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Joseph P. Heremans
In collaboration with: Roberto Myers, Christopher M. Jaworski, Steve Boona, Hyungyu Jin, Ezekiel Jonston‐Halperin, Shawn Mack and David D. Awschalom
KITP, Concepts in SpintronicsSanta Barbara, CA, Oct. 2, 2013
Funding: U.S. National Science Foundation CBET 1133589 "SpinCats"
Heat transport by magnons, phonon‐drag, and the Spin Seebeck Effect
KITP‐Spintronics 1
Measurements rely on inverse spin-Hall effect:
Spin-Seebeck effect definition
σJE S ISHEISHE D
Grossly exaggerated for effect
TSCoefSeebeckSpin
x
xxy
.
KITP‐Spintronics 2
Heat
Heat
Longitudinal Spin-Seebeck Effect (LSSE)
Transverse Spin-Seebeck Effect (TSSE)
COLD
HOT
VV1 V2 V3 V4
T, jq
zy
x
Hz
sjsjs
jsEihse
Eihse
Ferromagnet:
Metal: Pu (Uchida & al, Nature, 2008)Semiconductor: GaMnAs(Jaworski & al, Nat. Mater, 2010)Insulator: YIG(Uchida & al, Nat. Mater, 2010)
Pt
Ferromagnet: Can only be an Insulator: YIG(Uchida & al, APL2010) KITP‐Spintronics 3
Motivation: Solid State Heat Engines
Advantages:• No moving parts• Robust, infinite lifetime, no maintenance• Very high power density (specific power) => light weight
Disadvantage:• Lower efficiency
Thermoelectric generator
Heremans & al., Nature Nano (2013) KITP‐Spintronics 4
Structure of this lectureEmphasis on the thermal generation of the spin flux
1. Longitudinal spin SeebeckIn the Ferromagnet: Magnon thermal conductivity
2. Transverse Spin Seebeck effectNon‐local version of longitudinal spin Seebeck effectGaMnAs: the role of phononsPhonon drag
3. InSb, the giant spin Seebeck effect
4. Length Scales
KITP‐Spintronics 5
1. Longitudinal Spin Seebeck Effect
Pt/YIG
KITP‐Spintronics 6
x
z
y-x
K.Uchida & al. Appl. Phys. Lett. 97, 172505 (2010)
Longitudinal Spin‐Seebeck Effect YIG/Pt
KITP‐Spintronics 7
1. T drives the magnons out of thermal equilibrium: 1.1 magnon thermal conductivity1.2 phonon‐drag
2. Spin‐torque results from magnons striving back to equilibrium
3. Net spin flux diffuses into Pt
4. Spin‐orbit interactions in Pt convert JS => EISHE
Ferromagnet
ISHE mediumPlatinum
Js
T
• S. Hoffman & al., arXiv1304.7295v (2013)• J. Xiao et al., PRB 81, 214418 (2010).• H. Adachi, J.-I. Ohe, S. Takahashi, and S.
Maekawa, PRB 83, 094410 (2011).• H. Adachi et al., APL. 97, 252506 (2010).• K. Uchida et al., SSC 150, 524 (2010).
Understanding the Longitudinal Spin‐Seebeck effect
KITP‐Spintronics 8
Magnon density of states D(), ferromagnets
222 kJSagH zBk Magnons have only a single polarization for each value of k
Number of magnon states of frequency between and +d
/
/)(
zB
zB
gHJSa
gH
, 24
1 , 0
3/2
22
D
zBgH
D
Magnetic fields can freeze out magnons, 10‐4eV/T or 1.3 K / T
Kittel:
KITP‐Spintronics 9
Magnon specific heat
TkE
JSaTk
dTdUTC
dfTU
B
gMBMAGNON exp.)(
)()()(
3/2
2
00
21130
D
Phonons + magnons
phonons only
Assuming phonons and magnons are independent, one can assume additivity
Approximate: magnons and phonons hybridize
CPHONON
CMAGNON T1.1CTOTAL
KITP‐Spintronics 10
Magnon thermal conductivity in YIG
MAGNONMAGNONMAGNONMAGNON vC 31
TOTAL
PHONON
MAGNON
Same idea: freeze out magnons by applying magnetic field
along [100] axis
KITP‐Spintronics 11
Douglass, Phys. Rev. 129, 1132 (1963).Pan & al., arXiv1302.6739v1Boona & al., unpublished
SB
MAGNONQ jTkTj .
Magnon and phonon mean free paths (YIG)
MFPMAGNON
MFPPHONONPHONONPHONONPHONONPHONON
MAGNONMAGNONMAGNONMAGNON
vC
vC
3131
5000 ms‐1
8500 ms‐1crystalthickness
In YIG at low temperature the magnon “Energy mean free path” 5 to 50 m
KITP‐Spintronics 12
T‐0.7
Boona & al., unpublished
What can go wrong experimentally?Thermomagnetic & Galvanomagnetic Effects
• Hall effect (Ordinary, anomalous)
• Nernst effect (Ordinary, anomalous)
• Anisotropic magnetoresistance, planar Hall effect
• Anisotropic magneto‐thermopower, planar Nernst effect
KITP‐Spintronics 13
Longitudinal Spin‐Seebeck Effect ONLY on YIG/Pt
The planar Nernst effect has exactly the same symmetry as the longitudinal spin‐Seebeck effect
LSSE measurements impossible on electrically conducting ferromagnets
KITP‐Spintronics 14
2. Transverse Spin Seebeck Effect
• Lifts the requirement that the spin‐polarized material be electrically insulating
Ferromagnets: Metal: Pu (Uchida & al, Nature, 2008)Semiconductor: GaMnAs (Jaworski & al, Nat. Mater, 2010)Insulator: YIG (Uchida & al, Nat. Mater, 2010)
No exchange coupling: Semiconductor with large s/o interactions: InSb (Jaworski & al, Nature, 2012)
• Unresolved issue: the length scale
KITP‐Spintronics 15
Local vs non‐local spin injection
Non‐local electrical spin injection:• spin‐polarized charge current is driven
by an applied electric field.• spin current parallel to a charge current • => spin current diffuses from the
ferromagnet into the normal metal.
jC, jS, jQ
j C, j
S, j Q
Equivalent for electrical spin injection:
F. J. Jedema, A. T. Filip & B. J. van Wees, Nature 410 345 (2001)
KITP‐Spintronics 16
GaMnAs In‐plane easy axesMn content 7-18%
[-110]
[110]
[100] [010]
-75 -50 -25 0 25 50 75
-40
-20
0
20
40
50KM (e
mu/
cm3 )
B (Oe)[100]
[-110]
[110] 16% Mn[‐1,1,0] & [100] are easy axes
GaAs substrate
GaMnAs
InGaAs
[001]
Relaxed
Tensile strain
30 nm thick, 6% Mn
B (Oe)
-1000 1000-500 500
M (e
mu
* 10
-5)
-4
42
-2
[001]
KITP‐Spintronics 17
Image taken with thermometry attached (2nd or 3rd run)1st – 2nd run read voltage on Cu wires
THot
TCold
thermometry:cernoxresistors ~15mm
Heater
Heat Sink
QD PPMS brochure
GaMnAs: Measurement setup
Vy
Vy
Pt bars(10 nm)
ISHE
GaMnAs(30‐100nm)
KITP‐Spintronics 18
B // T // easy axes
KITP‐Spintronics 19
Jaworski & al, Nat. Mater, 2010
Dependences on temperature gradient
1. Dependence on temperature gradient is linear
=> can assign a "Seebeck coefficient" to the slope
2. Dependence on strip position is totally unusual for transport coefficient
Contrast with charge‐Seebeck between strips X
X
X
XXX
X
Y
X
YXY
TV
TE
wL
TV
TES
2
KITP‐Spintronics 20
Position dependence of Spin‐Seebeck Sxy
A skewed and off-center sinh(x)function, with a characteristic length scale of 4 -6 mm
