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
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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!!
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