Exotic spin-orbit torques from

topological materials and ferrimagnets

Hyunsoo Yang

Department of Electrical and Computer Engineering National University of Singapore

Charge electronics Spin electronics

Information transfer

= electron transfer

Information processing

= processing electron flow

Charge transfer and processing energy loss is huge

All spin electronics

http://imechanica.org/taxonomy/term/118?page=3

2

Spin wave

Spin transistor

MTJ memory

1998

50 MHz

3

STT-MRAMToggle-MRAM

Spin torque MRAM-Present STT-MRAM (Everspin) uses 90 nm node

-GF started to use 40, 28, 14 nm node

-TSMC, IBM, Samsung, TDK, Hynix, Sony,

Avalanche, Toshiba, Intel, Qualcomm…

16 Mb 256 Mb

SOT-MRAM

Everspin with

GlobalFoundries

2019 March

Samsung

28 nm FD-SOI

embedded

Spin Hall and Inverse Spin Galvanic effects

4

• Spin orbit coupling in the bulk of non-

magnet.

• Can be from intrinsic or extrinsic

(impurities).

• Quantified by spin Hall angle (SHA or sh)

• Structures with broken inversion symmetry

• Interfacial spin orbit coupling.

• Depends on the nature of the interface.

• Quantified by Rashba coefficient (

magnitude of E=-V)

JC

JS σJC= (e/m)p

E

Theory: D’yakanov and Perel (1971), Hirsch (1999), Edelstein (2000), Zhang (2000),

Murakami, Nagaosa, Zhang (2003), Sinova et al. (2004),…Manchon and Zhang (2008).

Experiments: (semiconductors) Ganichev et al. (2002), Kato et al. (2004), Wunderlich et al. (2005)

(metals) Valenzuela and Tinkham (2006), Saitoh et al. (2006), Kimura et al. (2007).

Spin Hall effect Rashba-Edelstein effect

Is spin accumulation direction the same for both cases?

Sign change of effective spin Hall angle

Nature Mater. 12, 240 (2013)

Appl. Phys. Lett. 108, 202406 (2016)

The SOT polarity is a function of heavy metal thickness

Thick regime: spin Hall dominant

Thin regime: interfacial spin-orbit with opposite sign to spin Hall

Ta

Hf

5

0SH

0SH

0SH

0SH

Is the sign of SH fixed for a given material?

-Sign of spin Hall angle changes across a transition thickness of SiO2 (t = 1.5 nm)

-Cannot be understood by spin Hall physics suggest the role of interface6

Si/SiO2 sub.

2 nm MgO

2 nm Pt

0.8 nm CoFeB

2 nm MgO

t nm SiO2

-300

0

300

t = 3

t = 2.1

t = 1.5

t = 1.2

-300

0

300

t = 0

-200

0

200

V (

V)

-400

0

400

-30000 0 30000

-400

0

400

H (Oe)

-2

0

2

-2

0

2

-1

0

1

V2 (

V)

-0.2

0.0

0.2

-0.5

0.0

0.5

I+

I-

V- V+

a b

c d

e f

-2

0

2

-2

0

2

t = 3

t = 2.1

t = 1.5

t = 1.2

t = 0

-1

0

1

RH (

)

-404

-2 -1 0 1 2

-4

0

4

I (mA)

0 1 2 3 4 5

-20

-10

0

10

20

HL (

Oe

)t (nm)

-1 0 1 2 3 4 5 6

-1

0

1

Ha

n/I

s (

T/m

A)

t (nm)

0 2 4-101

I s (m

A)

t (nm)

Si/SiO2 sub.

