e) 30 nm(200)µ0HA ≈ 12 T

3

(002)

0.0
-1.0

Ku = 4.71 MJ/m

:
:

30

40

50

60

70

2 theta (deg.)

(f)

36

80

38

80

82

Fig. 5. XRD patterns for Sm(Fe-Co)-B (100 nm)/ Al (35nm) thin films with annealing temperature of 450 ºC
for ta hours. Annealing time was changed between 0(w/o ann.) and 5 hours.
2.0 (a) w/o ann.
1.0
0.0
-1.0
Magnetization, µ0M (T)

1.0

Intensity (log. scale)

2.0 (a) w/o Al

(004)

INDEX

:
:

Ku = 5.33 MJ/m

µ0HA ≈ 12 T

µ0Ms = 1.34 Tµ0Hc = 1.50 T
Mr/ Ms = 80.9 %-2.0
2.0 (b) t = 0.5 hours

3.83 MJ/m

a

1.0
0.0

-2.0
2.0 (c) 1.0

3.70 MJ/m

1.0
0.0

-1.0
-6

-4

3

(d) 3.0

3.18 MJ/m

1.09 T
1.56 T
66.5 %(e) 4.0

3.26 MJ/m

1.16 T
1.71 T
73.8 %

-1.0

-2.0

3

-2

0

2

1.13 T
1.70 T
71.1 %

4

3

3

1.04 T
1.41 T
67.0 %
3

6(f) 5.0-6

3.03 MJ/m-4

Magnetic ﬁeld, µ0M (T)

-2

0

2

1.04 T
1.41 T
67.0 %

4

3

6

Fig. 6. Magnetization curves for Sm(Fe-Co)-B (100 nm)/Al (35 nm) thin films with annealing temperature of
450 ºC for ta hours. Annealing time was changed
between 0 (w/o ann.) and 5 hours.

thought that µ0Hc was decreased due to a magnetic
coupling between 1:12 grains or nucleation of thereverse magnetic domain in the Fe3Al phase which
exists in the GB phase at the upper region of the Sm(FeCo)-B layer or at the interface between the Al layer andthe Sm(Fe-Co)-B layer.
The annealing time was changed at low annealing
temperature of 400 ºC to suppress the formation of
Fe3Al compound and promote the diffusion of Al into theSm(Fe-Co)-B layer. XRD patterns of Sm(Fe-Co)-B (100nm)/ Al (35 nm) thin films with different annealing time
are shown in Fig. 7. The annealing time was changed
between 0 (w/o ann.) and 5 hours, while annealing
temperature was fixed at 400 ºC. The enlarged view ofthe (002) and (004) peaks from ThMn12 phase are also
shown. The peaks of (002) and (004) from 1:12 phasewere observed for all the samples. When the annealing
temperature was reduced to 400 ºC, the elongation of
the c-axis did not depend on the duration of theannealing time, indicating that the amount of Al
diffusion into 1:12 phase was decreased. Although,intensity of the peak from Fe3Al phase increases by
increasing annealing time, it was confirmed thatformation of the Fe3Al compound is suppressed

Journal of the Magnetics Society of Japan Vol.47, No.4, 2023

105

INDEX

(002)

(004)

(c) 1.0(d) 1.5(e) 2.0(f) 3.0(g) 4.0(h) 5.0

20

30

40

50

60

70

2 theta (deg.)

(a)

(a)

(b)

(b)

(c)

(c)

(d)

(d)

(e)

(e)

(f)

(f)

(g)

(g)

(h)

(h)

36

80

38

1.0
0.0
-1.0

:
:

Ku = 5.33 MJ/m

µ0HA ≈ 12 T

Magnetization, µ0M (T)4.88 MJ/m

a

0.0
-2.0
2.0 (c) 1.0

4.36 MJ/m

1.0
0.0

0.0
0.0

82

-2.0
2.0 (d) 1.5

4.19 MJ/m

1.0
0.0

-1.0
-4

-2

0

2

1.23 T
1.70 T
73.1 %

43

4.36 MJ/m

3

1.25 T
1.75 T
69.7 %
3(g) 4.0

3.88 MJ/m

3

1.17 T
1.78 T
69.0 %
3(h) 5.06-6-4

Magnetic ﬁeld, µ0M (T)3.24 MJ/m

-2

0

2

1.13 T
1.73 T
69.7 %

4

3

6

Fig. 8. Magnetization curves for Sm(Fe-Co)-B (100nm)/ Al (35 nm) thin films with annealing temperatureof 400 ºC for ta hours. Annealing time was changed
between 0 (w/o ann.) and 5 hours.

compared to the case where the annealing temperature
is 450 ºC.
Magnetization curves of Sm(Fe-Co)-B (100 nm)/ Al (35nm) thin films with different annealing time are shownin Fig. 8. Annealing time was changed between 0 (w/oann.) and 5 hours and annealing temperature was fixedat 400 ºC. The µ0Hc of 1.50 T was obtained for the film
without heat treatment (a). However, with increasing ta,
the highest µ0Hc of 1.78 T, µ0Ms of 1.17 T and Ku of 3.88
MJ/m3 were obtained for the film with annealing time of
4 hours (g). Further increase of ta to 5 hours, the µ0Hc
was slightly decreased to 1.73 T (h). It was confirmedthat the heat treatment at 400 ºC for 4 hours is found tobe very effective to increase µ0Hc for Sm(Fe-Co)-B thinfilm with diffusion of Al. This increase in µ0Hc isconsidered to be due to the reduction of Al diffusion into
the 1:12 phase and precipitation of the Fe3Al phase,suggesting that Al element existing in the grainboundary phase is responsible for the high coercivity.

106

Ta = 450 ºC

X = La50Ga50, µ0Hc = 1.27 T
Sm(Fe-Co)-B, µ0Hc = 1.20 T

w/oannealing

1.28 T
1.70 T
70.1 %(f) 3.0

X = Al, µ0Hc = 1.50 T
X = Si, µ0Hc = 1.32 T

1.0����������

4.21 MJ/m

1.23 T
1.66 T
73.2 %

-1.0

-6

3

Ta = 400 ºC

Sm(Fe-Co), µ0Hc = 0.1 T

80

1.23 T
1.66 T
77.1 %-1.0-2.0(e) 2.0µ0Ms = 1.34 Tµ0Hc = 1.50 T
Mr/ Ms = 80.9 %-2.0
2.0 (b) t = 0.5 hours
1.0

3µ0Hc = 1.78 T

0.5

Fig. 7. XRD patterns of Sm(Fe-Co)-B (100 nm)/ Al (35nm) thin films with annealing temperature of 400 ºC
for ta hours. Annealing time was changed between 0(w/o ann.) and 5 hours.
2.0 (a) w/o ann.

tSFCB = 100 nm

1.5

Coercivity µ0Hc (T)MgO (200)

V (200)

(002)

(200)

Intensity (log. scale)(a) w/o ann.
(b) ta = 0.5 hours

(004)

2.0

Main-phase (1-12)
Sub-phase (α-FeCo)
Fe3Al phase

1.0

2.0

Sm(Fe-Co)-B (100 m)/ Al (35 nm)
Sm(Fe-Co)-B (100 m)/ Si (8 nm)
Sm(Fe-Co)-B (100 m)/ LaGa (20 nm)
Sm(Fe-Co)-B (100 m)
Sm(Fe-Co) (100 nm)
3.0

4.0

5.0

Annealing time ta (hour)Fig. 9. Effect of annealing time on µ0Hc for Sm(Fe-Co)-B
thin films. Closed circles and open ones are denoted thefilms with Ta = 400 ºC and 450 ºC, respectively. For
comparison, µ0Hc of the film without B addition (□)12)and Sm(Fe-Co)-B ( ■)11), Sm(Fe-Co)-B/ La50Ga50 ( △ )17)
and Sm(Fe-Co)-B/ Si ( ▲ )16)-17) thin films are plotted.
Marks that overlap with the y-axis indicate the films
without post annealing.

µ0Hc of Sm(Fe-Co)-B/ Al thin films as a function of
annealing time are shown in Fig. 9. The filled circles
and open ones are denoted the films with Ta = 400 ºC
and 450 ºC, respectively. As comparison, µ0Hc of the film
without B addition (□), Sm(Fe-Co)-B (■), Sm(Fe-Co)-B/
La50Ga50 (△) and Sm(Fe-Co)-B/ Si (▲) thin films areplotted. The µ0Hc was increased above 1.2 T by the
diffusion of La50Ga50, Si, and Al into the Sm(Fe-Co)-B
layer16)-17). Among these materials, the highest µ0Hc of
1.5 T was obtained at the film with the diffusion of Al.
Further enhancement of µ0Hc was obtained byappropriate heat treatment. When the annealing
temperature was fixed at 450 ºC, µ0Hc increased by theshort annealing time of 0.5 hours, but it was decreased
by longer heat treatment. In contrast, the highest µ0Hc
of 1.78 T was obtained for longer annealing time of 4hours at annealing temperature of 400 ºC. It wasconsidered that the diffusion of Al element into Sm(FeCo)-B layer is a very effective approach to increase theµ0Hc for Sm(Fe-Co)-B thin film.
4.

Conclusion

The effect of Al cap layer deposition and different heat
treatments on the crystal structures and magnetic
properties for Sm(Fe-Co)-B thin films have been
investigated. The peaks of (002) and (004) from ThMn12type compounds were observed and their position were
shifted to lower angle with increasing the thickness of
Al cap layer, indicating that Al element was diffused
into Sm(Fe-Co)-B layer. In addition, µ0Hc of Sm(Fe-Co)B thin film was increased with increasing the thickness
of Al cap layer and the value of 1.50 T was obtained forSm(Fe-Co)-B (100 nm)/ Al (18 nm) thin film. Although
the µ0Hc of Sm(Fe-Co)-B (100 nm)/ Al (35 nm) thin filmwith annealing temperature of 450 ºC was decreased
with increasing annealing time, while at 400 ºC,
formation of the Fe3Al compound and Al diffusion into
1:12 phase were thought to be suppressed and µ0Hc
increased. As a result, the maximum µ0Hc of 1.78 T was

Journal of the Magnetics Society of Japan Vol.47, No.4, 2023

INDEX

obtained in this study. Therefore, it was considered thatthe diffusion of Al element into Sm(Fe-Co)-B layer is avery effective approach to increase µ0Hc for Sm(Fe-Co)-B
thin film, and it is believed that the result of diffusion/
infiltration in the GB phase can pave the way to realize
the application of Sm(Fe-Co)12 based permanent magnet.
Acknowledgements This work was performed at the

Research Institute for Engineering and Technology (HighTech Research Center) at Tohoku Gakuin University. This
work was partly supported by the Elements Strategy
Initiative Center for Magnetic Materials (ESICMM) of
National Institute for Materials Science (NIMS).

References
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4) P. Tozman, H. Sepehri-Amin, Y. K. Takahashi and K. Hono:
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8) X. C. Kou, T. S. Zhao, R. Grössinger, H. R. Kirchmayr, X. Li
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9) M. Artigas, C. Piquer, J. Rubin and J. Bartolome: J. Magn.
Magn. Mater., 196, 653 (1999).
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11) H. Sepehri-Amin, Y. Tamazawa, M. Kambayashi, G. Saito,
Y. K. Takahashi and D. Ogawa, T. Ohkubo, S. Hirosawa, M.
Doi, T. Shima, K. Hono: Acta Mater., 194, 337 (2020).
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Magn. Soc. Jpn., 45, 66 (2021).

