Spin caloritronics:
Moosa Hatami
spin-dependent thermoelectrics and beyond
Gerrit E.W. Bauer
Reimei
Institute for Materials Research & WPI-AIMR, Tohoku University
Kavli Institute of NanoScience, TU Delft
Spin caloritronics
Thermodynamic analysis of interfacial transport and of the
thermomagnetoelectric system
M. Johnson and R. H. Silsbee, Phys. Rev. B 35, 4959 (1987)
name
alternative name
electronics
spintronics
calorimetry
caloritronics
spin caloritronics
subject
control of charge
transport
spin electronics
control of spin &
charge transport
measuring heat
heattronics,
thermotronics
control of heat
transport
spin caloric transport
control of spin, charge
& heat transport
Spin Caloritronics 4
Spin caloritronics: G.E.W. Bauer, E. Saitoh & B.J. van Wees, In: Nature
Materials Insights “Spintronics”, Nature Materials 11, 391 (2012).
Contents
• Why?
• Heat
• Spin
• Spin and Heat
Physics of spin caloritronics
• Spin-dependent (magneto) thermoelectrics
o Spin-dependent Seebeck and Peltier effects
o Magneto-Seebeck tunneling
• Spin Seebeck/Peltier effects
• Thermal spin injection
• Thermal spin transfer torques
• Heat-driven magnetization dynamics
• Magnonic heat & spin transport
• Nanoscale magnetic heat engines
• Spin, planar and anomalous Nernst, Ettingshausen,
and Righi-LeDuc effects
• Spin-dependent heat conductance (spin heat valve)
• General spin-dependent irreversible thermodynamics
Not: magnetocalorics (adiabatic demagnetization)
1
STT MRAM
Applied thermoelectrics
Peltier spot cooling
of integrated circuits
© nextreme.com
STT-M
+ IBM/Micron, Sony, Intel, Qualcomm, …
Energy waste in Gcal/year
underground
train stations
Thermoelectric conversion of waste heat
Toshiba Review 63, 7 (2008)
mheat scavenging/harvesting
unrecycled waste heat
transformer
steel furnace-related waste incinerators
© cosmosmagazine.com
温度（°C)
Contents
Metals
• Why?
• Heat
• Spin
• Spin and Heat
Thomas Johann
Seebeck
(1770-1831)
 Jc 

 V  T  0
V1
Jc
V2
G 
T1
JQ
T2
 J 
Ke   Q 
 T  J
Wiedemann-Franz Law:
Lorenz number:
c
0
Ke
 L0T
G
2
2
  kB 
L0 


3 e 
lim
T 0
2
Thermoelectric power
T1
Peltier effect
 V 
S 

 T  J c  0
T2
T
JQ  Jc 
J 
 Q 
 J c  T 0
T2=T
Seebeck coefficient
Peltier coefficient
V
Thermoelectric heat pump:
Thermocouple:
T1
SA
T2
J Q
A
J Q
J Q    A   B  J c
Jc
 V   S B  S A  T
B
SB
Heat transport in metals
Heat and charge transport (electron like)
E
E
Je> Jh
Je
kBT(x)
EF
kBT(x)
EF
x
x
Jh
Jh
g(E)f(E,x)
f(E,x)
lim S  
T 0
eL0T g ( )
0
g ( F )  
F
Heat and charge transport (hole like)
Lars Onsager Memorial at NTNU Trondheim
E
Je< Jh
kBT (x)
EF
x
The Nobel Prize in
Chemistry 1968:
“for the discovery of the
reciprocal relations bearing his
name, which are fundamental
for the thermodynamics of
irreversible processes”
Jh
g(E)f(E,x)
lim S  
T 0
eL0T g ( )
0
g ( F )  
F
Lars Onsager
3
Figure of merit
Thermoelectrics
 V
 J c   L11 L21  
J   
  T
L
L
 Q   12 22  
 T
L12  L21
 V   R
J 
 Q  