2 nm MgO

2 nm Pt

0.8 nm CoFeB

2 nm MgO

t nm SiO2

-300

0

300

t = 3

t = 2.1

t = 1.5

t = 1.2

-300

0

300

t = 0

-200

0

200

V (

V)

-400

0

400

-30000 0 30000

-400

0

400

H (Oe)

-2

0

2

-2

0

2

-1

0

1

V2 (

V)

-0.2

0.0

0.2

-0.5

0.0

0.5

I+

I-

V- V+

a b

c d

e f

-2

0

2

-2

0

2

t = 3

t = 2.1

t = 1.5

t = 1.2

t = 0

-1

0

1

RH (

)

-404

-2 -1 0 1 2

-4

0

4

I (mA)

0 1 2 3 4 5

-20

-10

0

10

20

HL (

Oe

)

t (nm)-1 0 1 2 3 4 5 6

-1

0

1

Ha

n/I

s (

T/m

A)

t (nm)

0 2 4-101

I s (

mA

)

t (nm)

Nat. Nano. 10, 333 (2015)

0SH

0SH

Reverse switching polarity by oxygen engineering

Adv. Mat. 30, 1705699 (2018)

Electric-field control of effective spin Hall sign

-4

-2

0

2

4

-2

0

2

4

6

-2

0

2

4

6

-15 -10 10 15

-2

0

2

4

6

After

Vg = 4 V

After

Vg = 4 V

After

Vg = 4 V

Initial stateGdOx

Pt

GdOx

Pt

GdOx

Pt

GdOx

Pt

RH

(Ω)

Ipulse (mA)

Competition b/w bulk spin Hall vs.

interfacial SOC with opposite sign

Device can switch to either up or

down depending on its programmed

SOT state reconfigurable spin logic

Pt (1.5 - 2 nm)

Co (0.8 nm)

GdOx (3 nm)

Nat. Commun. 10, 248 (2019) 8

Je

0 1 0

0SH

0SH

0SH

0SH

First principle calculations

∞ S S-2 S-4 I-4 I-2 I-5

0

5

P

R (

me

V Å

)

Oxygen position

First principle calculations performed in Prof. Nicholas Kioussis’s group, California State University.

The effective Rashba parameter (PαR) changes sign as oxygen is filled at the Pt/Co interface.

The spin accumulation direction changes sign when the negative effective Rashba torque

exceeds the spin Hall torque.

Effective Rashba coefficient changes its sign for 30% oxidization.

0.0 0.2 0.4 0.6 0.8 1.0

-6

-4

-2

0

2

P

R (

meV

Å )

Interfacial NO/NCo

Nat. Commun. 10, 248 (2019) 10

Pt

Co

Gradual modulation of SOTs

0 4 8 12 16

-0.10

-0.05

0.00

0.05

0.10

60 s60 s20 s

20 s

20 s

5 s

5 s

7 s60 s

40 s

20 s

20 s

30 s

30 s

40 s

50 s 5 V30 s

eff

SH

E

Vg application events

5 V

Application of Vg pulses on a Pt (1.5 nm)/Co (0.8 nm) device.

Thin gate oxide results in modulation at room temperature.

The sign of effective spin Hall angle of the material can be changed using electric-

field.

Gradual modulation of SOTs can be applied to neuromorphic devices.

E O2

Vg > 0

E O2

Vg < 0

Phys. Rev. Appl. 11, 054065 (2019), Nat. Commun. 10, 248 (2019) 11

12

Spike temporal dependence

Frequent stimulation results in larger modulation of weight.

The magnetic synapse follows the STDP curve.

Closely spaced pre- and post-synaptic spikes results in larger weight modulation.

0 400 800 1200

3

4

5

RA

HE ()

No. of Vg pulses

Pulse delay

10 ms

20 ms

40 ms

60 ms

80 ms

100 ms

200 ms

400 ms

-40 -20 0 20 40

-30

-20

-10

0

10

20

30

R

AH

E (

%)

t (ms)

Spike-timing dependence plasticitySpike-rate dependence

15Phys. Rev. Appl. 11, 054065 (2019)

Learning, forgetting & training

After removing the stimulation the weight starts decreasing again similar to

forgetting behavior of human brain.

With increasing number of training pulses the forgetting rate decreases.

0 200 400 600 800

3

4

5

RA

HE ()

Time (s)

Learning: Vg 10 V 100 ms

Forgetting

Learning & forgetting Training

16Phys. Rev. Appl. 11, 054065 (2019)

0 10 20 30 400

400

800

1200

1600

(s

)No. of training pulses (N)

Scanning photovoltage microscope with currents

19

𝑉𝑝ℎ𝑜𝑡𝑜𝑣𝑜𝑙𝑡𝑎𝑔𝑒 = 𝑉𝑅𝐶𝑃 − 𝑉𝐿𝐶𝑃

RCP light excites spin up electron, while LCP light excites spin down electron.