13) A. K. Srinithi, H. Sepehri-Amin, X. Tang, P. Tozman, J. Li,
J. Zhang, S. Kobayashi, T. Ohkubo, T. Nakamura and K.
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Ohkubo, Y.K. Takahashi, T. Shima and K. Hono: Acta
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16) M. Kambayashi, H. Sepehri-Amin, Y. Mori, Y. K. Takahashi,
T. Ohkubo, M. Doi, T. Shima and K. Hono: 170th JIM
Spring Meeting, online, S7.12 (2022).
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Received Nov. 04, 2022; Revised Dec. 15, 2022; Accepted Mar.
19, 2023

Journal of the Magnetics Society of Japan Vol.47, No.4, 2023

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Copyright ©2023 by the Magnetics Society of Japan.
This article is licensed under the Creative Commons Attribution International License (CC BY 4.0)
http://creativecommons.org/licenses/by/4.0/

J. Magn. Soc. Jpn., 47, 108-114 (2023)<Paper>L a s e r I n d u c e d S p in C u r r e n t in G d F e C o /C u /F e C o T r ila y e r s
T r ig g e r e d b y U lt r a s h o r t P u ls e d L a s e r
K. Seguchi, E. Watanabe, D. Oshima, and T. Kato*

Department of Electronics, Nagoya Univ., Furo-cho, Chikusa-ku, Nagoya 464-8603, Japan*Institute of Materials and Systems for Sustainability, Nagoya Univ.,

Furo-cho, Chikusa-ku, Nagoya 464-8603, JapanThe magnetization dynamics of GdFeCo / Cu / FeCo trilayers were studied by the time-resolved magneto-optical
Kerr effect (TRMOKE) using an all-optical pump-probe technique. When the pump beam was illuminated from the
FeCo layer side, the magnetization precession of the GdFeCo layer was confirmed to be enhanced compared with thecase without the FeCo layer. Moreover, the precession angular frequency w and inverse of the relaxation time 1/t of
the GdFeCo layer were confirmed to be decreased by pumping the FeCo layer. The decreases in w and 1/t wereremarkable when the external field direction approached to the film normal. We considered spin transfer torque (STT)
due to the spin current injected by triggering the precession of the FeCo layer, and we obtained a positive field-like
STT and negative anti-damping STT acting on the GdFeCo layer. Moreover, the spin current Js injected from the FeColayer can be expected to be ~ 1 MA/cm2 from the magnitude of the anti-damping STT.
Key words: magnetic recording, soft magnetic material, superconductor, magneto-optical recording, thin film
1. Introduction

The spin polarized current is known to exert torques(spin transfer torque: STT) that switches themagnetization of magnetic materials1), 2), and it ispractically used as an efficient writing scheme in themagnetic random access memories (MRAMs). A purespin current can also exert torques on magnetization3)
and it can be generated by flowing the charge current in
non-magnetic materials through the spin Hall effect4), 5).
This phenomenon is known as spin-orbit torque (SOT),and SOT switching has been extensively studied as anext-generation MRAM technology6), 7), since it isexpected to be ten-times faster and ten times moreenergy efficient compared with STT switching8).
A pure spin current is also reported to be generated bypumping ferromagnetic thin films using an ultrashortpulsed laser. Ultrafast demagnetization of ferromagnets
through the illumination of an ultrashort pulsed laser
launches the spin current into the adjacent non-magnetic
layer9), 10), which results in the precession and theswitching of another ferromagnetic layer through thetransfer of angular momentum between two
ferromagnetic layers11)–13). However, further study isnecessary to understand spin currents launched andtransferred by an ultrashort pulsed laser.
Here, we report the magnetization dynamics of
GdFeCo / Cu / FeCo trilayers pumped by the ultrashortpulsed laser. The laser pulse excites the electrons in the
FeCo layer and launches the spin current to the adjacentCu layer. The spin current affects the magnetization
precession of the ferrimagnetic GdFeCo layer, which isprobed by the time resolved magneto-optical Kerr effectCorresponding author: T. Kato(e-mail: kato.takeshi.i6@f.mail.nagoya-u.ac.jp).

108(TRMOKE). The GdFeCo amorphous alloy films are
known to exhibit a perpendicular magnetic anisotropy,
and Gd moments are antiferromagnetically coupled to
FeCo moments. The net magnetization and net angularmomentum of GdFeCo are known to be easily tuned byvarying its composition14), 15); thus, GdFeCo is aninteresting material to discuss the relationship between
the injected spin current and the angular momentum of
the magnetic materials. We have studied STT16)–18) andSOT switching for GdFeCo19), and we reported anincrease in the damping-like and field-like SOT effective
fields near the compensation composition and the signchange of the field-like SOT effective field across thecompensation composition20). This report also studied theeffective fields due to the spin current injection triggeredby an ultrashort pulsed laser.
2. Experiments

Samples with a stack of SiO2 substrate / Fe90Co10(0 or
2 nm) / Cu(tCu nm) / Gd21(Fe90Co10)79(10 nm) / SiN(5 nm)
were prepared by an RF magnetron sputtering system,
where the Cu thickness tCu was varied from 40 nm to 160
nm. The GdFeCo layer was deposited by co-sputtering of
Gd and Fe90Co10 targets, and the SiN layer was depositedusing an Si3N4 alloy target. Hysteresis loops were
measured by an alternating gradient field magnetometer(AGM). The magnetic properties of GdFeCo and FeCo
were checked by a magneto-optical Kerr spectrometer,where the light was incident from the GdFeCo or FeCo
side. The magnetization dynamics of GdFeCo weremonitored by TRMOKE using an ultrashort pulse fiber
laser with a pulse width of 500 fs, a wavelength of l =1040 nm, and a repetition frequency of 100 kHz. As
shown in Fig. 1 (a), a pump beam with l = 1040 nm wasincident from the substrate side, and a frequency doubled
probe beam with l = 520 nm was focused on the GdFeColayer to monitor the precession after the pump beam

Journal of the Magnetics Society of Japan Vol.47, No.4, 2023

INDEX

Fig. 1

Schematic of experiments. (a) Back sidepumping illumination: the pump beam isilluminated from the substrate (FeCo) side.
(b) Front side pumping: the pump and probe
beams are illuminated on the same surface.

illumination. An external field Hext of up to 5 kOe wasapplied in the direction of q H = 0–60˚ from the film
normal. We refer to this TRMOKE setup as back sidepumping.
Astandard
all-opticalpump-probe
measurement shown in Fig. 1 (b) was also carried out tomonitor the magnetization precession of the GdFeCo and
FeCo layers. We refer to this setup as front side pumping,
and an external magnetic field Hext in the range of 4–14
kOe was applied in the direction of q H = 40–85° from thefilm normal for this case.
3. Results and Discussions

anisotropy field was ~ 1 kOe. The estimated effective
anisotropy and perpendicular anisotropies were 2 × 105
erg/cc and 5 × 105 erg/cc, respectively. As for the trilayer
film, the hysteresis loops had two contributions:perpendicular magnetized GdFeCo and in-planemagnetized FeCo. The magnetizations per unit area of
the GdFeCo and FeCo were estimated to be 200µemu/cm2 and 360 µemu/cm2 by assuming themagnetizations of 200 emu/cc and 1800 emu/cc,
respectively. The estimated magnetizations agreed wellwith the experimental loops shown in Fig. 1 (b), and the
GdFeCo and FeCo layers are considered to be completely
decoupled by a thick Cu layer.
Figure 3 shows TRMOKE waveforms of the GdFeCo /Cu (80) bilayer and GdFeCo / Cu (80) / FeCo trilayer,
where the pump beam was illuminated from thesubstrate side (back side pumping). An external field Hextof 5 kOe was applied along q H = 15˚ from the film normal.
The pump power was 350 mW, which corresponds to afluence of 4.4 mJ/cm2, in order to trigger a significant
precession of the FeCo layer with the pump beam (seeAppendix). As shown in Fig. 3, the precession amplitudeof the GdFeCo layer was confirmed to be enhanced bypumping the FeCo layer. Moreover, the precession
frequency of the GdFeCo was reduced from 19 GHz to 16
GHz by inserting the FeCo layer, which will be discussed
in detail later. This suggests that the spin current
injected from the FeCo layer has an influence on themagnetization precession of the GdFeCo layer.

Figure 2 shows hysteresis loops of (a) GdFeCo / Cu (80)bilayer and (b) GdFeCo / Cu (80) / FeCo trilayer. The
magnetic field was applied perpendicular (blue) andparallel (red) to the film plane. The vertical axis for thetrilayer (Fig. 1 (b)) is shown in a magnetic moment perunit area M·d, where M and d are the magnetization andtotal thickness of the magnetic layer, respectively. From
Fig. 1 (a), the GdFeCo exhibited perpendicular magnetic
anisotropy, whose magnetization was ~ 200 emu/cc andFig. 3Fig. 2Hysteresis loops of (a) GdFeCo / Cu (80)bilayer and (b) GdFeCo / Cu (80) / FeCo
trilayer. Magnetic field was applied
perpendicular (blue) and parallel (red) to thefilm plane. Magnetization of the (b) trilayer
is shown per unit area.

TRMOKE waveforms of GdFeCo / Cu (80)bilayer and GdFeCo / Cu (80) / FeCo trilayer,
where the pump beam was illuminated fromthe substrate side (back side pumping).

Figure 4 shows the Cu thickness dependence of theprecession amplitude of GdFeCo estimated fromTRMOKE waveforms of the GdFeCo / Cu (tCu) bilayer and
GdFeCo / Cu (tCu) / FeCo trilayer for back side pumping.
As shown in Fig. 4, the GdFeCo of the trilayer exhibiteda larger precession amplitude than the GdFeCo of thebilayer. When the Cu thickness tCu was no less than 80
nm, the precession amplitude of the GdFeCo / Cu bilayer

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Fig. 4 Cu thickness dependence of precession
amplitude of GdFeCo estimated fromTRMOKE waveforms of GdFeCo / Cu (tCu)bilayer and GdFeCo / Cu (tCu) / FeCo trilayer
for back side pumping. Inset shows lognormal plot of the tCu dependence of thedifference in precession amplitude between
GdFeCo / Cu / FeCo trilayer and GdFeCo /Cu bilayer.

became quite small due to the low transparency throughthe thick Cu layer. In the inset of Fig. 4, we plot tCu
dependence of the difference in the precession amplitudeof the GdFeCo between the trilayers and bilayers on alog-normal plot. From the slope of the inset, the spin
diffusion length of the Cu layer was estimated to be l =130 nm, which is smaller than the values in previous
reports10), 21), 22). However, the spin diffusion length of Cu
is sensitive to the crystal disorder of the Cu layer22). The
Cu layer in this study was grown on bcc FeCo (2 nm),which may induce the crystal disorder in the Cu layercompared with a Cu layer grown on the film with an fcc
structure10).
Figure 5 shows the dependence of the precession
angular frequency w of the GdFeCo layer on the external
field angle q H measured for the samples of the GdFeCo /Cu (80, 120) / FeCo trilayers and GdFeCo / Cu (80, 120)bilayers. The external field Hext was 5 kOe and a pumpbeam with a power of 120 mW was illuminated as in Fig.
1 (a) (back side pumping). Here, we do not use the data
for Cu (160 nm), since the perpendicular anisotropy of the
GdFeCo was significantly reduced (not shown here) bydepositing GdFeCo on a thick Cu (160 nm) layer. For the
GdFeCo / Cu bilayers, the precession angular frequency
w increased as q H decreased, which is typical for themagnetic materials with perpendicular anisotropy. The
effective anisotropy fields Hkeff estimated from the q Hdependence of w were 1.3 and 0.95 kOe for the GdFeCo /Cu (80) and GdFeCo / Cu (120) bilayers, respectively. andthese values roughly agreed with Hkeff estimated from thecorresponding hysteresis loops (see Fig. 2 (a) for the110

Fig. 5 External field angle q H dependence of theprecession angular frequency w of the
GdFeCo layer for the samples of GdFeCo /Cu (80, 120) / FeCo trilayers and GdFeCo /Cu (80, 120) bilayers. External field Hext was
5 kOe and the pump beam of 120 mW was
irradiated from the back side as in theschematic illustrations.