)]2
(sinh[)( 0xLxxS XY
Similar to T(magnons) in D. J. Sanders and D. Walton, Phys. Rev. B 15 1489 (1977) KITP‐Spintronics 21
GaAs substrate
GaMnAs
InGaAs
Easy axis[001]
Relaxed
Tensile strain
Easy axis out‐of‐plane
Out of plane uniaxial
[001]
Q
B
M
10o
B
T + T
z
y
M[001]
x
T
10°
ĵs
T
σ
0σJDJ sc => We expect no signal KITP‐Spintronics 22
• Indium point contacts give large signal• True Nernst signal• Has NO spatial dependence
• The Pt strips give no signal• The Pt strips short out the Nernst
signal• We are not measuring parasitic Nernst
effect on Pt strips
B
T + T
z
y
M[001]
x
T
10°
ĵs
T
σ
0σJDJ sc
-750
0
750
V y (n
V)
0
5
10
15
20
25
Mom
ent (
emu
cm-3
)
-2000 -1000 0 1000 2000B 10o tilt off [001] (Oe)
-60
0
60
Vy
(nV
)
[001] 10o tilt
Hot Point Contact
ColdPoint Contact
Hot Strip
Cold Strip
Strips
MISSING 53K SQUID
Transverse Nernst‐Ettingshausen effect
KITP‐Spintronics 23
• No change in signal
• Spin-Seebeck does not result from a macroscopic spin-current in the plane.
• The substrate, not the film, carries the mm-range information
Spin Seebeck is NOT due to spin current along
2L
2L
0
Scratch #1Scratch #2
Vy
Hotend
Coldend
Crack
40 60 80 100 120 140Tavg (K)
-1.2
-0.8
-0.4
0
S xy
V y/
T x (V
/K)
Intact
B // [110]
40 60 80 100 120 140Tavg (K)
-1.2
-0.8
-0.4
0
S xy
V y/
T x (V
/K)
Intact1 Scratch
B // [110]
40 60 80 100 120 140Tavg (K)
-1.2
-0.8
-0.4
0
S xy
V y/
T x (V
/K)
Intact1 Scratch
Both Scratches
B // [110]
KITP‐Spintronics 24
The Maekawa‐Adachi Anzats: it’s the phonons in the subtrate that are the driving force ( Adachi, Appl. Phys. Lett. 97 252506 (2010))
Phonon‐drag in GaAs substrate of GaMnAs
0
0.3
0.6
0.9
|Sxy
(V
K-1
)|
0
0.5
1
1.5
(G
aAs)
(W
cm
-1K-
1 )
0
25
50
75
M (e
mu
cm-3
)
0 40 80 120 160T (K)
0
10
20
xx
(V
K-1
)
1 10 100T (K)
0.01
1
100
Cp
(J k
g-1 K
-1)
a+bT-1
a+bT1.5
bT-1
a+bT3
(a)
(b)
(c)
b(Tc-T)-
b(Tc-T)-
0
2
4
6
| Sxy
(V
K-1
) |
5
10
15
(G
aAs)
(W
cm
-1 K
-1)
10 100T (K)
0
0.25
0.5
0.75
xx
(mV
K-1
)
0
25
50
M (e
mu
cm-3)
(a)
(b)
Thermal conductivity of substrate
High Low
SpinSeebeck
Phonon- Drag
Thermo-power
Big Small
Big Small
Jaworski et al., Phys. Rev. Lett. 106186601 (2011)
KITP‐ 25
Phonon Drag
0
2
4
6
| Sxy
(V
K-1
) |
5
10
15
(G
aAs)
(W
cm
-1 K
-1)
10 100T (K)
0
0.25
0.5
0.75
xx
(mV
K-1
)
0
25
50
M (e
mu
cm-3)
(a)
(b)
A = oil dropletsB = air molecules
A = phononsB = electrons
A = phonons,B = magnons
When: 1. A‐B collisions dominate
both A‐scattering and B‐scattering
2. A‐particles have drift velocity
Then:1. A‐particles impel B‐
particles with momentum IN ONE DIRECTION
2. Out‐of‐thermal equilibrium3. Very intense
A – wall collisions dominate
A – B collisions dominate
How do “phonon‐drag” curves get to have a maximum in temperature?
