スピントロニクス・デザインコース
Spintronics Design Course

基 礎 １
Fundamentals 1

白 井 正 文Shirai, Masafumi

東北大学 電気通信研究所
Research Institute of Electrical Communication, Tohoku University

東北大学 スピントロニクス学術連携研究教育センター
Center for Spintronics Research Network, Tohoku University
第31回 CMD Workshop（2017年9月11日～15日，大阪大学基礎工学研究科）

1

Outline
0. スピントロニクスと社会– Spintronics and the human society
1. トンネル磁気抵抗
Tunneling magnetoresistance (TMR)– 高スピン偏極（ハーフメタル）材料
High spin-polarization (half-metallic) materials
2. 界面磁気異方性Interface magnetic anisotropy– 電圧制御voltage control2

０. スピントロニクスと社会Spintronics and the human society

3デジタル情報の年間生産量と記録可能容量Produced digital information / Available recording capacity• デジタル情報生産量は5年で10倍増加
Digital information has been expanding 10 times over 5 years.
4• 記録媒体の容量は大幅に不足 Insufficient recording capacity急増する情報通信機器の電力使用量
Rapid increase of power consumption of ICT equipments

CONSUMED POWER (M Wh)

1200

情報通信(ICT)機器の電力使用量（日本）1000

The power consumption of ICT equipments
In Japan:800• 2008年： 全電力使用量の約 6%• 2030年：〃約40%• 2050年：
〃約60%

600

TOTAL

400

ICT

20002006 2010 2015 2020 2025 2030 2035 2050

YEAR

60%

スピントロニクスによる省エネルギー・環境調和型デバイスの必要性

We need energy-saving /environmentally harmonic devices
based on spintronics.
5出典） 経済産業省 METI / Estimation of Green IT (2008)

Conventional Technology in Electronics
ProcessingSemiconductordevices© IntelStorage
Ferromagneticdevices

Electronic Degrees of Freedom
NChargeSpin–eSpintronics

S© Everspin Technologies• High-performance devices in the next generation
High speed, Large scale, Low power consumption• New paradigm in information technology
6

MRAM (Magnetoresistive Random Access Memory)• 不揮発Non-volatile• 高速入出力 Fast read/write• 高集積化

Scalability• 高耐久性High endurance

Magnetic tunnel junctions (MTJ)
Ferromagnet
Insulator
Ferromagnet“1”
S.S.P. Parkin (IBM)“0”© Everspin Technologies
7Requirements for Magnetic Tunnel Junction (MTJ)• Non-volatility: Δ = EB / kBT > 60 (for enough endurance)• High output: TMR ratio > 100%
• Low switching current: Ic0 < F μA (for cell size F nm)• Fast read and write• CMOS compatibility• Low resistance• Low error rate
• Low cost

© S. S. P. Parkin (IBM)81. トンネル磁気抵抗
Tunneling Magneto-Resistance (TMR)

9トンネル磁気抵抗効果の起源
The origin of TMR effect

低抵抗Low resistance

Jullier’s model

RAP  RP
2 PFM1PFM2
TMR 
RP
1  PFM1PFM2

高抵抗High resistance

スピン偏極率 spin polarization

PDMaj  Dmin
DMaj  Dmin 10

Half-metallic ferromagnets
Unique electronic structure:• Metallic for spin-up
Semiconducting for spin-down

EF• Complete spin polarization at EFD  DP
1D  D

Dσ: Density of states at EF

R AP  RP
2 PFM1PFM2
TMR RP
1  PFM1PFM2
Potential materials for electrodes of MTJ11

Half-metallic ferromagnets (theoretical prediction)• Half Heusler alloys: NiMnSb, PtMnSb
R.A. de Groot, et al., Phys. Rev. Lett. 50, 2024 (1983).

• Full Heusler alloys: Co2MnGe, Co2MnSi
S. Ishida, et al., J. Phys. Soc. Japan 64, 2152 (1995).