• 𝑉𝑝ℎ𝑜𝑡𝑜𝑣𝑜𝑙𝑡𝑎𝑔𝑒 > 0 local spin direction is spin down.

• 𝑉𝑝ℎ𝑜𝑡𝑜𝑣𝑜𝑙𝑡𝑎𝑔𝑒 < 0 local spin direction is spin up.

DC current is applied to induce

spin accumulation.

Circularly polarized light normally

incidents on the sample.

Magnetic circular dichroism.

Photovoltages are detected by

lock-in amp.

Piezo sample stage enables

mapping.

Nat. Comm. 9, 2492 (2018); Adv. Opt. Mat. 4, 1642 (2016)

21

Accumulated spin imaging in Pt and Bi2Se3

Sign switches in opposite edges and with reversing currents.

Both semiconductors and metals work.

Can extract spin Hall angle and spin lifetime without a ferromagnet.

Nat. Comm. 9, 2492 (2018)

In-plane and out-of-plane SOT efficiency in Bi2Se3

0 50 100 150 200 250 3000.0

0.1

0.2

0.3

0.4 D 1

D 2

D 3

By Vs Only

D 1

D 2

D 3

T (K)

By Vs/V

a

0 50 100 150 200 250 300

0.0

0.1

0.2

0.3

0.4

T (K)

D 1

D 2

D 3

PRL 114, 257202 (2015)23

|| increase by 10 times at low temperature (upto ~ 0.42).

has the same order of magnitude compared to ||.

Origin of the observed spin-orbit torques is topological surface states in

Bi2Se3.

Hexagonal warping in the TSS of Bi2Se3 can account for .

3D topological insulators (TIs)

Spin polarized surface currents

Spin-momentum locking giant spin Hall angle?

28

EF

Exotic spin Hall angles from topological insulators

29

spin Hall angle (SH) = 2~3.5

ST-FMR (Cornell)

Nature 511, 449 (2014)

PRB 90, 094403 (2014)

SH = 0.42 (low temp)

ST-FMR (NUS)

SH = 140-425 (low temp)

spin-orbit switching (UCLA)

Nat. Mater. 13, 699 (2014)

PRL 113, 196601 (2014)

SH ~ 1 × 10-4

Spin-pumping (Tohoku)

Bi2Se3

CoFeB

Js

Hrf

Jc

W

L

SH = 0.01

Spin-pumping (NUS)

PRL 114, 257202 (2015)

SH = 0.01-0.4

Spin-pumping (Minnesota)

Nano Lett 15, 7126 (2015)

tBiSe = 8 nm tBiSe = 20 nm

tBST = 3 nm

tBSTS = 100-300 µm

tBiSe = 5-35 nmtBiSe = 5 and 10 nm

30

[1] Nat. Mater. 13, 699 (2014)

[2] PRB 91 235437 (2015)

[3] Nature 511, 449 (2014)

[4] Nat. Commun. 8 1364 (2017)

100 101 102 103 104 105

10-4

10-3

10-2

10-1

100

101

102

103

Bi2Se3, spin pumping, RT [7]

Sp

in H

all

an

gle

TI thickness (nm)

(Bi,Sb)2Te3, 1.9K, SOT switching [1]

(Bi,Sb)2Te3, <200K, spin tunneling [2]

Bi2Se3, RT, ST-FMR [3]

Bi2Se3, RT, ST-FMR and SOT switching [4]

Bi2Se3, <50 K, ST-FMR [5]

Bi2Se3, spin pumping, RT [6]

Bi1.5Sb0.5Te1.7Se1.3, spin pumping, low temp [8]

[5] PRL 114, 257202 (2015)

[6] PRB 90, 094403 (2014)

[7] Nano Lett 15, 7126 (2015)

[8] PRL 113, 196601 (2014)

Review: J. Phys. D: Appl. Phys. 51, 273002 (2018)

-TI is not a good

insulator.

-EF is pinned in

conduction band.

