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1 Institute for Materials Research & WPI-AIMR, Tohoku University Kavli Institute of NanoScience, TU Delft Modelling and Simulation a physicist’s point of view Part 2 Who’s Afraid of YIG? Barnett Newman, Who’s Afraid of Red, Yellow and Blue III, 1967-68 Contents • YIG electronic and magnetic structure • Spin Hall magnetoresistance of YIG|Pt • Spin Seebeck effect in YIG vs. GdIG Yttrium Iron Garnet Y 3 (3+) Fe 2 (3+) (Fe (3+) O 4 (2-) ) 3 © A.R. Chakhmouradian Yttrium Iron Garnet Y 3 (3+) Fe 2 (3+) (Fe (3+) O 4 (2-) ) 3 - 80 atoms & 20 moments/unit cell - ferrimagnetic insulator - Curie temperature 550 K - man-made near perfection with Gilbert damping ~10 -5 Tabuchi et al. (2014)

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Page 1: Modelling and Simulation a physicist’s point of view Part 2 School... · 2017-03-28 · Sharvin G G 22 Sharvin nm nm ee GN hh Spin waves in YIG RT (Plant, 1983) Lars Onsager Memorial

1

Institute for Materials Research & WPI-AIMR, Tohoku UniversityKavli Institute of NanoScience, TU Delft

Modelling and Simulationa physicist’s point of view

Part 2

Who’s Afraid of YIG?

Barnett Newman, Who’s Afraid of Red, Yellow and Blue III, 1967-68

Contents

• YIG electronic and magnetic structure

• Spin Hall magnetoresistance of YIG|Pt• Spin Seebeck effect in YIG vs. GdIG

Yttrium Iron Garnet Y3(3+) Fe2

(3+) (Fe(3+)O4(2-))3

© A

.R. C

hakh

mou

radi

an

Yttrium Iron Garnet Y3(3+) Fe2

(3+) (Fe(3+)O4(2-))3

- 80 atoms & 20 moments/unit cell- ferrimagnetic insulator- Curie temperature 550 K- man-made near perfection with

Gilbert damping ~10-5

Tabuchiet al. (2014)

Page 2: Modelling and Simulation a physicist’s point of view Part 2 School... · 2017-03-28 · Sharvin G G 22 Sharvin nm nm ee GN hh Spin waves in YIG RT (Plant, 1983) Lars Onsager Memorial

2

Spintronics with magnetic insulators

FINM T

T, V SMR, transverse spin Seebeck

Longitudinal spin Seebeck and Peltier effects, magnon Bose condensation

acoustic spin pumpingelectrically detected FMR

YIG band structure Jia et al., EPL (2011)

0.33eVGGAgE

1.4 eVUgE

Mixing conductance of YIG|Ag (Jia et al., 2011)

spin current absorption

Confirmed by experiments:Burrowes et al. (2012), Azevedo et al. 2012),Weiler et al. (2013) …

2 *

nm nm nmnm

eG r r

h

Sharvin

GG

2 2

Sharvinnm

nm

e eG N

h h

Spin waves in YIG

RT

(Plant, 1983)

Lars Onsager Memorial at NTNU Trondheim

Lars Onsager

The Nobel Prize in Chemistry 1968:“for the discovery of the reciprocal relations bearing his name, which are fundamental for the thermodynamics of irreversible processes”

Onsager symmetry (1931)

Xi

m mn nn

J L X linear responseiJ

generalized forcesgeneralized currents

i ii

S X J entropy creation rateIf:

ij jiL L Onsager relationsthen:

i = {mass, charge, energy, volume, (angular) momentum, …}

When time reversal symmetry is broken:

, ,ij ext i j ji extL L m H m H

1 even (charge) when variable 1 odd (spin)i i

Page 3: Modelling and Simulation a physicist’s point of view Part 2 School... · 2017-03-28 · Sharvin G G 22 Sharvin nm nm ee GN hh Spin waves in YIG RT (Plant, 1983) Lars Onsager Memorial

3

Thermoelectrics

TV

T＋TV+V

c

Q

V R S JJ K T

R = 1/G electrical resistanceK thermal conductanceS Seebeck coefficient Peltier coefficient= STOnsager-Thomson (Kelvin)relation

11 21

12 22

c

Q

VJ L LTJ L L

T

12 21L L Onsager reciprocity

Spin-dependent thermoelectrics

Johnson and Silsbee (1987)Hatami et al. (2009)Slachter et al. (2010)Flipse et al. (2012)

20

/ 211 / 2

/

c

s

Q

V VJ P STJ G P P ST V VJ ST P ST L T T T

F

E

E E

PGPG

spin-dependent Seebeck effectspin-dependent

Peltier effect

Contents

© Vadym Zayets

• YIG electronic and magnetic structure• Spin Hall magnetoresistance of YIG|Pt• Spin Seebeck effect in YIG vs. GdIG• Strong coupling with microwaves