• Fe3O4 A. Yanase, et al., J. Phys. Soc. Jpn. 53, 312 (1984).
• CrO2

K. Schwarz, J. Phys. F: Met. Phys. 16, L211 (1986).

• (La,Sr)MnO3, Sr2FeMoO6• zinc-blende CrAs, CrSb
H. Akinaga, et al., Jpn. J. Appl. Phys. 39, L1118 (2000).
M. Shirai, Physica E 10, 143 (2001).
J. Appl. Phys. 93, 6844 (2003).
12

湯浅新治（産総研）
S. Yuasa (AIST)CMS (001)(amorphous)

CMS (001)

宮﨑照宣（東北大学）
T. Miyazaki (Tohoku Univ.)13

コヒーレント・トンネル効果
Coherent tunneling effectCo

反平行磁化配置MgO

Co

Δ1対称性をもつ電子
Δ1 –symmetry electrons

減衰が緩やか
slow decay

トンネル透過率Δ1↓
優先的に透過predominant transmission

Δ5
D1

Δ2

D1

原子層

Δ1: s, pz, dz2

D5D2Co(001)MgO(001)z

Δ2: dxy, dx2-y2

D1Co(001)

Δ5: px, py , dyz , dzx
W.H. Butler et al., Nature Mater. 3, 845 (2004).

14コヒーレント・トンネル効果
Coherent tunneling effectHigh spin polarization for Δ1 band.
1.5

1.5

D11.0

D10.5

D1E －EF (eV)E －EF (eV)

Fe

1.0

Selective transmission via Δ1 channel.

0.5

0.0

D1D5

D2Fe(001)
MgO(001)

0.0-0.5GHk // [001]majority-spin

-0.5
GH

k // [001]minority-spink// dependence of transmittancemajority-spinminority-spin

D1Fe(001)

J. Mathon and A. Umerski,
Phys. Rev. B 63, 220403R (2001).
W.H. Butler et al.,Phys. Rev. B 63, 054416 (2001).
15

Several orders of magnitude smaller

Large magnetic anisotropy
for high thermal stability
EB / kBT > 60

Small magnetic anisotropy
for low switching current

trade-off

Ic0 < F μA (for cell size F nm)
Ic0 ∝ α E / g(P)EB = KuV

α : magnetic damping constantg : spin-transfer efficiency
P : spin polarization
Ku : magnetic anisotropy energy
V : volume of ferromagnetic layer

High magnetic anisotropy (Ku), High spin polarization (P), andLow magnetic damping (α) are required for electrode materials.
16

Half-metallic Heusler alloys: Co2YZ• High Curie temperatures- advantage for room-temperaturedevice applications.

Ordered L21 structure• High spin polarization at the Fermi level- even in disordered B2 structure.
Y. Miura, K. Nagao, M. Shirai,Phys. Rev. B 69, 144413 (2004).
J. Appl. Phys. 95, 7225 (2004).

• Low magnetic damping- even in disordered B2 structure.
S. Mizukami, et al.,J. Appl. Phys. 105, 07D306 (2009).

Disordered B2 structure17Effects of Atomic disorder on Spin polarization

ordered L21

Spin Polarization1.0DOS (states/eV)

Co2CrAl (L21)
8Total DOS
6420-2-4
LDOS Co 3d-6
LDOS Cr 3d-8-5 -4 -3 -2 -1

0.6

E-EF [eV]1disordered B2

0.4
0.2
0.0

(Co2-yCry)(Cr1-yCoy)Al

-0.2
0.0

P=100%
0Co2(Cr1-yAly)(Al1-yCry)

0.8

23

0.1 0.2 0.3 0.4
Disorder-level ydisordered D03

0.5
KKR-CPAY. Miura, K. Nagao, M. Shirai,Phys. Rev. B 69, 144413 (2004).

18Effects of B2 disorder (Cr-Al substitution)
Molecular orbitals(minority-spin)

Total Density of State [arb. Units]

Co2CrAl(L21 Structure)

CrCo(Cr0.5,Al0.5)(B2 Structure)-6-5-4-3-2-101

23E-EF [eV]Near-edge states of the minority-spin band gap:

Galanakis, et al.,Phys. Rev. B 66, 174429 (2002).

Non-bonding Co 3d orbitals
Y. Miura, K. Nagao, M. Shirai, Phys. Rev. B 69, 144413 (2004).

19

8(Co1.9Cr0.1)(Cr0.9Co0.1)Al

40-4In-gap states-8-6-4-20E－EF (eV)2Local DOS (eV-1/atom)

Total DOS (eV-1/formula)

Effects of D03 disorder (Co-Cr substitution )420(Co1.9Cr0.1)(Cr0.9Co0.1)Al-2-4-64Co 3danti-siteordinary site

Cr 3d20-2anti-site Co-4-6-4Y. Miura, K. Nagao, M. Shirai, Phys. Rev. B 69, 144413 (2004).

-20E－EF (eV)220

Co2MnSi / MgO / FM (001) magnetic tunnel junctions
Remarkabletemperature dependence
Co2MnSi / MgO / CoFe MTJ
TMR = 753% at 4.2K
= 217% at RT
S. Tsunegi, et al.,Appl. Phys. Lett. 93, 112506 (2008).

