sse present
TRANSCRIPT
-
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
-
8/3/2019 SSE Present
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)
-
8/3/2019 SSE Present
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
-
8/3/2019 SSE Present
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),
-
8/3/2019 SSE Present
5/18
Dissipative spin currents :
spin
j j j
j j j
= + = Insulating magnets are good spin current conductors!!
-
8/3/2019 SSE Present
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!
-
8/3/2019 SSE Present
7/18
Model for spin injection by thermal magnons
(c.f., J. Xiao and G. Bauer)
-
8/3/2019 SSE Present
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)
-
8/3/2019 SSE Present
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)
-
8/3/2019 SSE Present
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
-
8/3/2019 SSE Present
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)
-
8/3/2019 SSE Present
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!
-
8/3/2019 SSE Present
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
-
8/3/2019 SSE Present
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)
-
8/3/2019 SSE Present
15/18
Spin Seebeck eff. without global spin current
Our interpretation
Phonon drag: Effective at low-T.
GaMnAs: low Curie temp
-
8/3/2019 SSE Present
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)
-
8/3/2019 SSE Present
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)
-
8/3/2019 SSE Present
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!!