-Current shunting

thru bulk reduces

the efficiency!

Current induced magnetization switching in Bi2Se3/Py

• TI magnetization switching reported in a Cr doped TI at 1.9 K with an

external magnetic field [Nat. Mater. 13, 699 (2014)].

• Demonstrated magnetization switching of Bi2Se3/NiFe at room temp with a

low critical current density (JC~6×105 A/cm2) and without a magnetic field.

• A giant TI = 1.75.

JC = 0105 A cm–2 3.3105 A cm–2 4.7105 A cm–2 5.2105 A cm–2 5.7105 A cm–2

JC = 0105 A cm–2 3.8105 A cm–2 5.2105 A cm–2 5.7105 A cm–2 6.2105 A cm–2

20 m

aM

M

I

I

xz

y

b c d e

f g h i j

M

M

32

Bi2Se3 (8 QL)/NiFe (6 nm)/MgO (1 nm)/SiO2 (4 nm)

Nat. Comm. 8, 1364 (2017)

Sputtered Bi2Se3

33

M M

MM

I

I

JBiSe = 4.53 103 A/cm2

Jtotal = 9.74 106 A/cm2

JBiSe = 4.17 103 A/cm2

Jtotal = 8.97 106 A/cm2

J = 0 A/cm2

(Remanence)

J = 0 A/cm2

(Remanence)

y

x

a) b)

c) d)

J. Phys. D: Appl. Phys. 52, 224001 (2019)

-Extremely large spin Hall angle, but large power consumption due to large resistivity

-J.P. Wang (Minnesota) also reported sputtered Bi2Se3 (Nat. Mater. 17, 800 (2018))

= 18.6, Jc = 4.3 × 105 A cm–2

TI = 45 for 10 nm

Si/SiO2 sub/Bi2Se3 (t)/Py (6 nm)/SiO2 (5 nm)

Spin relaxation time in Bi2Se3

34

0 1 2 3 4 5

0

5

10

15

20 +

-

Kerr

rota

tion (

a.u

.)

Delay (ps)0 1 2 3 4 5

0

5

10

+-

- (a.u

.)

Delay (ps)

- Signal sensitive to bulk due to large penetration depth of light

- Oscillation frequency is 2.13 THz from coherent vibrations of

the A1g longitudinal optical phonons of Bi2Se3

- Exponentially decay with a characteristic time of 1.3 ps

Time-resolved magneto optical Kerr effect

Adv. Opt. Mat. 4, 1642 (2016)

Weyl semimetal background

Conductive surface: spin-

momentum locked surface

states (P ~ 20-50%)Conductive surface: SML

Fermi arc states (P ~ 80%)

Topological insulator (TI):

Weyl semimetal:

Conductive bulk: strong spin

orbit coupling (P ~ 40%)

Td-WTe2 : Weyl semimetal, strong Edelstein

effect, good conductivity, 2D layered TMD

material, less roughness than MBE grown TI

such as Bi2Se3, etc.

Ideal material to achieve the spin

orbit torque driven magnetization

switching.

S. Xu, et al. Phys. Rev. Lett. 116, 096801 (2016)

P. K. Das, et al. Nat. Commun. 7, 10847 (2016)

S. Xu, et al. Nat. Commun. 6, 6870 (2015)

35

SOT driven magnetization switching-I along b-axis

• Charge current is applied in the b-axis.

• Spin current is generated along the a-axis.

-25 0 25H (Oe)

M (

a. u

.)

1.0

0.5

0

-0.5

-1.0

H//a

-25 0 25H (Oe)

M (

a. u

.)