T
V
T＋T
V+V

S 1 , R1 , K 1
W
Onsager reciprocity
R = 1/G
K
S
 = ST
electrical resistance
thermal conductance
Seebeck coefficient
Peltier coefficient
Onsager-Thomson (Kelvin)
relation
TH
1  ZT  1
1  ZT 
TL
TH
S 1  S 2  T
R1  R2 K 1  K 2 
2
ZT 
S 2 , R2 , K 2
S   Jc 
K   T 
W
T

JQ TH
TL
C.B. Vining, An inconvenient
truth about thermoelectrics,
NatMat (2009).
Electron spin
Contents
up
• Why?
• Heat
• Spin
• Spin and Heat
© U. Regensburg
down
Spin-accumulation and spin-current
Stoner metallic ferromagnet
F
EF
N
Nsd  D sf
py
2
pF

pF

px
Nsd
D
 sf
spin-flip diffusion length
diffusion constant
spin-flip relaxation time
4
Spin valve and giant magnetoresistance (GMR)
Current-induced spin-transfer torque
N
F

GMR 
R AP  RP
R AP


m
2

 R  R 
2
 
 P
 R  R  
z
y



ISN
ISF  0

T  I SN  g  VN VN / 2
g 
↑
Onsager reciprocals
(Brataas et al., 2011)
LLG equation
Magnetization motion causes spin currents
(spin pumping, Tserkovnyak, 2002).
Heff
spin transfer torque
  L
M
mm
 
J
 s   L sm
L ms   Heff 
L ss   Vs 
L sm Μ  L
T
ms
 Μ  g

e Vs  s     
N


Berger (1996)
Slonczewski (1996)
spin accumulation
• Why?
• Heat
• Spin
• Spin and Heat
spin mixing conductance
Thermal spin-injection by metals
FM
Js

M
spin conductance
spin pumping
↓
Contents
Spin torque and spin pumping
Spin currents cause magnetization motion
(spin transfer torque, Slonczewski, 1996).
spin-mixing conductance
Thermal spin-injection by metals
 Jc 
 
 Js   G
J 
 Q
 1
 P

 ST

P
1
P ST
ST
P ST
L0T 2
spin-dependent
Peltier effect
  V  V   / 2 

  V V




  T / T 


P 
 E PG
E G
EF
spin-dependent
Seebeck effect
JQ
Mark Johnson and R. H. Silsbee (1987)
5
Single particle spin caloritronics (expt.)
Experiment
Spin-dependent Seebeck effect
Magneto-Seebeck tunneling and
magneto heat conductance
Tunneling anisotropic magnetothermopower in GaMnAs/GaAs
Reference
Slachter et al.
Walter et al., Liebing
et al., Lin et al.
Zhang et al.
Naydenova et al.
Thermal spin injection into Silicon Le Breton et al.
Spin-dependent Seebeck effect
≠ spin Seebeck effect!
Year
2010
2011
2012
2013
2011
T
2011
Spin-dependent Peltier effect
Flipse et al.
2012
Spin heat accumulation
Dejene et al.
2013
Slachter et al.
(2010)
Spin-dependent Peltier effect
Collective effects in insulators
magnetic
(electric) insulator
NM
Onsager reciprocity holds
between spin-dependent
Seebeck and Peltier effects.
Flipse et al. (2012)
(Longitudinal) spin Seebeck effect
Spin Hall effects
V [V]
≠ spin-dependent Seebeck effect!
spin Hall effect
inverse spin Hall effect
Uchida et al. (2010/2011)
6
Noise-induced spin currents
(Longitudinal) spin Seebeck effect
≠ spin-dependent Seebeck effect!
V [V]
FM
N
© Kajiwara et al.
Foros et al. (2005)
Xiao et al. (2009)
Uchida et al. (2010/2011)
Onsager analysis of sSe (magn. insulators)
Origin of spin Seebeck effect
TF TN
LsQ 
Xiao et al. (2010)

m
m0  Heff
Js  Js
pump
 Js
J-N noise

 A ' g  T FM  T Ne

Xiao et al. (2010)
Adachi et al. (2010)
Collective spin caloritronics (expt.)
Experiment
Reference
Year
Spin Seebeck effect
Uchida et al.
Jaworski et al.
2008,2010
2010
Magnon-drag thermopower
Costache et al.
2011
Thermal spin torque in spin
valves
Magnon heat conveyor belt
Yu et al.
2010
Saitoh c.s.
2013.
Parkin c.s.
Unpublished.
Heat current-induced domain
wall motion
Vs
   L mm
M
  
J
 s    L sm
 J Q   L mT
   Qm 0
V ISHE  AJ s
  Re g T
M sVcoh
thermal field
L ms
L ss
LQs mT0
magnon Peltier effect
spin Seebeck effect
m0LmQ   Heff

m0LsQ   Vs

LQQ   T / T





heat conductance
spin Peltier effect
Potential applications of spin caloritronics
• Heat management and enhanced logics by
magnetic tunnel junction
• Spin Seebeck planar thermoelectric generator
• Spin Seebeck position sensitive heat detector
• Highly efficient thermal magnetization
reversal
• Spin caloritronic nanomachines
7
Magnetic tunnel junctions
Thermopower of magnetic tunnel junctions
MgO (optical): Walter et al. (2011)
MgO (electrical): Liebing et al. (2011)
Al2O3 (optical): Lin et al. (2011)
MgO(electrical): Zhang et al. (2012)
Fe () | MgO | Fe (/)
1 nm
MgO
CoFeB
TMR 
- large thermopower
(> 1 mV/K)
- switchable thermopower
(TMS > 200 %)
- low heat conductance,
large ZT?
- thermal switching?
R AP  RP
RP
 1000%
Walter et al. (2011)
John Slonczewski (2010)
John Slonczewski (2010)
I
V
Torque generation efficiency:
J. Xiao et al. (2010)
I
torque/ eV

current/e
F
Heat assisted magnetic recording (HAMR)
magnetic
coherence
volume
spin
pumping
V
spin torque
I z  S S T F  T N 
spin torque
torque/ eV
~
I /e

1 terabit per-square-inch breakthrough © Seagate/2012
8
Planar spin Seebeck generator
Thermopile
JQ
V  const . J Q L
L~1m
 1V

m
YIG
t ~10-50 nm

V
Kirihara et al. (2012)
Uchida et al. (2012)

Position sensitive heat detector
Spin Seebeck generators
Image reconstruction
Uchida et al. (2011)
Primitive magnetic heat engine
ferromagnets
Magnetic nanoscale heat engines
T1
T2
T1
Brownian motor:
© www.imagesco.com
T2
Continuum version
of Feynman’s ratchet & pawl
Heat pump:
Motor:
Kovalev et al. (2010,2011)
Bauer et al. (2010)
9
Conclusions
• Spin, charge, and heat transport are coupled in
magnetic nanostructures -> spin caloritronics.
• In magnetic metals the spin-dependence of the
conductance causes spin-dependent
thermoelectric effects.
• The collective dynamics in magnetic insulators
cause completely new phenomena such as the
spin Seebeck effect.
• Spin caloritronics provides new strategies for
waste heat scavenging and heat management in
nanostructures.
Collaborators
Sendai
Oleg Tretiakov
Adam Cahaya
Takahiro Chiba
Saburo Takahashi
Isaac Acosta
Europe
Alireza Quaiumzadeh
Arne Brataas
Hans Skarsvåg
Paul Kelly
Delft
Yanting Chen
Peng Yan
Fateme Joibari
Yunshan Cao
Hujun Jiao
Akashdeep Kamra
Yaroslav Blanter
US
Yaroslav Tserkovnyak
Sendai
Hiroyasu Nakayama
Eiji Saitoh
Koki Takanashi
Kenichi Uchida
Subrojati Bosu
Asia
Ke Xia
Jiang Xiao
Yan Zhou
Hedyeh Keshtgar
Sadamichi Maekawa
Munich
Sebastian Gönnenwein
Mathias Althammer
Michael Weiler
Groningen
Bart van Wees
Fasil Kidane
Nynke Vlietstra
10