Remaining problems Elucidating the origin of remarkable reduction ofTMR ratio with increasing temperature.
 How to improve TMR ratio at room temperature.

21

Gilbert damping constants of Co2FeAl
Ferromagnetic resonance (FMR)
calculation

6G (107 rad/s)

10

54
3

5
2
1
00

0.2

A2

0.4

0.6

0.8

Order parameterSG   ( D  D )2SO

1D(EF) (1 / eV / f.u.)

experiment

A20B2(Kambersky)

S. Mizukami, et al., J. Appl. Phys. 105, 07D306 (2009).

B222

2. 界面磁気異方性Interface magnetic anisotropy

23Perpendicular magneto-crystalline anisotropy (MCA)
observed at CoFeB / MgO interfaces.
In-plane MCA

Perpendicular MCA

Interfacial MAE density:
Ki = 1.30 erg/cm2
S. Ikeda, et al., Nature Mater. 9, 721 (2010).

E / kBT = 43
TMR ratio: 124%
Ico = 49 μA (ϕ = 40 24nm)

Large magnetic anisotropy
for high thermal stability
E / kBT > 60

Small magnetic anisotropy
for low switching current

trade-off

Ic0 < F μA (for cell size F nm)
Ic0 ∝ α E / g(P)E = KuVα : magnetic damping constantg : spin-transfer efficiency
P : spin polarization
Ku : magnetic anisotropy energy density
V : volume of ferromagnetic free layer

Ic0 Vsw tsw ≈ 50 μA × 0.5 V × 1 ns
≈ 2.5×10-14 J
60 kBT ≈ 60 × 1.38×10-23 J/K × 300 K ≈ 2.5×10-19 J

25

Large magnetic anisotropy
for high thermal stability

Small magnetic anisotropy
for low switching current

E / kBT > 60

Ic0 < F μA

Vg = 0trade-off(for cell size F nm)

E = KuV
E = KuVVg ≠ 0

Outlook: Another solution to overcome the trade-off relation isElectric-field control of magnetic anisotropy.

26

Electric-field modulation of interfacial magnetic anisotropy
Experiment

Theory・ Au / Fe80Co20 (0.5nm) / MgO -37.2 fJ/Vm

・ MgO / Fe (9ML) / Cu(001)32 fJ/Vm
M. K. Niranjan et. al.,Phys. Rev. Lett. 96, 222504 (2010).

・ Au (3ML) / Fe (3ML) / MgO

8.1 fJ/Vm
T. Nozaki, et al., Appl. Phys. Lett. 96, 022506 (2010).

・ Ta / Co40Fe40B20 / MgO -33 fJ/Vm

K. Nakamura, et. al.,Phys. Rev. B. 81, 220409(R) (2010).

・ MgO / Fe (2ML) / Au(001)

11.6 fJ/Vm
M. Tsujikawa, et al.,J. Appl. Phys. 109, 07C107 (2011).
M. Endo et. al., Appl. Phys. Lett. 96, 212503 (2010).

27

Magnetic anisotropy

Magnetic damping

28

A. Okada et al., Appl. Phys. Lett. 105, 052415 (2014).

Electric-field effect on Curie temperature
Pt / Co / Ionic liquid

Pt / Co / MgO

Tc = 300 K
DTc ~ 100 K

Pt / Fe / Ionic liquid

Tc = 326 K

DTc ~ 10 K

D. Chiba, et al., Nature Mater. 10, 853 (2011).
K. Shimamura, et al., Appl. Phys. Lett. 100, 122402 (2012).
M. Kawaguchi, etal., Appl. Phys. Express 5, 063007 (2012).

Magnetization switching by voltage pulses

Y. Shiota, et al., Nature Mater. 11, 39 (2012).

30

Magnetization switching by voltage pulses

Probability P to AP

Perpendicular magnetization
CoFeB/MgO/CoFeB MTJ (ϕ = 70 nm)
1.00.8
0.6
0.4
0.2
0.0
02468

tpulse (ns)1012Switching probability vs. Voltage-pulse duration tpulse

S. Kanai, et al., Appl. Phys. Lett. 101, 122403 (2012).

31

SummaryRequired magnetic materials for spintronics:
 High spin polarization (for high magetoresistance)
 High magnetic anisotropy (for high thermal stability) Low magnetic damping (for low switching current) Small magnetization (for low switching current and stray field)
Required innovative functionality for spintronics:
 Voltage control of magnetic properties
e.g. magnetic anisotropy, damping, Curie temperature(for magnetization switching with low power consumption)32