GdFeCo / Cu (80) bilayer). On the other hand, for the
GdFeCo / Cu / FeCo trilayers, the precession angularfrequency w of GdFeCo increased when q H decreased
from 60˚ to 30˚ and then decreased when q H decreased
from 30˚ to 0˚. This trend was remarkable for the trilayer
with a thinner Cu layer. The reduction in w at a small q H
was disappeared, when a thin Pt (4 nm) layer wasinserted in the Cu layer (see Appendix). This suggests theexistence of a spin transfer torque due to the spin current
injected from the FeCo layer by the back side pumping of
the GdFeCo / Cu / FeCo trilayers. One possible origin of
the spin current is the precession of the FeCo layer
triggered by ultrashort pulsed laser. The precession of
FeCo was confirmed to be increased by increasing thepump fluence and external field angle q H (see Appendix).
From the TRMOKE waveforms, the inverse of therelaxation time 1/t of the precession of GdFeCo wasestimated together with the angular frequency w (see Eq.
(A1)). Figure 6 shows the q H dependence of 1/t of GdFeCo
precessions estimated for the samples of the GdFeCo / Cu
(80, 120) / FeCo trilayers and GdFeCo / Cu (80, 120)bilayers. The inverse of the relaxation time 1/t is known
to be proportional when the extrinsic contributions, suchthe anisotropy distribution and two magnon scattering23),24), are ignored, and it is expressed as,

1/⌧ = ↵e↵ !,(1)where aeff is the effective Gilbert damping. As shown in
Fig. 6, the 1/t for the GdFeCo / Cu (80, 120) bilayers
gradually increased as q H decreased, which roughly
agreed with the proportional relation between 1/t and w
in Eq. (1). From Eq. (1), the effective damping aeff ofGd21(Fe90Co10)79 was estimated to be 0.03–0.04, which isslightly larger than our previous report14), which is

Journal of the Magnetics Society of Japan Vol.47, No.4, 2023

INDEX

dynamics under the injection of the spin current as,◆✓g?
s ⇥ H e↵ṡ = − 1 −
He↵
✓
◆
g//
s
⇥ ṡ ,−↵e↵ 1 +(4)↵e↵ γHe↵ |s|Fig. 6 External field angle q H dependence of theinverse of relaxation time 1/t of the GdFeColayer for the samples of GdFeCo / Cu (80,120) / FeCo trilayers and GdFeCo / Cu (80,120) bilayers. The external field Hext was 5
kOe and the pump beam of 120 mW was
irradiated from the back side as in theschematic illustrations.

probably due to the anisotropy distribution of the
GdFeCo grown on the Cu layer. For the samples of the
GdFeCo / Cu (80, 120) / FeCo trilayers, a significant
reduction in 1/t was confirmed compared with those for
the GdFeCo / Cu (80, 120) bilayers. For instance, 1/t ~ 4.5
GHz around q H ~ 20˚ for the GdFeCo / Cu (80) bilayer
significantly reduced to 1/t ~ 3 GHz for the GdFeCo / Cu(80) / FeCo trilayer (~30% reduction), while w reduced
from 115 Grad/s to 105 Grad/s (only ~10% reduction) as
shown in Fig. 5. This suggests a reduction in the effective
damping aeff due to the spin current injected from the
FeCo layer by the back side pumping of the GdFeCo / Cu
/ FeCo trilayers.
In order to discuss the variation in the magnetization
dynamics of GdFeCo between the GdFeCo / Cu / FeCo
trilayers and GdFeCo / Cu bilayers, we consider the spintransfer torque due to the spin current injected bytriggering the precession of the FeCo layer. The
divergence of the spin current Js is expressed by two
components, field-like and anti-damping terms, as
follows25),
1
sdivJ s = g? s ⇥ p + g//⇥ (s ⇥ p),
e
|s|

(2)

where e, s, and p are an electron charge, a local spin
vector per unit volume, and the spin direction of the spincurrent. g⊥ and g// are the coefficients of the field-like andanti-damping terms. By adding the spin current
contribution (Eq. (2)) to the following Landau–Lifshitz–
Gilbert equation,s⇥ ṡ ,ṡ = −γs ⇥ H e↵ − ↵e↵(3)|s|we have a differential equation for the magnetization

where g and Heff are a gyromagnetic ratio and an effective
field vector of GdFeCo layer. Here, we simply assumed
that p is parallel to Heff and also that the damping term
is much smaller than the precession term in Eq. (3). We
note that p is actually not parallel to Heff; however, thecomponent perpendicular to Heff has a smaller effect on
the precession frequency.
From the precession angular frequency for the GdFeCo/ Cu bilayers in Fig. 5, gHeff was roughly estimated to be
115 Grad/s around q H ~ 20˚. The precession angularfrequency reduced to ~100 Grad/s and ~104 Grad/s for
the GdFeCo / Cu (80) / FeCo and GdFeCo / Cu (120) / FeCo
trilayers, respectively. Thus, we can simply get g⊥ = 1.5 ×1010 s–1 and 1.1 × 1010 s–1 for the trilayers with tCu = 80
and 120 nm, respectively. Similarly, from the reductionof 1/t in the trilayers as shown in Fig. 6, we can roughly
obtain g// ~ –109 s–1 for both trilayers. One may note thatthe different sign between g⊥ and g//. This is consistent
with the results for the SOT of the GdFeCo / Ta bilayers,
where the sign of the field-like SOT changes across themagnetization compensation point and Gd21(Fe90Co10)79
exhibits a negative damping-like SOT and positive fieldlike SOT20). However, in the previous study, the field-like
SOT was reported to be much smaller than the dampinglike SOT, although the field-like g⊥ is roughly 10 times
larger than the anti-damping g// in this study. The
temperature increase of the GdFeCo layer due to thepump illumination is ruled out in describing the large
field-like g⊥, since the GdFeCo / Cu bilayers (see Fig. 5)
and GdFeCo / Cu / Pt / Cu /FeCo (see Appendix) did notshow a decrease in the precession frequency. The reason
for the large field-like g⊥ is partly due to the variation of
the effective anisotropy in GdFeCo between bilayer andtrilayer as described in Appendix, however more detailed
study will be necessary to discuss the effects onsuperdiffusive spin currents due to hot electrons26) andspin currents due to spin Seebeck effect10), 12). Also, thetime dependent spin current should be considered for thedetailed analysis10), 12). The superdiffusive spin current,
spin current due to spin Seebeck effect, and ultrafast
demagnetization of FeCo are considered to relax inpicosecond time scale, however, such pulse spin currents
may induce the precession of GdFeCo in nanosecond
timescale12). As described in Eq. (2), the decayed
precession of FeCo (see Apendix) will generate constantspin current in nanosecond time scale. The origin of thespin current for the precession of GdFeCo will be studiedin future work. Finally, we discuss the magnitude of Js
from the anti-damping |g//| ~ 109 s–1. If we assume thatthe net spin angular momentum per atom S and atoms
per unit volume N of GdFeCo are S = 0.1 and N = 6 × 1022
cm–3 27), respectively, the magnitude of local spin vector s

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4. Summary

The magnetization dynamics of GdFeCo / Cu / FeCo
trilayers after pumping the FeCo side with an ultrashortpulsed laser were studied and the results were comparedwith those of GdFeCo / Cu bilayers. The magnetic
properties of the GdFeCo / Cu / FeCo trilayers showedthat the GdFeCo layer exhibits perpendicular anisotropy,
and the GdFeCo and FeCo layers are considered to be
decoupled by a thick Cu layer. The precession amplitudeof the GdFeCo layer was confirmed to be enhanced bypumping the FeCo layer, and the amplitude decreased as
the intermediate Cu thickness increased. The precession
frequency and inverse of the relaxation time of the
GdFeCo layer were confirmed to be decreased bypumping the FeCo layer. The decreases in the precession
frequency and inverse of the relaxation time wereremarkable when the external field angle q H from thefilm normal was reduced. We considered spin transfer
torque due to the spin current injected by triggering theprecession of the FeCo layer to understand the themagnetization dynamics of the GdFeCo / Cu / FeCo
trilayers. Positive field-like and negative anti-damping
torques due to the injection of the spin current wereobtained, which is consistent with the results for the SOTof GdFeCo / Ta bilayers. From the magnitude of the antidamping torque (|g//| ~ 109 s–1), the spin current Js
injected from the FeCo layer can be expected to be ~ 1
MA/cm2. However, 10 times larger field-like torque than
the anti-damping torque was obtained, and further study
will be necessary to understand the magnetization
dynamics of GdFeCo / Cu / FeCo triggered by an
ultrashort pulsed laser.
Appendix

Effect of insertion of thin Pt in Cu layer
Figure A1 shows the external field angle q Hdependence of the precession angular frequency w of the
GdFeCo layer for the samples of GdFeCo / Cu (120),
GdFeCo / Cu (120) / FeCo, and GdFeCo / Cu (58) / Pt(4) /Cu (58). An external field Hext was 5 kOe and a pumpbeam of 120 mW was irradiated from the back side as inFig. 1 (a). The angular frequency w for the GdFeCo / Cubilayer monotonically increased as q H decreased, while w
for the GdFeCo / Cu / FeCo trilayer exhibited a maximum
near q H ~ 30 deg as discussed in Fig. 5. When a thin Pt(4 nm) layer was inserted in Cu layer, the reduction of w
at small q H disappeared as shown in Fig. A1. Thissuggests that the spin current produced by pumping the
FeCo layer was blocked by thin Pt layer, since Pt exhibits
much shorter spin diffusion length than Cu.

112

125

Angular frequency ω (Grad/s)

in Eq. (2) is calculated to be |s| = SN = 6 × 1021 cm–3.
Thus, Js is estimated to be Js = eg// |s|tGdFeCo ~ 1
MA/cm2 from Eq. (2), which will be sufficient enough to
induce the precession of the GdFeCo(tGdFeCo = 10 nm)
layer. Thus, it is concluded that a large Js of ~ 1 MA/cm2
is injected from the FeCo layer triggered by ultrashortpulsed laser.

J J J

110

J
J
J
J J J
J
J
J
J J J
J
J J
J J
J J
J
J J

95

80

Cu(120)/GdFeCo
J

FeCo/Cu(58)/Pt(2)/Cu(58)/GdFeCo

J
J

J J

J
J
J

FeCo/Cu(120)/GdFeCo
0

20

40

60

External field angle θH (deg)Fig. A1 External field angle q H dependence of theprecession angular frequency w of the
GdFeCo layer for the samples of GdFeCo /Cu (120), GdFeCo / Cu (120) / FeCo, and
GdFeCo / Cu (58) / Pt(4) / Cu (58) / FeCo. The
external field Hext was 5 kOe and the pumpbeam of 120 mW was irradiated from theback side as in Fig. 1 (a).

Magnetization dynamics of GdFeCo in trilayers
The magnetization dynamics of the GdFeCo in GdFeCo/ Cu / FeCo trilayers were confirmed by front sidepumping as shown in Fig. 1 (b). For the front sidepumping setup, the applied field angle can be varied q H= 40–85° from the film normal direction. Thus, we havemeasured w of the GdFeCo under the applied field Hext of
4–14 kOe along q H = 40˚. The Hext dependence of w was
fitted with Shul's equation28), and the detail of the fitting
was described in our previous paper29). Table A1summarizes Hkeff and g-factor of the GdFeCo for GdFeCo/ Cu / FeCo trilayers. Moreover, from the q H dependenceof w of the GdFeCo / Cu bilayers shown in Fig. 5, Hkeff andg-factor of the GdFeCo in GdFeCo / Cu bilayers were
estimated, which were also listed in Table A1. In Table
A1, the w values under the condition q H = 0 were also
listed, which were estimated using the following equation,µ0 e!=g(Hext + Hke↵ ),(A1)2mewhere µ0, e, me are the permeability of vacuum, electron
Table A1 g-factor, Hkeff and w at q H = 0˚ of GdFeCo
in GdFeCo/Cu bilayers and GdFeCo / Cu /FeCo trilayers.

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INDEX

charge, and electron mass, respectively. An external field
was Hext = 5 kOe. As in Table A1, due to the deviation in
Hkeff of the GdFeCo among 4 samples, the w values at q H= 0 deg were slightly distributed from 106 to 120 Grad/s.
However, the reduction of w at small q H as discussed inFig. 5 is not explained by the variation of theperpendicular anisotropy of the GdFeCo.
Magnetization precession of FeCo layer
The magnetization precession of the FeCo layer of
GdFeCo / Cu (80) / FeCo was monitored by TRMOKE,
where the pump and probe beams were irradiated fromthe substrate side (front side pumping). Figure A2 shows
the typical magnetization precession of the FeCo for apump fluence of 3.8 mJ/cm2, which corresponds to a pump
power of 300 mW. An external field of 7 kOe was appliedalong 40˚ from the film normal. Clear damped precession
was confirmed, and the waveform was fitted with thefunction,f (t) = A exp( t/⌧ ) sin(!tφ0 )+B exp( t/⌧0 ) + C ,(A1)

Fig. A3 Pump power dependence of the precession
amplitude of the FeCo layer for the samplesof GdFeCo / Cu (80) / FeCo trilayers, where
the pump beam was illuminated from thesubstrate side as in the schematic
illustrations. External field of 14 kOe wasapplied q H = 40˚ from the film normal.

where the w and t are the angular frequency and decayof the FeCo precession, respectively, and t0 is the decayof the recovery of the FeCo magnetization after the laser
induced demagnetization at t = 0. The coefficients A, B,
and C are fitting parameters, representing the amplitude
of FeCo precession, intensity of laser induced
demagnetization, and DC bias of the TRMOKE waveform,
respectively. Figure A3 shows the dependence of theprecession amplitude A on the pump power (pumpfluence). The precession amplitude of FeCo became
obvious when the pump power was more than 100 mW,
corresponding to a fluence of 1.25 mJ/cm2.
Figure A4 shows the dependence of the precession
amplitude of FeCo on the direction of the external field
Fig. A4 External field angle q H dependence of theprecession amplitude of the FeCo layer forthe samples of GdFeCo / Cu (80) / FeCo
trilayers, where the pump beam was
illuminated from the substrate side as in theschematic illustrations. Pump power was
300 mW and the external field of 7 kOe wasapplied.

Fig. A2TRMOKE waveforms of FeCo layer of
GdFeCo / Cu (80) / FeCo trilayer, where thepump beam was illuminated from thesubstrate side as in the schematic
illustrations. External field of 7 kOe wasapplied q H = 40˚ from the film normal.

q H from the film normal. From Fig. A4, the amplitudedecreased as q H increased, since the stable angle q of
FeCo moments from the film normal, which isdetermined by the competition between demagnetizing
field and external field, increases with increasing q H. In
Fig. A4, a curve fitted with a function of D sin2q· sinq ,which is proportional to the amplitude of magnetization
precession of the FeCo moment30), is also shown. It is
confirmed that the dependence of the precession
amplitude A on the direction of the external field q H isroughly fitted with the function of D sin2q· sinq.

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Acknowledgements The authors would like to thank Mr.
M. Kumazawa, Nagoya University for the assistance inthe experiments. This work was supported in part by
JSPS KAKENHI Grant Number of 17K19068 and
20H02182. This work was also supported in part by the
Project of Creation of Life Innovation Materials forInterdisciplinary
andInternational
Researcher
Development of the Ministry of Education, Culture,
Sports, Science and Technology (MEXT), Japan. A part ofthis work was performed under the Research Program of“Dynamic Alliance for Open Innovation Bridging Human,
Environment and Materials” in "Network Joint ResearchCenter for Materials and Devices." A part of this work
was conducted at the Next-generation biomaterials Hub,
Nagoya University, supported by "Advanced Research
Infrastructure for Materials and Nanotechnology inJapan" of MEXT, Japan.
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R eceiv ed S e p . 2 9 , 2 0 2 2 ; A ccep ted M a r. 2 9 , 2 0 2 3

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Copyright ©2023 by the Magnetics Society of Japan.
This article is licensed under the Creative Commons Attribution International License (CC BY 4.0)
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J. Magn. Soc. Jpn., 47, 115-117 (2023)<Letter>First-order reversal curve analysis of superparamagnetic nanoparticles
with oriented easy axis of magnetization
Eisuke Sasaoka, Chao Yang*, Suko Bagus Trisnanto, Zenglu Song*, Satoshi Ota**, andYasushi Takemura

Division of Electrical and Computer Engineering, Yokohama National University, Yokohama 240-8501, Japan*

School of Electrical Engineering, Nanjing Vocational University of Industry Technology, Nanjing 210023, China**

Department of Electrical and Electronic Engineering, Shizuoka University, Hamamatsu 432-8561, JapanWe analyzed the magnetization process of magnetic nanoparticles using first-order reversal curve (FORC) analysis
and verified a superparamagnetic feature and the orientation of the easy axis of the particles. The FORCs and FORC
diagram of magnetic nanoparticles dispersed in water exhibited a superparamagnetic feature. The differences in themagnetizations and distributions of the coercive force of the solid-state samples were used to identify the orientationof the easy axes of magnetization.
Key words: magnetic nanoparticles, first-order reversal curve (FORC), superparamagnetism, magnetic anisotropy,
magnetization easy axis
1. Introduction

2. Experimental method

Magnetic nanoparticles are expected to be used invarious biomedical applications1). To prevent aggregationof particles in blood vessels, superparamagnetic
nanoparticles with diameters of or less than 10–20 nm
and exhibiting no residual magnetization have been
widely studied. In our previous studies, we reported thestatic and dynamic magnetization properties of magnetic
nanoparticles and found that the self-heating
characteristic of hyperthermia can be enhanced byorienting the easy axes of the magnetic particles2-4).
The current study aims to evaluate the magnetization
properties of magnetic nanoparticles with oriented or
non-oriented easy axes. We performed a first-orderreversal curve (FORC) analysis5,6). FORC is an advanced
hysteresis measurement method used for deriving the
distribution of and information regarding themagnetization properties of magnetic materials, which
can otherwise not be achieved using the normal
hysteresis curves of magnetization measurement thatprovides a total or average magnetization property inmagnetic materials.
In this paper, we report a superparamagnetic featureand the distribution of the coercive force ofsuperparamagnetic nanoparticles evaluated using FORC
analysis. A reversible change in magnetization without
any remanent magnetization or a coercive field wasobserved in the magnetic nanoparticles dispersed in aliquid medium; however, remanent magnetization was
clearly observed in the nanoparticles that remained fixed
in a solid state. The distribution of the coercive force andinteraction fields according to the direction of the easy
axis of magnetization was identified in the FORC
diagrams of the solid-state samples.

A commercial magnetic fluid distributed as a contrast
agent in magnetic resonance imaging, Resovist®
(FUJIFILM RI Pharma, Japan), was employed in thisstudy. It contains multi-core particles of γ-Fe2O3
dispersed in water. The single core diameter and effective
multi-core diameter were 5–10 nm and 5–30 nm,
respectively7,8). We prepared three samples from
Resovist®: one liquid sample and two types of solid
samples. The density of all the samples was adjusted to
2.8 mg-Fe/ml. The liquid sample was prepared bydiluting Resovist® whose original density was 28 mgFe/ml.
The solid samples were prepared by mixing Resovist®
with epoxy (CEMEDINE, Japan). A DC magnetic field of
μ0H = 870 mT was applied to one of the solid samples
using NdFeB magnets during epoxy solidification. The
magnetization of the original Resovist® in its liquid state
under this intensity of the applied magnetic field was
0.95 M/Ms, where M/Ms denotes the magnetization
normalized by saturation. The easy axes of the magnetic
nanoparticles were aligned in this solid sample. The
magnetic field applied during the FORC measurement of
this sample was either parallel (easy axis field) or
perpendicular (hard axis field) to the oriented easy axis,
respectively, as shown in Fig. 1.
Another solid sample was prepared without applying amagnetic field during the epoxy solidification. The easy
axes of the particles were randomly oriented. The detailsof the sample preparation and both static and dynamic
magnetization measurements have been previously
reported3,4).
Static magnetization curves, including the FORCs,
were measured using a vibrating sample magnetometer(model 8600 series, Lake Shore Cryotronics, USA) atroom temperature.

Corresponding author: Yasushi Takemura(e-mail: takemura@ynu.ac.jp).

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Fig. 1
Preparation of liquid and solid samples.
Magnetic field applied in FORC measurements waseither parallel (easy axis field) or perpendicular (hardaxis field) to oriented easy axes of solid sample.
3. Results and discussion
The FORCs were first measured, and the samples weresaturated in a large positive field, Hsat = 2.0 T/μ0. Then,the applied field intensity was decreased, thereby
forming a reversal magnetic field, Ha = −2.0 T/μ0. FORC
is defined as the magnetization curve derived byincreasing Ha to Hsat. This process was repeated forseveral values of μ0Ha to yield a series of FORCs. A sweep

rate of the applied magnetic field was 5 mT/s.
Figures 2(a)–(d) show the FORCs of the liquid,
random-oriented, and oriented easy axis samples,
respectively. As can be seen, the FORCs of the liquidsample exhibit a superparamagnetic feature without acoercive field and any remanent magnetization. The
curves traced using various overlapping values of Ha
suggest a reversal of magnetization. The two solid
samples exhibit remanent magnetization due to the fixed
easy
axes
havingmagnetic
anisotropy.
Themagnetization of the liquid sample is greater than thatof the randomly orientated solid sample because of theadditional magnetization reversal caused by particle
rotation4). The differences observed in the magnetization
processes of the three solid samples are consistent withthe previously reported major and minor magnetization
loops of our similar samples3).
The FORC distribution is defined as a mixed second
derivative and can be expressed as follows:𝜌𝜌�𝐻𝐻� , 𝐻𝐻� � � ��� ���� , �� ���� ���

(1)

Here, the magnetization value measured under a specificapplied magnetic field, μ0Hb is defined as M (Ha, Hb),
where Hb ≥ Ha. The calculated FORC distributions aredescribed as a contour plot of the parameter space of Ha
and Hb, which is called a FORC diagram6). To analyze thecoercive field, Hc, and the interaction field, Hu, the FORC
distribution of 𝜌𝜌�𝐻𝐻� , 𝐻𝐻� � was obtained via coordinate

Fig. 2 Magnetization reversal curves, FORCs (a-d) and FORC diagrams (e-h): (a, e) liquid sample, (b, f) randomoriented sample, (c, g) oriented sample under easy axis field, and (d, h) oriented sample under hard axis field.
Colors in FORC and FORC diagrams of each sample are corresponding.