SMR (Nakayama et al., 2013)

MR

PHE

Kato et al. (2004)

Ic

InGaAs

Spin current tensor, spin Hall angle

,

,

,

, ,s x

x y zs s s s s y

s z

J

JJ J J J

J

,ˆ

s SH c J J

xsJ

,s xJ

polarization of current x

current direction of polarization x

ˆc SH s

J J

Page 4: Modelling and Simulation a physicist’s point of view Part 2 School... · 2017-03-28 · Sharvin G G 22 Sharvin nm nm ee GN hh Spin waves in YIG RT (Plant, 1983) Lars Onsager Memorial

4

3D spin Hall effect

ˆ ˆ ˆ1/ 2ˆ 1 0 0/ 2ˆ 0 1 0

ˆ 0 0 1 / 2

c SH SH SHx

sxs SHNy

sys SHzs SH sz

x y zVxVy

z V

Ejjjj

Onsager reciprocity in the spin Hall effect

spin Hall effect inverse spin Hall effect

Heterostructure

m

N FI

Exchange spin transfer torque

m

N FI

0FsI

Absorbed spin current = spin-transfer torque

2

2Re

2NS N N

F N N

Ge

Area k

IL

spin-mixing conductance

2 *

nm nm nmnm

eG r r

h

0NsI

A switchable mirror for spins

perfect mirror

*efficient absorber

Ferromagnetic insulator

F

Detection of spin current mirror

F

* 0, ˆz

s y SH cj j y SHE

SHE + ISHE

zx

Page 5: Modelling and Simulation a physicist’s point of view Part 2 School... · 2017-03-28 · Sharvin G G 22 Sharvin nm nm ee GN hh Spin waves in YIG RT (Plant, 1983) Lars Onsager Memorial

5

Contents

• YIG electronic and magnetic structure

• Spin Hall magnetoresistance of YIG|Pt• Spin Seebeck effect in YIG vs. GdIG

(Longitudinal) spin Seebeck effect

Uchida et al. (2010/2011)

V [

V]

≠ spin-dependent Seebeck effect!

Spin currents cause magnetization motion(spin transfer torque, Slonczewski, 1996).

Spin torque and spin pumping

Magnetization motion causes spin currents (spin pumping, Tserkovnyak, 2002).

Onsager reciprocals(Brataas et al., 2011)

G~

© Kajiwara et al.

FM N

Noise-induced spin currents

Foros et al. (2005)Xiao et al. (2009)

FM N

Noise-induced spin currents

Xiao et al. (2010)Adachi et al. (2011)

pump J-N noise M es s s F NJ J J g T T

Spin Seebeck Onsager matrixTF

sV

TN

Q

sJJ

effM H

heat conductancespin Peltier effect

eff

/ 2/

mm ms mQ

sm ss sQ s

Qm Qs QQ Q

s

zL L L HL L L V

T TL LJM

LJ

thermal fieldspin Seebeck effect

magnon Peltier effect

ijL spin-spin correlation functions at the interface

Page 6: Modelling and Simulation a physicist’s point of view Part 2 School... · 2017-03-28 · Sharvin G G 22 Sharvin nm nm ee GN hh Spin waves in YIG RT (Plant, 1983) Lars Onsager Memorial

6

Spin Peltier effect (Flipse et al., 2014)Pt (5 nm)

JQ JQ

YIG (200 nm)|GGG

200 m

VSPE

1st harmonic signals

Magnon transport

Corn

eliss

en e

t al.

(201

5)

(also Kajiwara et al. (2010))

RE-IG

Electroceramics: Materials, Properties, Applications, by A.J. Moulson & J. M. Herbert (Wiley, 2003) .

YIGGdIG

Geprägs et al. (2015)

Ohnuma et al. (2013)

Spin Seebeck effect and spin correlation

interface

, ,

, ,s

s

t tMJ V dt t

s ρ s ρρ

s ρ h ρ

, , ', 'ij i jS s t s t k r rFt

Spin-spin correlation power spectra: Equal time and position spin correlation function

Nxi ij i j

j iE J

S S

effi i i i i i S S B S S eff i

i ii

E t

B b

S

2 ik l kli

B

ib t b t tT t

Mk

Atomistic spin simulations:

Rare Earth Iron Garnets → GdIG

J. Barker (2015)

2

3 3

3

Page 7: Modelling and Simulation a physicist’s point of view Part 2 School... · 2017-03-28 · Sharvin G G 22 Sharvin nm nm ee GN hh Spin waves in YIG RT (Plant, 1983) Lars Onsager Memorial

7

Geprägs et al. (2015)

H


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