?
KITP‐Spintronics 26
3. InSb
• No exchange coupling: spin polarization from Landau levels
• No magnon conductivity: phonon drag• Giant spin‐Seebeck‐like effect
KITP‐Spintronics 27
InSb and its Landau levelsLandau level Orbital and Zeeman splitting
**
**
22
221
2)(
mHe
mHe
Hsgnmk
EE
x
c
xc
xBCc
x
0 1 2 3 4 5 6 7H (T)
0
0.02
0.04
0.06
0.08
0.1
E (e
V)
n=2.82x1015cm-3
EF
(0,)
(0,)
(1,)
(1,)
(2,)(2,)
(3,)(4,)
From this field on up, most electrons are on the last Landau level(ultra‐quantum limit), spin‐polarized by Zeeman splitting
- 2 - 1 1 2
- 100
- 50
50
100Polarization (%)
B (T)5K
KITP‐Spintronics 28
-8 -4 0 4 8Bx (T)
Sxy
(V
K-1)
4.3K2000V K-1
InSb Spin‐Seebeck data
xHx // xT
Hx(T)
1. Signal is very large, 8 mV/K
2. Even‐symmetric (mostly) as function of magnetic field
3. Even‐in‐field part: 1. large2. ultra‐quantum‐field region
Jaworski et al., Nature 487 213 (2012)
KITP‐Spintronics 29
Temperature‐dependence of amplitudesignature of Zeeman splitting
0 10 20 30 40T (K)
10
100
1000
10000
|Sxy
|max
(V
K-1) RT )sinh(
BgTk
BgTk
R
B
B
B
B
T
2
2
2
2
Ratio between thermal energy (kBT) and Zeeman energy (gBB) for electrons on helical orbitsOnly adjustable parameter = amplitude
Shoenberg D. Magnetic Oscillations in Metals, Cambridge 1984
• RT decays slower than SdH oscillations in resistivity
0 5 10T (K)
0.1
1
10
Am
plitu
de (A
rb. U
nits
)
• Spin‐Seebeck effect exists even when orbital quantization is no longer resolved
KITP‐Spintronics 30
Potential Parasitic Voltages
-8 -4 0 4 8Bx (T)
-1.2
-0.8
-0.4
0
xxx
(mV
K-1
)3.8K8.2K16.1K
-8 -4 0 4 8Bx(T)
-40
-20
0
xyx
(V
K-1
)
4.04K5.63K8.28K11.3K15.8K
)(/
)(/
xx
yxyx
xx
xxxx
BTWV
BTLV
-8 -4 0 4 8Bx (T)
Sxy
(V
K-1)
4.3K2000V K-1
Bx // xT
Vy
VxL
W
SSE configuration Longitudinal magnetothermopowe
KITP‐Spintronics 31
-8 -4 0 4 8Bz (T)
-1500
-750
0
750
1500
xyz
(V
K-1
)4.04K5.63K8.28K11.3K15.8K
-8 -4 0 4 8Bz (T)
-4000
-2000
0
xxz
(V
K-1
)
4.06K5.63K8.35K11.4K15.0K
)(/
)(/
zx
yxyz
zx
xxxz
BTWV
BTLV
-8 -4 0 4 8Bx (T)
Sxy
(V
K-1)
4.3K2000V K-1
Potential Parasitic Voltages
Vy
Vx
Bz
xT
Transverse magnetothermopowerConventional Nernst effect
KITP‐Spintronics 32
The physics:
1. Temperature gradient creates phonon fluxChange in phonon momenta:
2. Strong phonon‐drag impels additional momentum k to electrons:
3. Strong spin‐orbit interactions transform k into a change in Zeeman splitting energy:
We actually can estimate from publishedconcentration‐dependence of g‐factor no adjustable parameters, for T=5K, T=40 mK:
cTkq B
qkx
TkeV B of 25120 %k 0 1 2 3 4 5 6 7
H (T)
0
0.02
0.04
0.06
0.08
0.1
E (e
V)
n=2.82x1015cm-3
EF
(0,)
(0,)
(1,)
(1,)
(2,)(2,)
(3,)(4,)xk k
k
KITP‐Spintronics 33
Phonon‐drag: the length scale = ½ cm
V
QB Qs
VTB
TS Tx
SBV
TT
RRne
CTV
BS
3
Narrow arm: short RS small
Wide arm: long RB large
11
1
3
PED
PED
VPED
R
Rne
C
Electrons and diffusion thermopower cancel out
KITP‐Spintronics 34Jin & al, unpublished
4 mm
4 mm 1 mm
Au:FeChromelT V
TH,1x4
TC,1x4TC,4x4
TH,4x4
QB QS
When T = 0
SBV
TT
S
B
S
B
RRne
C
TV
BS
3
41
0
10
20
30
40
V (V
)
1000 2000 3000 4000Time (s)
-1.0
-0.5
0.0
0.5
1.0
Diff
eren
tial T
C (
V)
No Heat Heater On Heater Off150K
-0.5 -0.25 0 0.25 0.5Dif. TC (V)
-10
0
10
20
30
V
T x (
V K
-1)
y=37.7*x + 13.2
4 traces => vary QL & QB
Principle of measurement: thermal potentiometer
KITP‐Spintronics 35
Differential thermal thermopower purely due to phonon drag
SBV
TT
RRne
C
TV
BS
3
Pure phonon thermopower
Length scale > 0.4 cm
KITP‐Spintronics 36Jin & al, unpublished
4. SSE signals on Metglass
-400 -200 0 200 400H (Oe)
-60
-40
-20
0
20
40
60
Vxv
x (nV
)
T = 13.2K
Tavg = 72.4K Hot side
Cu + Pt
-400 -200 0 200 400H (Oe)
-120
-80
-40
0
40
80
120
Vxy
x (nV
)
Point contact
Cold side
T = 13.2K
Tavg = 72.4K Hot side
Cold side
20 40 60 80T (K)
0
1
2
3
4
5
xyx (
nV K
-1)
Point Hot
Point Cold
Pt Hot
Pt Cold
TSSE exceedingly small, a few nV/K
• Co80Si5BFeMoNi: Ferromagnetic BULK metallic glass (Metglas)
• High Tc, yet mostly localized phonon modes (Einstein modes)
• No phonon drag contribution• Sample is bulk => no
contamination with Z
Jin & al., Solid State Commun. (subm., 2013) KITP‐Spintronics 37
Conclusions
1. Longitudinal spin‐Seebeck effect understood.2. Transverse spin‐Seebeck effect:
the length scale of the effect is surprising1. Two mechanisms put spin‐waves out of thermal
equilibrium:1. Magnon thermal conductivity2. Phonon drag
2. Mechanisms, Length scales, and Magnitude of TSSE:
Material Mechanism Mean free path Magnitude of TSSE signal
InSb Phonons Sample size, 0.5 cm (<40K) 8 mV/K (4K)
GaMnAs PhononsMagnons
In GaAs substrate similar to InSb?
5 V/K (10K)< 1 V/K (80K)
YIG PhononsMagnons
Sample size (2K); 5 m (20K)50 m (2K); 5 m (20K)
LSSE only 0.5 to 1 V/K (300K) 10 V/K (50K)
Metglas PhononsMagnons
< nm? 3 nV/K
Spin
Charge
Heat
Spintronics
Thermoelectrics
SpinCaloritronics
KITP‐Spintronics 38