1.0

0.5

0

-0.5

-1.0

H//b

• Switching starts to happen at 1.58 × 105 A/cm2

• Domain wall moves in the direction of JC

Hysteresis loops of the device

MOKE microscopy

Nat. Nano. 14, 945 (2019)

Room-temperature nanosecond spin relaxation

37

0.6 1.2 1.8

-8

-4

0

4

8

Heig

ht (n

m)

Distance (m)

6.4 nm

Few-layer 1Tʹ-WTe2

SiO2/Si

120 150 180 210

A4

2A

4

1

A3

1

A9

1

Inte

nsity (

a.u

. )

Raman shift (cm-1)

A7

1

Inte

nsity (

a.u

. )

QWP

Pump 800 nm

Probe 400 nm

z

yBext

θ

HWP

M

BPD

Filter

WBSWTe2

Al2O3

SiO2

0.0 0.2 0.4 0.6 0.8 1.0-8

-4

0

4

8

Ke

rr r

ota

tio

n (

a.u

. )

Time delay (ns)

Kerr signals reverse signs

0.0 0.2 0.4 0.6 0.8 1.0

0

4

8

12

16

20

k (

a.u

. )

Time delay (ns)

1=33 ps 2=1.2 ns

0.0 0.2 0.4 0.6 0.8 1.0 1.2

R

/R (

a.u

. )

Time delay (ns)

f s

• Centimeter-scale, chemical vapor deposition (CVD)-grown few-layer 1Tʹ-W(Mo)Te2

• Room-temperature 1.2 ns spin relaxation

Adv. Sci. 5, 1700912 (2018)

Spin orbit torque in various magnets

1/tFM dependence of spin torque (surface torque)

Limitation on FM thickness

Thermal stability issue

How about a multilayer or ferrimagnet (FIM)?

-Easy perpendicular anisotropy, enough magnetic volume

Science 336, 555 (2012)

Science 351, 587 (2016)

Nature 476, 189 (2011)

Ferromagnet

Antiferromagnet

90 degree rotation

Not compatible with MTJs

Small MR slow reading

38

SOT in ferrimagnet : CoGd

Pt (10 nm)

Co1-xGdx ( 6 nm)

TaOx ( 1 nm)

Co dominated Gd dominated

Hext

Gd

Co

Films deposited with varying Co

and Gd compositions.

CoGd has bulk PMA.

Thermally stable thick magnetic

layer is grown.

Si/SiO2 substrate

40Phys. Rev. Lett. 118, 167201 (2017)

Gd

Co

(a)

(b)

20 25 30 35

0

2

4

6

8

Norm

aliz

ed a

nd 1

/Ms

x (Gd %)

1/Ms

0

2

4

6

(

10

-9 O

e/A

m-2

)20 25 30 35

0

20

40

1/Ms

No

rma

lize

d

x (Gd %)

0

2

4

6

8

10

Norm

aliz

ed H

L &

1/M

s

0

2

4

6 HL

1/Ms

HL (

kOe)

Anomalous scaling of SOT in ferrimagnets Switching efficiency ( = ),

HL and 1/Ms are normalized

with respect to their respective

values for Co80Gd20.

Exceptional and

disproportionate (to 1/MS)

change of η and HL cannot be

explained by existing SOT

understanding.

10 times increase in SH due to

negative exchange coupling

42Phys. Rev. Lett. 118, 167201 (2017)

/p sH J

TaOx

a

b

sin( )ex

b b aH

sin( )ex

a b aH

SOT

LH

SOT

LH

sinext aH

sinext bH

extH x

z

fm

SOT

LH

sinext aH

extH x

z(i) (ii)

PtCoGd

Si/SiO2

current

x

z

(a)

0 20 400

25

50

75

100

No

rma

lize

d H

L a

nd 1

/Ms

x (B % in A1-xBx)

Ferrimagnet

Equivalent ferromagnet

1/Ms

(b)

Co

Gd

AFM

FM

Pd (0.7nm)

Co (0.2nm)

Multilayer: structural asymmetry can be added up

-Two successive Co/Pd and Pd/Co interfaces are structurally dissimilar.