116

Journal of the Magnetics Society of Japan Vol.47, No.4, 2023

INDEX

transformation as follows:

μ0Hc � �μ0Hb �μ0Ha�/2

μ0Hu � �μ0Hb � μ0Ha�/2

�2�

�3�

An open-source software, FORCinel9) was used for
calculating the FORC distributions.
Figures 2(e)-(h) show the FORCs of the four samples.
The colors in the FORCs and FORC diagram of eachsample are corresponding. As shown in Fig. 2(e), theliquid sample has a negligible change of intensity in the
FORC distribution, 𝜌𝜌�𝐻𝐻� , 𝐻𝐻� � ; this change caused byslightdeviations
fromtheseveralrepeatedmagnetization curves.
A significant finding in this study is the apparent
differences in the FORC diagrams of the solid samples
depending on the orientation of the easy axis ofmagnetization. The peaks of 𝜌𝜌�𝐻𝐻� , 𝐻𝐻� � in the FORC
diagrams of the solid samples are observed on the Hu axis,
where Hc=0, suggesting that the magnetization property
is dominantly superparamagnetic. The diagram of therandomly oriented sample shows a distribution of thecoercive field in the range of 0–1 mT/μ0, as shown in Fig.
2(f). The particle diameter of Resovist® has a wide
distribution and ranges between 5 and 30 nm7,8). The
coercive force of the solid samples is commonly attributed
to the larger particles exhibiting ferromagnetism. The
distributions of 𝜌𝜌�𝐻𝐻� , 𝐻𝐻� � along the Hc axis of the solid
samples are attributed to the ferromagnetic particles,
whose contribution monotonically increases withincreasing their diameter. Additionally, the enhanced
anisotropic energy associated with the binding of theeasy axis induces a coercive field in the solid samples10,11).
The ferromagnetic particles in the liquid sample do notshow a coercive force because of particle rotation that is
sufficiently activated at room temperature. Thesefeatures are supported by Brownian and Néel relaxation
times depending on a particle diameter12). As for a 30-nm
particle, the Néel relaxation time is sufficiently long for
exhibiting ferromagnetism of solid samples. The
Brownian relaxation time is approximately 10 µs forparticles with 5–30 nm, resulting in superparamagnetic
properties of liquid samples.
The coercive field under an applied field along the easy
axis is more widely distributed toward the greater range
than that of the randomly oriented sample and under the
hard axis field. This demonstrates an enhanced magnetic
anisotropy caused by the alignment the easy axis ofmagnetization. Opposingly, the coercive field under the
hard axis field is the lowest among three measurementsof the solid samples as shown in Figs. 2(f)-(h). Thisdenotes magnetization rotation with small amplitude
responding to an applied magnetic field with small
intensity. The wider distribution of 𝜌𝜌�𝐻𝐻� , 𝐻𝐻� � under the

hard axis field is observed along the large Hc region thanthose of the other solid samples. This suggests thatfurther rotation of magnetization toward the direction ofan applied field, which is a hard axis of magnetization
with higher anisotropic energy, requires an applied fieldwith higher intensity.
As shown by the dotted line in Figs. 2(f)-(h), a slightdifference in the distributions of the interaction field, Hu,
reflecting the magnetic interaction between theparticles13) was observed in the solid samples. However,
the intrinsic mechanism modifying Hu by the orientationof the easy axis of magnetization is not elucidated in thisstudy.
In summary, the FORCs and FORC diagrams of themagnetic nanoparticles were studied. The liquid sample
exhibited a superparamagnetic feature; however, thesolid samples had coercive forces depending on theorientation of the magnetization easy axes. These results
are explained by the distribution of particle size in thesamples and the magnetic anisotropy associated with theeasy axis of the samples.
Acknowledgements This work was partially supportedby the JSPS KAKENHI JP20H05652 and JP20H02163.
References
1) Q. A. Pankhurst, N. K. T. Thanh, S. K. Jones, and J. Dobson:
J. Phys. D, 42, 224001 (2009).
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Enpuku, T. Viereck, M. Schilling, and F. Ludwing: J. Magn.
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3) G. Shi, R. Takeda, S. B. Trisnanto, T. Yamada, S. Ota, and
Y. Takemura: J. Magn. Magn. Mat., 473, 148 (2019).
4) T. Yamaminami, S. Ota, S. B. Trisnanto, M. Ishikawa, T.
Yamada, T. Yoshida, K. Enpuku, and Y. Takemura: J. Magn.
Magn. Mat., 517, 167401 (2021).
5) S. Okamoto, T. Yomogita, K. Miyazawa, N. Kikuchi, O.
Kitakami, N. Watanabe, and N. Suita:. Mater. Jpn., 56, 533(2017) [in Japanese].
6) C. Pike, A. Roberts, and K. Verosub: J. Appl. Phys., 85, 6660
(1999).
7) S. Ota, S. B. Trisnanto, S. Takeuchi, J. Wu, Y. Cheng, and Y.
Takemura: J. Magn. Magn. Mat., 538, 168313 (2021).
8) T. Yoshida, N.B. Othman, and K. Enpuku: J. Appl. Phys.,
114, 173908 (2013).
9) R. J. Harrison and J. M. Feinberg: Geochem. Geophys.
Geosyst., 9, Q05016 (2008).
10) R. Takeda, S. Ota, T. Yamada, and Y. Takemura: J. Magn.
Soc. Jpn., 42, 56 (2018).
11) S. Ota and Y. Takemura: J. Magn. Soc. Jpn., 43, 34 (2019).
12) R. Kötitz, W. Weitschies, L. Trahms, W. Brewer, and W.
Semmler: J. Magn. Magn. Mater., 194, 62 (1999).
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Miyamura, and B. Jeyadevan: J. Phys. Commun., 5, 045003(2021).
Received Jan. 03, 2023; Revised Jan. 31, 2023; Accepted Apr. 20,
20 23

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Copyright ©2023 by the Magnetics Society of Japan.
This article is licensed under the Creative Commons Attribution International License (CC BY 4.0)
http://creativecommons.org/licenses/by/4.0/

J. Magn. Soc. Jpn., 47, 118-127 (2023)<Paper>Development of Ultra-Low Field Magnetic Resonance Imaging System at 1 mT
D. Oyama1, N. Tsuyuguchi1,2,3, J. Hirama4, Y. Adachi1, and J. Kawai1

1Applied Electronics Laboratory, Kanazawa Institute of Technology, 3 Amaike, Kanazawa, Ishikawa, 920-1331, Japan

377-2 Ono-higashi, Osakasayama, Osaka, 589-8511, Japan
1-10-3 Daikoku, Naniwa, Osaka, Osaka, 556-0014, Japan
4 Department of Electrical and Electronics Engineering, Kanazawa Institute of Technology, 7-1 Ohgigaoka, Nonoichi, Ishikawa,
921-8501, Japan
2 Department of Neurosurgery, Kindai University,
3 Neurosurgery, Naniwaikuno Hospital,

Ultra-low field (ULF) magnetic resonance imaging (MRI) is considered an innovative MRI technique that can be
combined with magnetoencephalography (MEG). In this study, a 1-mT ULF-MRI system without a pre-polarization
technique aiming at combining an MEG system is developed. The intensity of the static magnetic field B0 is decided
considered to be 1 mT because of the limitation of the magnetic field exposed to our MEG sensor made ofsuperconducting quantum interference devices (SQUIDs). A square-shaped (750 mm × 750 mm) B0-coil based on a
Merritt-type configuration is fabricated. The inhomogeneity of B0 is less than 0.07 % in the ±125 mm area. Further,
an induction coil is employed to detect the magnetic resonance signal instead of the SQUID sensors of the MEG to
confirm the feasibility of realizing MRI measurement at 1 mT without the pre-polarization technique. Relaxation timemeasurements and MR imaging of a phantom made of a CuSO4 aqueous solution are performed. Reasonablelongitudinal and transverse relaxation times are obtained, and clear shapes of the phantom are obtained using thegradient- and spin-echo pulse sequences with this ULF-MRI system. These results indicate the potential of the
proposed 1-mT ULF-MRI to effectively integrate ULF-MRI and MEG systems without pre-polarization.
Key words: magnetic resonance imaging, magnetoencephalography, ultra-low field MRI
1. Introduction
Magnetic resonance imaging (MRI) is an indispensable
imaging tool used in modern medicine. Superconducting
magnets are widely used in clinical applications togenerate a high magnetic field (>1 T) because theamplitude of the MR signal is approximately
proportional to the square of the magnetic flux density.
Therefore, the quality of the obtained MR image cangenerally be improved by increasing the static magnetic
field B0 of the MRI.
Recently, MRI systems with much lower magnetic
fields have been developed1). A lower magnetic field hassome benefits to compensate for some of thedisadvantages of high-field MRIs, such as initial andrunning costs, portability, weight, size, sound noise, andsafety. Several research groups have developed low-field
MRI systems using magnetic fields between several mT
to several tens of mT and realized the imaging of ahuman head with a quality to distinguish some lesions2)–
4).
Further, MRI measurements in the magnetic fields ofmicro-Tesla range, called ultra-low field MRI (ULF-MRI),
have also been studied as innovative MRI since the early
2000s5)–7). An expected application of the ULF-MRI is
combining it with magnetoencephalography (MEG)
measurements. MEG observes the magnetic signals
generated by neuronal activities in the human brain
using ultra-high-sensitivity magnetic sensors, such as                     Corresponding author: D.
neptune.kanazawa-it.ac.jp).

118

Oyama

(e-mail:superconducting quantum interference devices (SQUIDs).
The source of the magnetic signal can be estimated from
the MEG signal detected by a multi-channel magnetic
sensor array, normally several tens or over 100 channels.
An anatomical image is necessary to precisely estimate
the signal source and show the results of signal source
localization. MR images are commonly employed for thispurpose; however, the co-registration error between the
MEG and MRI systems causes source localization errors.
Therefore, both MEG and MRI data must be acquired
using a single modality. High-field MRI cannot be
combined with the MEG machine because a highmagnetic field, which is usually greater than the criticalmagnetic field of SQUID, disrupts the superconductivityof SQUID sensors. ULF-MRI has the best prospect for
combining the MEG and MRI measurements.
Several research groups have developed SQUID-based
ULF-MRI systems using magnetic fields ranging fromtens of T to 200 T to capture human head MR image8)14). We also developed a ULF-MRI system to combine
small-animal MEG with a B0 of 33 T15), 16). In these ULFMRI systems, a pre-polarization technique that applies amagnetic field pulse (Bp-pulse) to the samples or subjects
was used to increase the amplitude of the MR signal. The
Bp-pulse has to be much stronger than B0; therefore, theintensities of the Bp-pulse in previous studies were morethan 10 mT (sometimes over 100 mT). Even though theprotection techniques for SQUID sensors have been
proposed and included in the developed ULF-MRI
systems7), 9), 10), 17), 18), some difficulties still arise for theiroyama@

Journal of the Magnetics Society of Japan Vol.47, No.4, 2023

DCPS (±28V)

Amplifier(Gradients)

DCPS (±12V)
D/A

Amp. (RF)Amplifier andband-pass filter

Gradient &RF coils
B0 coil
Magnetically shielded room

Fig. 1

D/A
DCPS (±12V)
A/D

Measurement& Control
software

DCPS (±12V)※ DCPS : DC Power Supply

Computer

Block diagram of our ULF-MRI system.

practical applications, such as increase in themeasurement time due to applying the Bp-pulse,
difficulty in avoiding the eddy current in the metalmaterial such as electromagnetic shields, and increasing
the equipment scale to generate the Bp-pulse.
The purpose of this study is to develop a ULF-MRI
system integrated with MEG. Rather than applying a Bppulse to boost the amplitude of the MR signal to be
detected, the static magnetic field was increased from 33
T to 1 mT. As described above, increasing B0 not only
increases the amplitude of the MR signal but also affects
the SQUID sensors. The static magnetic field was set to
1 mT, in reference to the limitation in the magnetic field,
whereby the SQUIDs of the MEG system could maintaintheir frequency response sufficient for detecting the MR
signal (refer to Appendix A).
However, no research has been conducted todemonstrate the possibilities of MRI measurement at
approximately 1 mT1). This study aims to fabricate a 1mT ULF-MRI system and reveal the advantages,
possibilities, and problems in realizing MRI
measurements at 1 mT without pre-polarization
techniques. Section 2 presents the system configuration.
Sections 3 and 4 present some experiments, including
relaxation time and MRI measurements using a phantom.
Section 5 discusses the advantages and problems of the 1-mT ULF-MRI.
2. Instrumentation
2.1 System overview
Fig. 1 shows the configuration of the ULF-MRI system.
The coil set to generate the B0-field, gradient fields, andRF pulse was installed inside a magnetically shieldedroom made of two layers of mu-metal and one layer ofcopper.
These coils were driven by current-amplifierelectronics. The DC current of the B0-coil was manually
tuned to generate the desired magnetic field density. The
current pulses for the gradient fields and RF pulse are
generated by digital-to-analog (D/A) converters (for thegradient fields: DAQe-2502, ADLINK Inc., for the RF
pulse: PCIe-6353, National Instruments) with sampling
frequencies of 100 kHz and 2 MHz, respectively.
Further, an induction coil was employed to detect theMR signal instead of SQUID sensors to demonstrate thepossibility of MRI measurements without prepolarization at 1 mT. The induced voltage was recorded
using an analog-to-digital (A/D) converter (PCIe-6353,

DC
B 99 234 turns
A
845
234 99helmet for Region of interest
MEG cryostat
subject’s headB0 coil≒200

Amplifier (B0)750

Detection coil

750

INDEX

Z
Y
X

750
90

38

38

90

≒180

750

Fig. 2 Simplified drawings of the designed static
magnetic field (B0) coil and the MEG cryostat.
National Instruments) with a sampling frequency of 1.25
MHz. Although a high-field MRI system typically uses a
signal mixer to generate the RF pulse or record the MR
signal, the proposed system generates the RF pulse andrecords the MR signal directly by the D/A and A/Dconverters because the sampling frequencies of thedevices are much higher than the signal frequency(approximately 42–43 kHz).
2.2 B0-coil
A Merritt-type configuration was employed for the B0coil19). The Merritt-type configuration generates a
uniform magnetic field distribution compared with othercoil configurations, such as the Helmholtz-type
configuration coil20). One purpose for developing the
ULF-MRI was to combine it with our MEG system21). Fig.
2 shows simplified drawings of the designed B0-coil which
is virtually combined with the MEG cryostat. To observe
the human head, the size of the region of interest (ROI)
and length of the coil side were set to 250 and 750 mm,
respectively.
The total number of turns of the coil was 666 and theestimated magnetic flux density was 1.0 mT by applying
an electric current of 1.79 A. A copper wire with adiameter of 1.4 mm was wound on a frame made of resin.
The total resistance and inductance were 24.1  and 300
mH, respectively. The total weight of the B0-coil wasapproximately 30 kg. The coil frames, labeled as A-D
shown in Fig. 2 (a), can be separated; therefore, this B0coil can be easily carried and assembled by a single
person.
Fig. 3 shows the magnetic field inhomogeneity of theB0-field calculated based on the B0-coil design. The
magnetic field strength can be calculated using the Biot–
Savart law, assuming a 666-turn coil as 2664 (4×666)
linear currents. Inhomogeneity was defined as thedifference from the magnetic flux density at the coilcenter (X = 0, Y = 0, and Z = 0) in percentage. An
inhomogeneity of less than 0.07 % (700 ppm) was
obtained in the designated ROI (±125 mm), as indicatedby dashed lines.
Typically, a magnetic field inhomogeneity of less than
50 ppm is necessary for high-field MRIs. To confirm thatthe uniformity of our B0 field has acceptable for MRI
measurements, an MRI measurement was simulated

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Region of interest (±125 mm)

Gz-coil

Region of interest (±125 mm)

RF-coil

Z (mm)Y (mm)

Gy-coilGx-coilZ
Y (mm)Y

X (mm)

Fig. 3 Calculated magnetic field distribution of thedesigned B0-coil; owing to the symmetry, thecalculation is performed only in positive quadrants(X ≧ 0, Y ≧ 0, and Z ≧ 0). The values on thecontour lines indicate the difference in percentage
from the magnetic flux density at the center of thecoil (X = 0, Y = 0, and Z = 0).
50 mm

Y

X

Y

750 mm50 mm

Z

detectioncoil(f 360 mm)

100 mm(a)

X (mm)
0
-62.5
125

125

62.5

62.5

X (mm)
0
-62.5

-125

-125

(b)

-125

-62.5

0
Y (mm)

(c)

62.5

125

-125

-62.5

0
Y (mm)

62.5

125

(d)

Fig. 4 Simulation of the effect of the distortion of thestatic magnetic field. (a) Simulation model, (b)arrangement of the coils, (c) obtained MR image at 1
mT, and (d) obtained MR image at 10 mT.
using the calculated magnetic field distribution; thesimulation conditions are shown in Figs. 4 (a) and (b).
The subject model of the MRI simulation consisted of 13
cylinders, as shown in Fig. 4 (a), and a circular coil witha diameter of 360 mm was assumed as the detection coil,
as shown in Fig. 4 (b). The MR signals were calculated
assuming the gradient-echo pulse sequence, andsubsequently, the MR images were reconstructed. The
algorithm of the simulation is presented in Appendix B.
To reduce the calculation time, two-dimensional (2D)
imaging in the X-Y plane sequences was assumed, andthe reconstructed images showed the projection image on
the Z-axis. For comparison, MRI measurements at 1 and10 mT were simulated, as shown in Figs. 4 (c) and (d),respectively. The magnetic field distribution with B0 = 10mT was calculated by applying an electric current of 17.9

120

X

Fig. 5 Coil-set for the gradient magnetic field andRF pulse coils.
A to the designed B0-coil. Therefore, the magnetic field
inhomogeneity was same as that shown in Fig. 3. As
shown in Fig. 4 (c), an MR image indicating 13 cylinders
was obtained with B0 = 1 mT. In contrast, the MR image
obtained with B0 = 10 mT was distorted owing to thestatic magnetic field inhomogeneity as shown in Fig. 4 (d).
These results show that the designed B0-coil has
sufficient magnetic field homogeneity for 1-mT ULF-MRI
measurements.
2.3 Current driver for the B0-coil
The signal frequency is given by fsignal = ・B0, where is the geomagnetic ratio (42.58 MHz/T for proton).
Therefore, the signal frequency is 42.58 kHz when B0 is
1 mT. The stability of the B0-field is important for
obtaining clear MR images. The current driver circuit for
the B0-coil was fabricated using a constant-current
circuit configuration to maintain the current fluctuation
within 1 mA. The corresponding fluctuation in B0 and
fsignal were calculated as 559 nT ( 1mT / 1.79 A × 1 mA)
and 23.8 Hz, respectively.
A dropper-type DC power supply (GPP-4323G, Good
Will Instrument Co., Ltd.) was selected to eliminate
magnetic noise from the power supply to the MRI and
MEG systems. The use of a benchtop DC power source
also helped keep the system compact. The power
consumption necessary to apply 1.79 A to the B0-coil was
estimated to be 77.2 W ( 24.1  × (1.79 A)2 ).
2.4 Gradients and RF pulse coils
In this study, these coils were designed to realize afield-of-view (FOV) of 120 mm for confirmation of themeasurement principle. Fig. 5 shows the coil set for thegradient field and RF pulse. This coil set was installed at
the center of the B0-coil that generates a static magnetic
field in the y-direction. The designed gradient fields were
GX = dBY/dX = 398 nT/mm/A, GY = dBY/dY = 631 nT/mm/A,
and GZ = dBY/dZ = 418 nT/mm/A.
The orientation of the RF pulse was set in the xdirection, and the strength of the RF pulse was calculated
minimized at 42.6 kHz, which corresponds to the Larmor
frequency of the proton at 1 mT by attaching acapacitance in series to the RF coils.

Journal of the Magnetics Society of Japan Vol.47, No.4, 2023

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0.1 % CuSO4
aqueous solution

f 62
90

f 50
f 42
f 30
f 22

(mm)

Fig. 7

Dimension of a phantom used for experiments.

RF
pulse

SignalFig. 6 Block diagram and characteristics of thedetection unit: (a) block diagram, (b) sensitivity
coefficient, and (c) noise spectrum.
2.5 Detection coil and amplifier
The detection coil has inner diameter, outer diameter,
and length of 76, 90, and 80 mm, respectively. The coil
was wound using a Litz wire and 583 turns in six layers.
The inductance and internal resistance of the coil were
17 mH and 9 , respectively. Fig. 6 shows the block
diagram and characteristics of the detection unit
consisting of the detection coil, amplifier (61 dB), and aband-pass filter (12–75 kHz).
Figs. 6 (b) and (c) show the sensitivity coefficient andnoise spectrum of the detection unit output, respectively.
The sensitivity coefficient was measured by applying auniform magnetic field to the detection coil, and the noiselevel was recorded when the current driver circuits forthe coil set were turned off. Although an additional
capacitor to make the LC resonance circuit was not
implemented between the detection coil and amplifier, apeak at 43 kHz appeared in both graphs. The LC
resonance was assumed to occur due to the inductanceand stray capacity of the detection coil and input
capacitance of the amplifier circuit. The sensitivity
coefficient and voltage noise at 43 kHz were 4.6 V/nT and
16.7 V/Hz1/2, respectively. Therefore, the corresponding
noise level of the detection unit was estimated to be 3.6
fT/Hz1/2 at 43 kHz.
3. Experimental Method
3.1 Sample
Herein, the experiments were conducted using aphantom to confirm the feasibility of our MRI system.
The concentric container was made from acrylic plastic
tubes, and the gaps in the tubes were filled with a 0.1 %copper sulfate (CuSO4) aqueous solution, which is
employed for conventional MRI phantoms. The total
volume of the aqueous solution was approximately 190 g.

TR
180°

90°

180°

tI

SIR

(a)
RF
pulse

Signal

TR
90°

180°

tE /2

tE /2

90°

SSE

(b)
Fig. 8
Pulse sequences for relaxation timemeasurement: (a) inversion recovery sequence and (b)spin-echo sequence.
3.2 Relaxation time measurements
To design the pulse sequence for MRI measurements,
the relaxation time of the aqueous solution of thephantom must be known. Herein, the relaxation time
was measured using the inversion recovery (IR) sequence
for the longitudinal relaxation time (T1) and the spinecho (SE) sequence for the transverse relaxation time (T2),
as shown in Fig. 8.
In the IR sequence, 180° and the 90° pulses wereapplied to the phantom, and the free-induction-decay(FID) signal was observed immediately after the 90°
pulse. By changing the time gap of the pulses (tI), theamplitude of the FID signal SIR varied as follows.
𝑡𝑡

− 𝐼𝐼

𝑆𝑆𝐼𝐼𝐼𝐼 (𝑡𝑡𝐼𝐼 ) = 𝑆𝑆0,𝐹𝐹𝐹𝐹𝐹𝐹 × (1 − 2𝑒𝑒 𝑇𝑇1 ) ,(1)where S0,FID is the FID signal amplitudes when the
protons are in the thermal equilibrium state. The
relaxation time T1 is the time constant of the exponential
curve; thus, it can be estimated by solving an inverse
problem, such as the least-squares method. Herein, T1
relaxation time was measured with tI = 20, 30, 40, … 330
ms and a repetition time of TR = 800 ms.
In the SE sequence, the 90° and the 180° pulses wereapplied to the phantom with a time gap tE/2;
subsequently, the echo signal was observed tE/2 after the
180° pulse. By changing tE, the amplitude of the echo
signal SSE varied as follows.
𝑡𝑡

− 𝐸𝐸

𝑆𝑆𝑆𝑆𝑆𝑆 (𝑡𝑡𝐸𝐸 ) = 𝑆𝑆0,𝑆𝑆𝑆𝑆 × 𝑒𝑒 𝑇𝑇2 ,(2)where S0,SE is the echo-signal amplitudes when tE is

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121

Voltage (mV)INDEXTime (ms)Signal density (a.u.)(a)Frequency (Hz)(b)

Fig. 9 Pulse sequences for MRI measurements: (a)spin-echo and (b) gradient echo.

Fig. 10 Results of the spin-echo signal recording: (a)waveform and (b) frequency spectrum.

assumed to be zero. Similar to the T1 relaxation time, thevalue of T2 can be estimated by solving the inverse
problem. Herein, the T2 relaxation time was measured
with tE = 20, 30, 40, … 330 ms and a repetition time of TR= 800 ms.

measurements. Herein,  for the GE sequence was 72°.

3.3 Imaging
In this study, two pulse sequences, namely spin-echo
and gradient-echo (GE) sequences, were demonstrated
for the 2D MRI measurements, as shown in Fig. 9.
Generally, the SE sequence is more robust against theinhomogeneity of the static magnetic field compared with
the GE sequence; however, it requires a longer
measurement time because the repetition time (TR) mustbe much longer than the T1 relaxation time of theaqueous solution. The GE sequence is easily influenced
by the inhomogeneity of the static magnetic field;
however, the measurement time can be reduced by short
TR with an arbitrary flip angle () of the RF pulse.
These encoding schemes were designed based on the
2D Fourier protocol with a frequency encoding gradient
GY = ±195 nT/mm (8.33 Hz/mm, 31.25 Hz/pixel) and aphase-encoding gradient GX = ± 390 nT/mm/32-steps(1.04 Hz/mm). The size of the produced image was 32 ×
32 pixels, and the FOV was set to 120 mm × 120 mm in
the X- and Y-directions, respectively. Therefore, the pixel
size was calculated to be 3.75 mm × 3.75 mm.
The timing parameters of TR and TE for the SE pulse
sequence and TR for the GE sequence were 350, 32, and100 ms, respectively. These values were defined based on
the relaxation-time measurements reported in the next
section. The recording was repeated 100 times foraveraging; therefore, the total acquisition times were1120 and 320 s for the SE and GE sequence, respectively.
The amplitude and exposure time of the RF pulse were
adjusted to maximize the MR signal before the MRI

122

4. Results
A direct current was applied to the gradient coils tocompensate for the static magnetic field inhomogeneity
owing to the background magnetic field distribution in
the MSR. The intensity of the applied current was tuned
to maximize the amplitude of the observed magnetic
resonance signal.
4.1 Spin-echo signal
First, the SE signal was recorded to confirm that theMR signal can be detected by the 1-mT MRI system. The
pulse sequence shown in Fig. 8 (b) with tE = 20 ms wasused for measurements. Each data point was obtained by
100-times averaging and applying a digital band-passfilter (42.6±0.5 kHz) after recording.
The shape of the obtained echo signal is shown in Fig.
10 (a). The spin-echo magnetic resonance signal istypically observed as a bilaterally symmetric waveform,as shown in Fig. 8 (b). In this experiment, the attenuation
time of the magnetic resonance signal caused by theinhomogeneity of the static magnetic field, usuallydenoted as T2*, was much longer than the echo time tE.
Therefore, the echo signal was observed as a simple
attenuation waveform, not bilateral symmetry.
Fig. 10 (b) shows the frequency spectrum of theobserved signal. The peak frequency of 42.57 kHz wasgood agreement with the Larmor frequency at 1 mT.
Therefore, it was confirmed that the SE signal was
successfully observed by the 1-mT ULF-MRI system
without pre-polarization technique.

Journal of the Magnetics Society of Japan Vol.47, No.4, 2023

measured
estimated(i)Voltage (mV)

Signal intensity (a.u.)

INDEX

(ii)

tI (ms)Time (ms)

(a)

(a)

(ii)

Voltage (mV)measuredestimated

Signal intensity (a.u.)frequency-converted(i) by SINE function(ii) by COSINE function(i)Time (ms)tE (ms)4.3 Imaging
Fig. 12 shows the results of the MRI measurements
using the GE and SE sequences, as shown in Fig. 9. The
recorded data were preprocessed (100-times averaging
and band-pass filtered), as described in subsections 4.1
and 4.2; subsequently, they were digitally frequencyconverted using the sine and cosine function with afrequency of 42.6 kHz corresponding to the Larmor
frequency at 1 mT. Figs. 12 (a) and (b) show the

-60
60

30

X (mm)0 -30-60
X (mm)
0 -30
30

-60

-30

30
0
Y (mm)

60

-60

(c)

-30

30
0
Y (mm)

60(d)
Pixel intensity (a.u.)

4.2 Relaxation time
Fig. 11 shows the results of the relaxation timemeasurements for (a) T1 and (b) T2 relaxation times. The
recorded data were preprocessed (100-times averaged
and band-pass filtered), as described in the data shownin Fig. 10, and then the signal amplitudes SIR and SSE
were calculated and plotted in Figs. 11 (a) and (b) as
circles, respectively. The lines are the fitting curves
obtained using the estimated variables included inequations (1) and (2). The relaxation times T1 and T2 ofthe phantom were estimated as 71.7 ms and 69.6 ms,
respectively. The timing parameters of TR and TE for the
SE imaging sequence were TR > T1 and TE < T2.

60

Additionally, the sufficient stability of the signal
frequency was also confirmed by continuous recording of
the SE signal. The frequency shift in 3 hours wasapproximately 14 Hz (refer to Appendix C). This signal
frequency shift is less than 31.25 Hz, which corresponds
to one pixel of the MR image in the frequency-encoding
direction as defined in Subsection 3.3, confirming thatthe generated static magnetic field is sufficiently stablefor ULF-MRI measurements.

(b)

Pixel intensity (a.u.)(b)Fig. 11
Results of the relaxation timemeasurements: (a) T1 and (b) T2 relaxation time.

frequency-converted(i) by SINE function(ii) by COSINE function

Y (mm)Y (mm)(e)(f)

Fig. 12 Results of the MR imaging using the (a), (c),(e) spin-echo and (b), (d), (f) gradient-echo sequences;(a), (b) observed echo signals, (c), (d) reconstructed
MR images, and (e), (f) pixel intensity along the line
indicated by arrows in (c) and (d), respectively.
preprocessed waveforms and frequency-converted
signals with the SE and GE sequences, respectively,
when the phase encoding (Gx) pulses were zero. The
frequency-converted signal was down sampled to 1 kHz
to ensure that the number of data points per recordingwas 32. The number of phase encodings was 32; therefore,
the size of the k-space data matrix was 32 × 32 for eachdataset.
Figs. 12 (c) and (d) show the reconstructed MR images
obtained by applying a 2D fast Fourier transform (FFT)

Journal of the Magnetics Society of Japan Vol.47, No.4, 2023

123

INDEX

to the k-space data. Concentric circles separated by a 4mm-thick cylinder, as shown in Fig. 7, clearly appear inboth figures. Figs. 12 (e) and (f) show the pixel intensityof the MR images shown in Figs. 12 (c) and (d) along theline indicated by the arrows. The pixel intensity was
normalized to the pixel intensity at the center of the MR
image. Assuming that the MR signal was not included in
the images with |Y| > ±31 mm, the noise levels were
estimated to be 0.20 and 0.31 in Figs. 12 (c) and (d),respectively. Therefore, the signal-to-noise ratio (SNR)
was estimated as 5.0 and 3.2 in Figs. 12 (c) and (d),respectively.
5. Discussions
In this study, a 1-mT ULF-MRI system without a prepolarization technique was proposed and the feasibilityof MRI measurement was demonstrated. The static
magnetic field was set to 1 mT to balance the intensity of
the MR signal and the compatibility for integrating with
the MEG system. This attempt is the first to achieve
ULF-MRI measurements at approximately 1 mT1).
The highest static magnetic field with the Bp-pulse andthe lowest without the Bp-pulse were 200 T 13) and 6.5
mT 2), 22), respectively. Compared with these MRI systems,
the proposed 1-mT MRI system does not require largescale equipment, such as a larger power supplier or
cooling system for the coils. The power consumption
necessary to generate the Bp-pulse of 100 mT and B0 of
6.5 mT were 14.8 kW13) and 67 kW 22), respectively. As
described in Subsection 2.3, the power consumption of
the 1-mT ULF-MRI system to generate the static
magnetic field was 77.2 W. Utilizing the small electric
power supply has the benefit of power saving andsuppression of magnetic noise interference into the MEG
system. This is particularly relevant because the MEG
system is sensitive to magnetic noise, including powerline noise.
By employing the Merritt-type configuration for the B0coil, both weight savings and sufficient homogeneity ofthe static magnetic field were achieved. The weight of theB0-coil was approximately 1/10 that of the 6.5-mT MRI
system (~ 340 kg22)). Although the inhomogeneity of 700
ppm was worse than that of the 6.5-mT MRI system (350ppm), it was negligible for MRI measurement at 1 mT
because the robustness against the inhomogeneity was
improved by employing a lower static magnetic field, as
shown in Figs. 4 (c) and (d).
The suitable homogeneity of B0 also aided in the
reduction of the recording time enabling the use of the
GE sequence. Whereas the GE imaging sequence is moreeasily influenced by the inhomogeneity of the static
magnetic field compared with the SE imaging sequence,
the MR image obtained using the GE sequence is not
distorted, as shown in Fig. 12. In the GE imaging
sequence, the repetition time TR was set to less than thelongitudinal relaxation time T1, which is suitable for fast
imaging. The recording time with the GE sequence was
1/3.5 shorter than that with the SE sequence.

124

Furthermore, using the Bp-pulse requires TR > T1
(normally more than 4–5 times), even when using the GE
sequence. It is because the exposure time of the Bp-pulse
has to be longer than T1 (normally more than 2–3 times).
Therefore, the recording time of the ULF-MRI can be
reduced by avoiding the use of a Bp-pulse.
The spatial resolution and SNR of the obtained MR
images were 4 mm and 3.25.0, respectively. Although
the Bp-pulse was not used to boost the MR signal, theresolution and SNR were comparable with those ofprevious studies that used the Bp-pulse to combine MEG
systems 11), 13). However, the SNR must be considerably
improved to realize three-dimensional MR imaging andreduce the recording time for practical use in humanheads. In this study, an induction coil was used insteadof the SQUID sensors of the MEG system to detect MR
signals. As described in Subsection 2.5, the noise level ofthe detection unit composed of the induction coil andamplifiers (3.6 fT/Hz1/2) was comparable to that of
SQUID sensors (approximately 5 fT/Hz1/2) 21). Although
the SNRs of single sensors are comparable, it is expectedthat using a SQUID sensor array composed of more than
100 SQUID sensors will be effective in improving the
SNR of the MR image. Optimization of the sensor arrayfor MRI measurements is underway to realize theintegration of ULF-MRI and MEG systems.
The experiments were conducted in a smaller FOV
than that of the MEG system to investigate the feasibilityof MRI measurements at 1 mT without the Bp-pulse. In
the future, we aim to develop larger gradients and RF
coils to ensure the homogeneity of B0 in the entire ROI
and expand the FOV for capturing the human head.
6. Conclusion
A ULF-MRI system with a static magnetic field of 1 mT
was fabricated for integration with the MEG system.
Suitable homogeneity and stability of the static magnetic
field were successfully generated using a Merritt-type
coil driven by MEG-compatible electronics. MRI
measurements at 1 mT without a pre-polarization
technique were performed using a phantom. The spatial
resolution and signal-to-noise ratio were comparable tothose obtained in previous studies using the prepolarization technique. The signal-to-noise ratio of the
MR image must be improved for practical MRI
measurements.
Appendix A
In this appendix, the influence of applying a strong
magnetic field to SQUIDs and the basis for determining
a static magnetic field of 1 mT are presented.
Generally, the critical current of Josephson junctions
decreases in a strong magnetic field23). This results in the
SQUID’s inoperative condition in a strong magnetic field
because the output voltage of the SQUIDs also decreases
following the decrease in the critical current. Thisdecreasing trend depends on the orientation of themagnetic field applied to the SQUID24).

