Sadamichi Maekawa Advanced Science Research Center (ASRC),

Japan Atomic Energy Agency (JAEA) at Tokai

and CREST-JST.

at Rome, Italy (September 18, 2013)

Spin Current and Spin Seebeck Effect

Co-workers: 　　　Theory: H. Adachi and Y. Ohnuma (ASRC, JAEA), Experiment: K. Uchida and E. Saitoh (IMR, Tohoku University)、

Contents:

1)  Introduction of spin current and spin Hall effect,

2) The linear response theory of spin current generation, 3) Spin current generation by heat, i.e., Spin Seebeck effect,

Refs.: * H. Adachi , K. Uchida, E. Saitoh and S. Maekawa: Rep. Prog. Phys. 76, 036501 (2013), *S. Maekawa, H. Adachi, K. Uchida, J. Ieda and E. Saitoh: J. Phys. Soc. Jpn. (2013), * “Spin Current” eds. S. Maekawa et al. (Oxford Univ. Press, 2012).

Contents:

1)  Introduction of spin current and spin Hall effect,

2) The linear response theory of spin current generation, 3) Spin current generation by heat, i.e., Spin Seebeck effect,

Refs.: * H. Adachi , K. Uchida, E. Saitoh and S. Maekawa: Rep. Prog. Phys. 76, 036501 (2013), *S. Maekawa, H. Adachi, K. Uchida, J. Ieda and E. Saitoh: J. Phys. Soc. Jpn. (2013), * “Spin Current” eds. S. Maekawa et al. (Oxford Univ. Press, 2012).

Spintronics utilizes charge and spin currents on an equal footing

Charge current: flow of charges

Spin current: flow of spins

Spin current carried by conduction electrons

Spin-wave (magnon) spin current

Spin Hall Effect / Inverse SHE

Conversion between charge and spin current

Charge curent →Spin current

Spin current →Charge current

Contents:

1)  Introduction of spin current and spin Hall effect,

2) The linear response theory of spin current generation, 3) Spin current generation by heat, i.e., Spin Seebeck effect,

Refs.: * H. Adachi , K. Uchida, E. Saitoh and S. Maekawa: Rep. Prog. Phys. 76, 036501 (2013), *S. Maekawa, H. Adachi, K. Uchida, J. Ieda and E. Saitoh: J. Phys. Soc. Jpn. (2013), * “Spin Current” eds. S. Maekawa et al. (Oxford Univ. Press, 2012).

Spin current generation by FMR (Spin pumping) :

YIG (yttrium iron garnet): a magnetic INSULATOR ! FMR spin pumping is unaccompanied by charge transfer

FMR spin pumping is free from impedance mismatch problem (spin injection into GaAs: Ando et al., Nature Materials 2011)

Jc =ΘHσ × Js

Spin Hall effect

Spin Pumping; Tserkovnyak, Brataas (2002)

Pt

Exchange  coupling  at  the  interface  :  Jsd  

Spin  accumula8on  :  s  

Interface exchange interaction (Jsd) Between normal metal (Pt) and ferromagnet

Hsd=J

sdSA(ri) ⋅s

ri∈interface∑ (r

i)+J

sdSB(rj) ⋅s(r

j)

rj∈interface∑

Electric and thermal generation of spin current:

Theoretical modeling of FMR spin pumping

Bloch eq. (s: spin accumulation)

Landau-Lifshitz-Gilbert eq. (m: localized moment)

Jsd

Nonmagnetic metal (N)

Ferromagnet (F)

dtdm_ mdt

d m Jsd ms H0

smJsddtd s0DN+=s s m( )K( )62

Microwave: h

+= m+a ( + h1 )

Response to h1

Linear response (busy slide, but important) !! ∂ts = Jsdm× s+ (DN∇

2 −Γ)(s− s0m)Bloch eq.:

LLG eq.: ∂tm = Jsds×m+γ (H0 +h1)×m+αm×∂tm

Jsin ≡<∂ts

z >=Jsd

AcontactIm dω∫ < s+(ω)m−(−ω)>From Bloch equation:

(s0 = χN Jsd )

Jsin = −

Jsd2

Acontactdω∫ Im χN (ω) | XF (ω) |

2< γh1+(ω)γh1

−(−ω)>

s+(ω) = JsdχN (ω)XF (ω)γh1+(ω)

m−(ω) = XF (ω)γh1−(ω)

χN (ω): spin susceptibility of NXF (ω): spin susceptibility of F

1) Define the spin current injected into N by Jsin =(1/Acontact)<dsz/dt>.

2) Linearize above two equations with respect to sx, sy, mx, my.

3) Substitute 2) into 1) and obtain the following result:

This is the general expression valid for any types of spin pumping!

Acoustic spin pumping:

⇒ h1 = gm−p(∇⋅u)∇2mEmag−ph = gm−p(∇⋅u)(m ⋅∇

2m)

Jsin = −(Jsd

2 / Acontact ) dω∫ Im χN (ω) | XF (ω) |2< γh1

+(ω)γh1−(−ω)>

Jsin = −(Jsd

2 / Acontact )B(gm−pK0uK0 )2

Because magnons are OFF resonance with phonons, any phonon frequencies are allowed to excite magnons.

Start from general expression of spin pumping (derived at the beginning)

Jsd

Pt

YIG

electron

Phonon

magnon

Piezoelectric actuator

B = dω∫ Im χN (ω)ImXF (ω) | XF (ω) |2

× coth ω −ν2T

$

%&

'

()− coth

ω2T$

%&

'

()

*

+,

-

./

Analogue to the phonon-drag spin Seebeck effect

For details, see Adachi et al., Rep. Prog. Phys. (2013)

Acoustic spin pumping (mx,y-square coupling)

Single-ion (spin-orbit) magnetostriction is important

f~3.5MHz

Uchida et al., Nature Mater. 10, 737(2012)

: magnons are OFF resonance with phonons

Volume (exchange) magnetostriction is important

Emag−ph = gm−p(∇⋅u)(m ⋅∇2m) ~ gm−p(∇⋅u)(m

+∇2m− + c.c.)

Contents:

1)  Introduction of spin current and spin Hall effect,

2) The linear response theory of spin current generation, 3) Spin current generation by heat, i.e., Spin Seebeck effect,

Refs.: * H. Adachi , K. Uchida, E. Saitoh and S. Maekawa: Rep. Prog. Phys. 76, 036501 (2013), *S. Maekawa, H. Adachi, K. Uchida, J. Ieda and E. Saitoh: J. Phys. Soc. Jpn. (2013), * “Spin Current” eds. S. Maekawa et al. (Oxford Univ. Press, 2012).

Lower T end Higher T end

Pt: spin detector (4 mm x100 µm x10 nm)

NiFe: thermo-spin generator (4 mm x6 mm x20 nm)

spin Hall effect: ESHE = DISHE Js × σ

magnitude & polarization of Js

K. Uchida et al.: Nature 455, 778 (2008)

　 No conduction electrons in YIG　

　 spin-wave mediated spin current!

K. Uchida et al.: Nature Mater. 9, 894 (2010).

Spin Seebeck effect (SSE): Universal phenomenon of ferromagnets Metal (Ni, Fe, Ni-Fe alloy; Uchida et al. 2008) Semiconductor (GaMnAs; Jaworski et al. 2010) Insulator (Yttrium Iron Garnet, Ferrite; Uchida et al. 2010)

Spin Hall effect

Jc =ΘHσ × Js

Magnon spin current

Transverse SSE device

(c.f., J. Xiao et al.: Phys. Rev. B81, 214418 (2010))

H. Adachi et al.: Phys.Rev. B83, 094410 (2011)).

(Fluctuation-Dissipation theorem) N

F

Spin diffusion eq.:

LLG eq.:

Injected spin current:

" Jspump " Js

back

(H. Adachi et al.: Phys.Rev. B83, 094410 (2011)).

(c.f., J. Xiao et al.: Phys. Rev. B81, 214418 (2010))

H. Adachi et al.: Phys.Rev. B83, 094410 (2011)).

(Fluctuation-Dissipation theorem) N

F

(Field theoretical calculation of　Green’s function)

Local non-equilibrium

To get the non-equiliburium condition, we need heat flow!

No temp-diff. between Pt and YIG in the experiment !need to consider the effect of temp-gradient in YIG

Consider the following model

Static condition: Local equilibrium

Magnon

Magnon

Field theoretical calculation of the Green function

Dynamics gives rise to the non-equilibrium !

Heat transport Q:

In ferromagnetic insulators,

Q = Q(magnon) + Q (phonon)

Phonon drag process; Magnons dragged by nonequilibrium phonons " spin injection

Phonon drag gives low-T enhancement of SSE due to the rapid suppression of umklapp scatt.

Phonon-drag spin Seebeck effect Uchida et al., Nature Mater. 10, 737(2012)

Only phonons in the nonmagnetic substrate can sense gradT!

Importance of phonons

T. Ota et al., (submitted).

Pronounced peak consistent with our prediction!

YIG GaMnAs

Spin Seebeck Effect

A variety of spin Seebeck devices!

In ferromagnetic insulators, Q = Q(magnon) + Q (phonon)

At the Interface, Spin flow, not Charge flow!! (different from spin-dependent Seebeck effect)

Phonons ferromagnets, substrates, piezoelectric actuators,…

In Summary: