heat transport by magnons, phonon drag, and the spin...

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

.


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


1. Longitudinal Spin Seebeck Effect

Pt/YIG


x

z

y-x

K.Uchida & al. Appl. Phys. Lett. 97, 172505 (2010)

Longitudinal Spin‐Seebeck Effect YIG/Pt


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


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:


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


Magnon thermal conductivity in YIG

MAGNONMAGNONMAGNONMAGNON vC 31

TOTAL

PHONON

MAGNON

Same idea: freeze out magnons by applying magnetic field

along [100] axis


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


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


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


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


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)


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]


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)


B // T // easy axes


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


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


• 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]


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?

?


3. InSb

• No exchange coupling: spin polarization from Landau levels

• No magnon conductivity: phonon drag• Giant spin‐Seebeck‐like effect


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


-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)


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


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


-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


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


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

QQ

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


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


heat transport by magnons, phonon drag, and the spin...

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