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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)、
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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).
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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).
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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
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Spin-wave (magnon) spin current
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Spin Hall Effect / Inverse SHE
Conversion between charge and spin current
Charge curent →Spin current
Spin current →Charge current
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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).
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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)
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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:
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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
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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!
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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)
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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.)
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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).
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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)
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No conduction electrons in YIG
spin-wave mediated spin current!
K. Uchida et al.: Nature Mater. 9, 894 (2010).
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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
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(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
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Spin diffusion eq.:
LLG eq.:
Injected spin current:
" Jspump " Js
back
(H. Adachi et al.: Phys.Rev. B83, 094410 (2011)).
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(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
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(Field theoretical calculation of Green’s function)
Local non-equilibrium
To get the non-equiliburium condition, we need heat flow!
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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
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Magnon
Magnon
Field theoretical calculation of the Green function
Dynamics gives rise to the non-equilibrium !
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Heat transport Q:
In ferromagnetic insulators,
Q = Q(magnon) + Q (phonon)
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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.
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Phonon-drag spin Seebeck effect Uchida et al., Nature Mater. 10, 737(2012)
Only phonons in the nonmagnetic substrate can sense gradT!
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Importance of phonons
T. Ota et al., (submitted).
Pronounced peak consistent with our prediction!
YIG GaMnAs
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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: