sse present

8/3/2019 SSE Present

1/18

Sadamichi MaekawaAdvanced Science Research Center,

Japan Atomic Energy Agency at Tokai

and CREST-JST.

NEWSPIN2 at Texas (December 15-17, 2011)

Phonon-Drag on Spin Seebeck Effect


2/18

Seebeck effect vs. Spin Seebeck effect:

TSV =

TSV spinspin =

c.f., G. Bauers talk

(Inverse Spin Hall effect)

Electric voltage

Spin accumulation

(Spin voltage)


3/18

Seebeck effectEntropy flow vs. charge current,

Spin Seebeck effectEntropy flow vs. spin current.

c.f., S. Maekawa et a.:Physics of Transition metal oxides(Springer, 2004)

Inverse spin Hall effect


4/18

Content:

Spin wave Spin Current:

Linear response theory

* Spin Seebeck effect:

in YIG (K. Uchida et al.:Nature Materials ((2010))

in (Ga,Mn)As(C.M.Jaworski et al.:Nature Materials ((2010)).

* in Fe-Ni/Pt hybrid wires(K.Uchida et al.:Nature Materials ((2011)).

Theory:

H,Adachi, J.Ohe, S, Takahashi, J. Ieda (JAEA).

Experiment:

E. Saitoh, K. Uchida, Y. Kajiwara, K. Ando (Tohoku University),J. Heremans and his colleagues (Ohio State University).

Acknowledgements:

G. Bauer (Tohoku/Delft), J. Xiao (Fudan), B. Hillebrants

(Kaiserlautern),


5/18

Dissipative spin currents :

spin

j j j

j j j

= + = Insulating magnets are good spin current conductors!!


6/18

SpinSeebeckeffectisageneralphenomenoninferromagnets:

Ferromagne7cmetalsPy.Fe,CoNietc.Ferromagne7cinslatorsYIG,Ferrites.

Ferromagne7csemiconductors(Ga,Mn)As:MichiganStateU.+UCSB

+==q

qqqqs vnvnnjq

qqv qv

qD2=

n : Magnon numbe

Propagating spin wave

qq

nn

qqnn

= :Standingwave

:Propaga7ngwave(spin-wavespincurrent)

Spin waves are common in ferromagnets

Spin current is a non-equilibrium quantity!


7/18

Model for spin injection by thermal magnons

(c.f., J. Xiao and G. Bauer)


8/18

Linear response of LOCAL spin injection by heat

"t

s = Jsd

m # s +(D

N

$2%&

)(s% s

0m

)+ l

Bloch eq.:

LLG eq.:

"tm = Jsds #m + $(Heff + h)#m +%m #"tm

Js

in"< #

tsz>= J

sdIm d$% < s+($)m&(&$) >Injected spin current:

(s0 = "NS0Jsd)

s+

(!) = !s0XF*("!)"

N

*("!)#h

+

(!)+ "N

*("!)l

+

(!)

m"(!) = X

F(!)#h

"(!)+ J

sdX

F(!)"

N(!)l

"(!)

(a

" ax ia

y)

Js

in

= Jsd

d"#1

"Im$

N(")ImX

F(") %s

0< &h

+

(")&h'('") > '(J

sd< l

+

(")l'('") >[ ]

Jspump Jsback

SSE is a competition between

pumping flow(noise in F) andback flow(noise in N)

!Jsin= Js

pump"Js

back= A(TF"TN)


9/18

local spin injection by magnons

Js

in

= A(TFT

N)

( AJsd2

d 1Im

N()ImX

F() )

Js

in= J

sdIm d < s+()m() >

(Field theoretical calculation of Greens function)


10/18

No temp-diff. between Pt and YIG in the experiment

need to consider the effect oftemp-gradient in YIG

Consider the following model

Static condition:

Local equiliburium


11/18

Interpretation by magnon effective temp.

Magnon at higher (lower) temp. feels lower (higher) temp.

Spin wave dynamics for spin Seebeck effect.

1z 2z 3z

Is

P3

P1

P2

P1

Is ( )1z

3z2z1z

Is ( )2z

Is ( )3z(b)

P2

TN1

z

(a)

~~ TPtTbath

~~

TYIG

Tmag

eff

(c) T

z

N3N1 N2

2F1F 3F

== T T1 =F2 2N2 = TT ==TN3 F3F1 T T T3

Spin wave

Spin wave

Js

in

= A(TFT

N)


12/18

T-dependence of Jsph-drag:Jsph-drag shows low-temp. enhancement due to the rapid suppressionof umklapp scatt.( Similar phenomenon known in thermoelectrics )

Jsphdrag

phT

Phonon: additional ingredient!


13/18

Phonon-drag contribution to SSEPhonon drag process;

Magnons dragged by nonequilibrium phonons

spin injection

Jsphdrag

phTPhonon draggives low-T enhancement of SSEdue to the rapid suppression of umklapp scatt.

TN1

1z 2z 3z

T2

T1

T3

z

(b)

T(z)

(a)

magnon

electron phonon

N3N1

3F1F 2F

N2

== T T1 =F2 2N2 = TT ==TN3 F3F1 T T T3


14/18

Fitting of the data by our theoryJ

s

phdrag(T) = constB

1

(T)B2

(T)ph(T)

B2(T) = (T/T

M)9 / 2 dvv

7 / 2

th(v /2)0

TM /T

B1(T) = (T/TD)5 duu

6

sh

2

(u /2)0

TD

/T

ph (T) = (0)

ph

1

1+ (1/a)exp[b(TD /T)]

1

1+ (1/c)(T/TD)


15/18

Spin Seebeck eff. without global spin current

Our interpretation

Phonon drag: Effective at low-T.

GaMnAs: low Curie temp


16/18

Longitudinal Spin Seebeck Effect:(Conventional vs. Longitudinal)

spin current

injected into Pt

NEGATIVE spin injection

@ colder side@ colder side

POSITIVE spin injection

HOT

COLD

HOT

COLD

LongitudinalConventional

Heat current

Pt Pt Pt

YIG YIG

Pt

(Transverse)


17/18

Theory of Longitudinal SSE

Electron-phonon coupling > Phonon-Magnon coupling,

Pt is heated by phonon heat current greater than YIG.

KEY: Heat current flows through Pt terminal

in case of the longitudinal SSE.

=

COLD

HOT

T2

T1

T2

T2

T2

T1

COLD

HOT

T2

T2

T1

COLD

HOT

Pt

YIG

YIG

YIG

YIG

Pt

Phonon

electron

spin accumulation

YIG

Pt

YIG

magnon

(a) (b) (c)


18/18

Summary:

1) Spin-Wave Spin Current,Linear Response Theory of Spin-Wave Spin Current

Magnetic insulator is a good spin current conductor!

2) Spin Seebeck effect in a variety of systems,

Conversion among heat, electric and magnetic energies

In the same way as Seebeck effect,Spin Seebeck effect may be applied to a variety of

Energy saving devices!!

sse present

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