1

Magnetic Insulators(with emphasis on YIG)

ESM 2015, Gerrit Bauer, Part II

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)

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

2

Spin waves in insulators Spin waves in YIG

RT

(Plant, 1983)

Contents

Magnon-phonon coupling

© Vadym Zayets

[Spin Mechanics 4 in Banff (Ca), Feb. 2017]

Magnetoelastic coupling

- thermalization of lattice and spin- magnon-phonon drift- magnon-polarons (Kittel, 1958)

Dynamic effects of magnon-phonon interaction

Magnon-polarons

Kamra et al. (2015)

3

Magneto-polaron propagation (Shen, 2015)

Satoh et al. (2012)

Excitation by – Inverse Faraday effect– Heat

Detection by – Faraday or Kerr rotation

Femto-second optical excitation

Hashimoto et al. (unpublished).

Magneto-polaron propagation (Shen, 2015)

pumpprobe

xLine source excitation with IFE.

W

1 m spot excitation 5 ns coda

inverse Faraday excitation

Magneto-polaron propagation (Shen, 2015)

1 m spot excitation 5 ns coda

pressure wave excitation

Magneto-polaron propagation (Shen, 2015)

1 m spot excitation 5 ns coda

Shear deformationexcitation

Magneto-polaron propagation (Shen, 2015)

Strong coupling with microwaves

4

0B

1( ) i trfH t H e

0.1 meVFMR B B T

“precession cone”~ intensity of rf

~

r

0 0.01 in bulk metals, ~10-5 in best YIG

FerroMagnetic Resonance

m

Landau-Lifshitz-Gilbert equation; Gilbert damping constant

eff m m B m

Thin films in microwave cavities

Cao et al. (2015)Bai et al. (2015)

spin wave resonance electric readout

Ultra strong coupling with microwaves

Zhang et al.(2014)

Rameshti et al. (2015)[spherical cavity]

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

Contents

Spin Hall magnetoresistance

SMR (Nakayama et al., 2013)

MR

PHE

5

SMR vs. AMR (out of plane magnetization),

N

IF

x

yz

Nd

cj

0z N

IF

x

yz

Nd

cj

0z

SMR = 0

02SMRym 2AMR

xA m

AMR = 0

x

yz

cj

x

yz

cj

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

6

Spin Caloritronics 4

SPIN

CALO

RITR

ON

ICS

VI

Spin Caloritronics VII, Utrecht, The Netherlands, 11-15 July 2016

Spin Caloritronics

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 conductance

=T=0

F N

0

20 0 0 0 0

1 /1 /

/

c c

s s

Q

J P ST eJ G P P ST eJ ST P ST L T T T

F

E

E E

PGPG

,T ,T

spin-dependent Seebeck effect

spin-dependent Peltier effect

Landauer-Büttiker formalism (Butcher, 1990)

0

2

2

2

2222

0

2

2

2F

F

B F

B

B F

B

E

g E

g E

g E

eG dEh E

k E EeGS dEh e E k

g E

G EeLT

f

fT

k E EeS G dET h e E k T

E

S Gf LT

,

2n m E

nmnmg E t

nmt transmission amplitude

total transmission probability n

m

,f E T Fermi-Dirac function

Enhanced spin Seebeck effect

Hu e

t al.

(201

4)

V V72 22K Ks cS S

1P

Contents

Spin Seebeck effect in YIG

7

(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~

Collinear spin configuration

m

N F

0FsI N

sI

Spin current conversion

m

N F

0FSI N

sI

Spin current conversion

m

N F

0FSI N

sI

Small angle spin transfer

magnon creation

magnon annihilation

8

© 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

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

JQ JQ

YIG (200 nm)|GGG20

0 m

VSPE

1st harmonic signals

Magnon transport

Corn

eliss

en e

t al.

(201

5)

(also Kajiwara et al. (2010)) Contents

Spin Seebeck effect in GIG

9

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

J. Barker (2015)

GdIG spin wave power spectrumand chirality.

Geprägs et al. (2015)

H

10

CollaboratorsSendaiOleg TretiakovAdam CahayaTakahiro ChibaSaburo TakahashiJoe Barker

DelftPeng YanYunshan CaoAkashdeep KamraYaroslav BlanterKa ShenYang Zhou

EuropeRembert DuineArne BrataasHans SkarsvågPaul Kelly

SendaiEiji SaitohDazhi HouHiroyasu NakayamaKoki TakanashiKenichi UchidaSubrojati Bosu

GermanyStefan GeprägsSebastian GönnenweinMathias AlthammerMichael SchreierMathias Kläui

AsiaKe XiaJiang XiaoBabak Zare RameshtiHedyeh KeshtgarSadamichi MaekawaYanting Chen

GroningenBart van WeesJoost FlipseFasil DejeneNynke Vlietstra

AmerikasYaroslav TserkovnyakAxel HoffmannIsaac Acosta