Journal of the Magnetics Society of Japan Vol.47, No.4, 2023

Flux (F0)(a)

Peak-to-peak voltage of
the SQUID’s output (V)

To investigate the acceptable magnetic flux density of
our SQUIDs, the output voltage of the SQUID was
measured by applying a DC external magnetic field to the
SQUID chip. Fig. A.1 shows the measurement results.
The flux–voltage characteristics of the SQUID wereobserved by applying a small AC magnetic flux signal to
the SQUID, as shown in Fig. A.1 (a) and the peak-to-peakvalues are plotted in Fig. A.1 (b).
Evidently, the output voltage of the SQUID was could
be maintained at 90 % of the maximum value of less than
1 mT when an external magnetic field was applied to the
SQUID chip in the parallel direction. Attenuation of the
SQUID output voltage commonly results in a decrease in
the bandwidth of the SQUID sensor. The frequency
response of the MEG system showed flatness below 50
kHz without applying a magnetic field 25). It is estimatedthat the flatness of the frequency response decreased toapproximately 45 kHz at 1 mT owing the attenuation of
the output voltage of the SQUID. Therefore, the static
magnetic field of the ULF-MRI was set to 1 mT, and thecorresponding magnetic resonance frequency was 42.58
kHz.

Voltage (V)

INDEX

〇 perpendicular to the SQUID chip
□ parallel to the SQUID chip

External magnetic flux density (mT)

Appendix B(b)

In this appendix, the simulation algorithm for the
ULF-MRI measurement is presented.
B. 1 Definition of simulation voxel and equivalentmagnetic moment
The cylindrical simulation models illustrated in Fig. 4(a) are virtually separated by small voxels. The size of thevoxel is 4 × 4 × 4 mm3, and the total number of voxels(Nvoxel) is 18768. Assuming that each voxel is filled withwater, the density of proton  can be given by𝜌𝜌 =2𝜌𝜌′ 𝑁𝑁𝐴𝐴
𝑀𝑀𝐻𝐻2𝑂𝑂,(A1)

where NA, MH2O, and ’ are Avogadro’s number, molar
mass, and molecular density of water, respectively. The
spin of the protons in the i th voxel was assumed to be an
equivalent magnetic moment Δmi. In the thermal
equilibrium state with the static magnetic field B0
applied along the y-axis, Δmi can be expressed as a vector(0, Δm0,i 0). The magnitude of the magnetic moment Δm0,ican be calculated as∆𝑚𝑚0,𝑖𝑖 =𝜌𝜌𝛾𝛾2 ℏ2 ∆𝑉𝑉
4𝑘𝑘𝐵𝐵 𝑇𝑇

𝐵𝐵,

(A2)

where ℏ , kB, T, ΔV, and B are the Planck constant,Boltzmann constant, temperature, voxel volume, andmagnetic field density, respectively.
B. 2 Precession of the magnetic moment
In the “real” MRI, the orientation of the magnetic
moment is controlled by RF pulses, such as 90- and 180degree pulses. In this simulation, the orientation waschanged numerically, that is, the magnetic moment in
the thermal equilibrium state (0, Δm0,i, 0) changed to (0,0, Δm0,i) by applying 90-degree pulse virtually. In thesimulation presented in Subsection 2.2, the gradient-Fig. A.1
Results of the SQUID’s output voltage
measurement when applying the external magnetic
field: (a) flux–voltage characteristic when the external
magnetic field was zero, (b) decline curves of the
SQUID’s output voltage by increasing the external
magnetic field.

GY(dBY/dY)
GX(dBY/dX)
Signal
tE

t=0

tACQ

Fig. B.1
Two dimensional gradient echo pulse
sequence that is used for the simulation.
echo pulse sequence shown in Fig. B1 was simulated. The
gradient fields GX and GY were applied to tE (8 ms) after
applying the virtual 90-degree pulse for 2D imaging.
Here, time t = 0 at the end of the phase encoding pulse𝑒𝑒
was defined. The phase shift 𝜑𝜑𝑥𝑥𝑥𝑥
of the magnetic
moment at t = 0 can be expressed as𝑒𝑒
𝜑𝜑𝑥𝑥𝑥𝑥= 𝛾𝛾 × (𝐵𝐵0,𝑖𝑖 + 𝐺𝐺𝑌𝑌 ∙ 𝑟𝑟𝑖𝑖,𝑦𝑦 + 𝐺𝐺𝑋𝑋 ∙ 𝑟𝑟𝑖𝑖,𝑧𝑧 ),(A3)

where ri = (ri,x, ri,y, ri,z) is the position of the magnetic
moment Δmi and B0,i is the static magnetic field at ri.
The precession of the spin is emulated as the rotationof the magnetic moment vector Δmi(t) = (Δmi,x (t), Δmi,y(t),Δmi,z (t)) as follows:∆𝑚𝑚𝑖𝑖,𝑦𝑦 (𝑡𝑡) = ∆𝑚𝑚0,𝑖𝑖 × (1 − 𝑒𝑒 −(𝑡𝑡+𝑡𝑡𝐸𝐸 )/𝑇𝑇1 )Journal of the Magnetics Society of Japan Vol.47, No.4, 2023

(A4)

125

𝑒𝑒
∆𝑚𝑚𝑖𝑖,𝑥𝑥 (𝑡𝑡) = ∆𝑚𝑚0,𝑖𝑖 × 𝑒𝑒 −(𝑡𝑡+𝑡𝑡𝐸𝐸 )/𝑇𝑇2 × sin(𝜔𝜔𝑖𝑖 𝑡𝑡 + 𝜑𝜑𝑥𝑥𝑥𝑥)

𝑒𝑒).
∆𝑚𝑚𝑖𝑖,𝑧𝑧 (𝑡𝑡) = ∆𝑚𝑚0,𝑖𝑖 × 𝑒𝑒 −(𝑡𝑡+𝑡𝑡𝐸𝐸 )/𝑇𝑇2 × cos(𝜔𝜔𝑖𝑖 𝑡𝑡 + 𝜑𝜑𝑥𝑥𝑥𝑥

(A5)
(A6)

In the above equations, i is the angular frequency of theprecession, given by𝜔𝜔𝑖𝑖 = 𝛾𝛾 × (𝐵𝐵0,𝑖𝑖 + 𝐺𝐺𝑌𝑌 ∙ 𝑟𝑟𝑖𝑖,𝑦𝑦 ),(A7)where B0,i is the static magnetic field at each voxel
position calculated based on the design of the Merritttype B0-coil. T1 and T2 are the longitudinal andtransverse relaxation times of the samples, respectively.
In this simulation, T1 and T2 are defined as 70 ms, inaccordance with those of the CuSO4 aqueous solution
phantom used for the experiments.
B.3 Magnetic resonance signal waveform
The detection coil is also defined, as shown in Fig. 4 (b).
The interlinking magnetic flux generated by each
equivalent magnetic moment ΔFi(t) can be calculated as∆𝛷𝛷𝑖𝑖 (𝑡𝑡) = ∆𝒎𝒎𝑖𝑖 (𝑡𝑡) ∙ 𝜷𝜷𝑖𝑖
(A8).
i is the lead-field vector given as𝜷𝜷𝑖𝑖 =μ0∫
4π 𝒍𝒍

𝑑𝑑𝒍𝒍×(𝒓𝒓𝑖𝑖 −𝒒𝒒),
|𝒓𝒓𝑖𝑖 −𝒒𝒒|3(A9)where 0 is the vacuum permeability, l is the path of
integration for the detection coil, and q = (qx, qy, qz) is thecenter of the detection coil.
As the sensor output, the magnetic flux density Bdetected
is calculated as follows:
𝐵𝐵𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑 (𝑡𝑡) =1

𝐴𝐴𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐

𝑣𝑣𝑣𝑣𝑣𝑣𝑣𝑣𝑣𝑣∑𝑁𝑁
𝑖𝑖=1 ∆𝛷𝛷𝑖𝑖 (𝑡𝑡) ,(A10),

where Acoil is the area of the detection coil.
The waveform of the simulated magnetic resonancesignal can be obtained by calculating every time point
between t = 0 and tACQ (16 ms in this simulation) withsampling frequencies of 500 kHz and 2 MHz for B0 = 1
mT and 10 mT, respectively. To obtain an MR image with
64 × 64 pixels, the calculation was repeated 64 times bychanging the intensity of the phase-encoding GX. The
obtained MR waveform data were preprocessed andfrequency-converted, and the MR images werereconstructed by applying 2D FFT, similar to theprocessing of the real experimental data. In this study,
the signal-to-noise ratio (SNR) was not considered in thesimulation to simply compare the influence of theinhomogeneity of the static magnetic field. To simulate
the SNR, the induced voltage of the detection coil can beobtained by multiplying the frequency of the MR signal,and voltage noise can be easily added to the calculated
induced voltage data.
Appendix C
As described in Subsection 4.1, the spin-echo (SE)signal was continuously recorded for approximately 4
hours after turning on the current driver for the B0-coil
to confirm the stability of the static magnetic field B0. Fig.
C.1 shows the frequency shift of observed SE signal. The
frequency rapidly decreased between 0 and 60 min and126

Frequency of observed
spin-echo signal (kHz)INDEXTime (min.)Fig. C.1

Frequency shift of observed spin-echo signal.

then slowly shifted. This frequency shift is assumed to becaused by the time required to stabilize the current
driver circuit, including the warm-up time of the circuit
elements. The shift from 60 to 240 min wasapproximately 14 Hz. The corresponding magnetic flux
density of B0 was calculated as 336 nT (0.0336 % of 1 mT).
Acknowledgements This work was partly supported by
JSPS KAKENHI (grant number: 20K12680). This study
includes some results of collaborative research withRICOH Co. Ltd. The authors are grateful to Mr.
Shinsuke Shibata formerly with RICOH Co., Ltd. forvaluable discussions and Ms. Miki Kawabata with theApplied Electronics Laboratory, Kanazawa Institute ofTechnology, for supporting the experiments. The authors
would like to thank Editage (www.editage.jp) for English
language editing.
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Editorial Committee Members・Paper Committee Members
S. Yabukami and T. Taniyama (Chairperson), N. H. Pham, D. Oyama and M. Ohtake (Secretary)
H. Aoki
M. GotoT. GotoK. Hioki
S, Inui
M. Iwai
Y. Kamihara
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T. Kojima
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A. YaoS. Yamada
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編 集 委 員・論 文 委 員
薮上 信（理事） 谷山智康（理事） Pham NamHai（幹事）
青木英恵
伊藤啓太
乾
成里
岩井守生
後藤太一
後藤
穣
佐藤
拓
仕幸英治
Kim Kong Tham
仲村泰明
西島健一
山田晋也
吉田征弘
脇谷尚樹

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神原陽一
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藏
裕彰
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鈴木和也
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野崎友大
日置敬子
増田啓介

桑波田晃弘
田中哲郎
八尾
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小嶋隆幸
都甲
大
家形
諭

安達信泰
関野正樹
成田正敬

小林宏一郎
田島克文
別所和宏

菅原
聡
土井正晶
室賀
翔

清野智史
直江正幸
吉村
哲

磯上慎二
田倉哲也
白
怜士

川口昂彦
田河育也
橋本良介

菊池伸明
竹澤昌晃
長谷川 崇

佐藤佑樹
田丸慎吾
本多周太

塩田陽一
土井達也
槙
智仁

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Journal of the Magnetics Society of Japan
Vol. 47 No. 4 (通巻第 328号) 2023年7月1日発行

Vol. 47 No. 4 Published Jul. 1, 2023

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