Sadamichi Maekawa

Advanced 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

Seebeck effect vs. Spin Seebeck effect:

TSV δδ =

TSV spinspin δδ =

c.f., G. Bauer’s talk

(Inverse Spin Hall effect)

Electric voltage

Spin accumulation (Spin voltage)

Seebeck effect： Entropy flow vs. charge current, Spin Seebeck effect： Entropy flow vs. spin current.

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

Inverse spin Hall effect

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), R. Ibarra (Zaragoza), S. Rezende (Recife).

Dissipative spin currents :

spin

j j jj j j

↑ ↓

↑ ↓

= +⎧⎨ = −⎩

Insulating magnets are good spin current conductors!!

Spin  Seebeck  effect  is  a  general  phenomenon  in  ferromagnets:  

Ferromagne7c  metals  Py.  Fe,  Co  Ni  etc.  Ferromagne7c  inslators    YIG,  Ferrites.    Ferromagne7c  semiconductors    (Ga,Mn)As:  Michigan  State  U.  +  UCSB  

∑∑ −−+==q

qqqqs vnvnnjq

qqv qvq D2= n : Magnon number

Propagating spin wave

qq nn −≠

qq nn −= :  Standing  wave  

:  Propaga7ng  wave  (spin-­‐wave  spin  current)  

“Spin waves are common in ferromagnets”

Spin current is a non-equilibrium quantity!

Model for spin injection by thermal magnons

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

Linear response of LOCAL spin injection by heat

!

"ts = J

sdm # s + (D

N$2%&)(s% s

0m) + lBloch eq.:

LLG eq.:

!

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

!

Js

in"< #

tsz

>= JsdIm d$% < s

+($)m&

(&$) >Injected spin current: !

(s0

= "NS0Jsd)

s+(!) = !s0XF*("!)"N

*("!)#h+(!)+ "N*("!)l+(!)

m"(!) = XF (!)#h"(!)+ JsdXF (!)"N (!)l

"(!)

!

(a±" a

x± ia

y)

!

Js

in= J

sdd"#

1

"Im$

N(")ImX

F(") %s

0< &h+

(")&h'('") > '(Jsd

< l+(")l'('") >[ ]é Js

pump é Jsback

SSE is a competition between pumping flow (noise in F) and back flow (noise in N)

!Jsin = Js

pump " Jsback = A(TF "TN )

local spin injection by magnons

€

∴Jsin = A(TF −TN )

€

( A∝ Jsd2 dω∫ 1

ωImχN (ω)ImXF (ω) )

€

Jsin ≡<∂ts

z >= Jsd Im dω∫ < s+(ω)m−(−ω) >

(Field theoretical calculation of　Green’s function)

No temp-diff. between Pt and YIG in the experiment èneed to consider the effect of temp-gradient in YIG

Consider the following model

Static condition: Local equiliburium

Interpretation by magnon effective temp.

Magnon at higher (lower) temp. feels lower (higher) temp. à Spin wave dynamics for spin Seebeck effect.

1z 2z 3z

Is

P3

P1

P’2

P’1

Is ( )1z

3z2z1z

Is ( )2z

Is ( )3z(b)

P2

TN1

z

(a)

~~ TPtTbath

~~ TYIGTmageff

(c) T

z

N3N1 N2

2F1F 3F

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

Spin wave

Spin wave

€

∴Jsin = A(TF −TN )

T-dependence of Jsph-drag:

Jsph-drag shows low-temp. enhancement due to the rapid suppression of umklapp scatt.

( ßSimilar phenomenon known in thermoelectrics )

€

€

Jsph−drag ∝τ phΔT

Phonon: additional ingredient!

Phonon-drag contribution to SSE

Phonon drag process; Magnons dragged by nonequilibrium phonons à spin injection

€

Jsph−drag ∝τ phΔT

Phonon drag gives low-T enhancement of SSE

due 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

Fitting of the data by our theory

€

Jsph−drag (T) = const ⋅ B1(T)B2(T)τ ph (T)

€

B2(T) = (T /TM )9/2 dvv7 / 2

th(v /2)0

TM /T

∫

€

B1(T) = (T /TD)5 duu6

sh2(u /2)0

TD /T

∫€

τ ph(T) = τ (0)ph1

1+ (1/a)exp[−b(TD /T)]⎛

⎝ ⎜

⎞

⎠ ⎟

11+ (1/c)(T /TD )⎛

⎝ ⎜

⎞

⎠ ⎟

Spin Seebeck eff. without global spin current

Our interpretation

Phonon drag: Effective at low-T. GaMnAs: low Curie temp

Longitudinal Spin Seebeck Effect: (Conventional vs. Longitudinal)

spin currentinjected into Pt

NEGATIVE spin injection@ colder side@ colder side

POSITIVE spin injection

HO

T

CO

LD

HOT

COLD

LongitudinalConventional

Heat current

Pt Pt Pt

YIG YIG

Pt

(Transverse)

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

YIGYIG

YIG

Pt

Phonon

electron

spin accumulation

YIG

Pt

YIG

magnon

(a) (b) (c)

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!!