-Lattice mismatch (9%) between Pd and Co Strain engineering

-This distortion is 30% stronger for Co/Pd than for Pd/Co interfaces

44

Ta (4 nm)

Co (0.2 nm)/

Pd (0.7 nm)/

multilayer

(22 times)

Ru5 nm

TEM

Pd (0.7nm)

Co (0.2nm)

Pd (0.7nm)

Co (0.2nm)

Ta (4nm)

Maesaka, IEEE Trans. Magn. 38, 2676 (2002)

Kim, PRB 53, 11114 (1996)

Phys. Rev. Lett. 111, 246602 (2013)

SH = 4

Ferromagnet vs. ferrimagnetNM FM

z

y

x

sy

NM FIM

sy

Site A Site B Site A Site B

Alternating exchange fields in ferrimagnet (FIM) on an atomic scale

much less spin dephasing long spin coherence length

Bulk-like torque in FIM (20 times enhanced SOT compared to FM)

45Nat. Mater. 18, 29 (2019)

SOT effective fields

2 4 6 8 10 12 14

0

5

10 H

L

HT

tCo/Tb

(nm)

Co/Tb

1 2 3

0.3

0.4

0.5

0.6

HL

HTH

L/T/J

HM (

10

-8 O

e c

m2/A

)

tCo/Ni

(nm)

Co/Ni

• FM Co/Ni: tCo/Ni ↑ SOT ↓. 1 sech

2

HM HML HM

S FM HM

J tH

e M t

h

• FIM Co/Tb: SOT diverges at compensation.

• SOT in FIM is ~20 times larger than that in FM.

• SOT in FIM shows bulk-like-torque characteristic.

Ferromagnet Ferrimagnet

poor compensation

47Nat. Mater. 18, 29 (2019)

Pt(4 nm)/[Co(0.3)/Ni(0.3)]N[Tb(0.34)/Co(0.32)]N/Pt(4 nm)

AFM

SOT current induced switching efficiency

-6 -4 -2 2 4 6

-0.5

0.0

0.5

RH (

)

J (1011

A/m2)

SOT switching efficiency: P WH J

Most switching through DW nucleation and propagation

• η is in line with that of SOT effective fields, decreasing for FM and diverging at

compensation.• In FIM system, η is ~20 times higher than FM system.

2 4 6 8 10 12 14

0

200

400

tFIM

(nm)

Co/Tb

1.0 1.5 2.0 2.5 3.0

4

6

8

10

12

14

(

10

-10 O

e m

2/A

)

tCo/Ni

(nm)

Co/NiFerromagnet Ferrimagnet

48Nat. Mater. 18, 29 (2019)

AFM

MS & tFM/FIM effect?

( ), 1/L SH M t

Surprisingly in FIM, the scaling trend of η and HL contradicts SOT governing

equation.

1 sech2

HM HML HM

S FM HM

J tH

e M t

h

1.0 1.5 2.0 2.5 3.0

0.0

0.5

1.0

No

rma

lize

d v

alu

es

1/(MStFM

)

HL

tCo/Ni

(nm)

Co/Ni

2 4 6 8 10 12 14

0

20

40

60

80

100

1/(MStFIM

)

HL

tCo/Tb

(nm)

Co/Tb

Ferromagnet Ferrimagnet

49Nat. Mater. 18, 29 (2019)

Spin pumping in a ferrimagnet

Spin dephasing length in Co/Tb > 13 nm

Spin dephasing in FM is 1.2 nm (PRL 117, 217206 (2016))

Substrate

Co/Ni or

Co/Tb

Co(20 nm)

Pt (10 nm)

Cu (2.4 nm)

-If spin coherence length is long,

a transverse spin current passes

through the Co/Ni or Co/Tb layer.

-VISHE is generated.

-2 0 2 4 6 8 10 12 14

0.00

0.02

0.04

0.06

0.08

0.10 7 GHz

8 GHz

9 GHz

VIS

HE/R

(

A)

tCoTb

(nm)

S

G

V

Hb

Substrate

Ni or TbCo ×N

Pt

Cu

…

Coa b

-0.6 -0.4 -0.2 0.0

0.0

0.5

1.0

Pt/Cu/Co Pt/[Co/Tb](5.3)/Cu/Co

Pt/[Co/Ni](0.9)/Cu/Co

Pt/[Co/Tb]/Cu

VIS

HE (

V)

Hb (kOe)

c d

50Nat. Mater. 18, 29 (2019)

Summary

• Spin orbit technologies

– Oxygen modulation in HM/FM interface can

switch spin Hall sign neuromorphic devices

– Spin accumulation imaging (www.tuotuot.com)

– Weyl semimetal spin sources

– Ferrimagnetic spintronics

51

Bulk-like