Spin Seebeck and Spin Peltier Effects

Transcription

1 at Hvar (October 1-7, 2017) Spin Seebeck and Spin Peltier Effects Sadamichi Maekawa Advanced Science Research Center, Japan Atomic Energy Agency, Tokai, Japan References: S. Maekawa(ed.) Concepts in Spin Electronics (Oxford University Press, 2006), *S. Maekawa et al. (eds.) Spin Current (Oxford University Press, 2017)

2 * Spin Current (First Edition) : (Oxford University Press, 2012) Second Edition: Published in September 2017

3 Spin Seebeck Effect and Spin Peltier Effect: i) Spin Seebeck Effect: Review Article, [K.Uchida, H.Adachi, T.Kikkawa, A.Kirihara, M.Ishida, S.Yorozu, S.Maekawa and E.Saitoh, Proc. IEEE 104, 1946 (2016)]. ii) Spin Peltier Effect: Y. Ohnuma, M.Matsuo and S.Maekawa: to be published in Phys. Rev. B (2017). Co-Workers: Theory: Y.Ohnuma (ASRC, JAEA), H.Adachi ( ASRC, JAEA Okayama U.), M.Matsuo (ASRC, JAEA). Experiment: E.Saitoh(Tohoku U.) and members in his group, K. Uchida (Tohoku U. NIMS, Tsukuba),

4 Heat vs. Electricity To get Electricity To get Heat Charge Seebeck effect Peltier effect Spin Spin Seebeck effect Uchida 2008 Spin Peltier effect Flipse 2014 Daimon 2016

5 Boiling of water Boiling of electrons (Seebeck effect) Boiling of spin current (spin Seebeck effect) 5

6 Combination of magnetic insulators and conductive films used for measuring SSE SSE is a universal phenomenon in magnetic materials ( + ) (-) Model system: Pt/Y 3 Fe 5 O 12 (YIG) junction K. Uchida, H. Adahci, T. Kikkawa, A. Kirihara, M. Ishida, S. Yorozu, S. Maekawa, and E. Saitoh, Thermoelectric generation based on spin Seebeck effects (IEEE Proc.,104, 1946 (2016))

7 Spin pumping (spin current genera.on by FMR) FMR NM Spin current 7

8 Spin current genera.on by FMR Bloch eq. (s: spin accumulation) d 2 s = J sd m s + ( D s dt N Γ) ( s m) 0 Nonmagnetic metal (SS) Spin sink J sd Spin injector Microwave: h Microwave: h 1 Ferromagnet (SI) d m = J α m dt sd s m +γ ( H 0 +h 1 ) m+ Landau-Lifshitz-Gilbert eq. (m: localized moment) d dt m

9 Bloch eq.: LLG eq.: Linear response (busy slide, but important)!! t s = J sd m s + (D N 2 Γ)(s s 0 m) t m = J sd s m +γ(h 0 + h 1 ) m +αm t m (s 0 = χ N J sd ) 1) Define the spin current injected into N by J s in =(1/A contact )<ds z /dt>. From Bloch equation: J s in < t s z >= J sd A contact Im dω < s + (ω)m ( ω) > 2) Linearize above two equations with respect to s x, s y, m x, m y. s + (ω ) = J sd χ N (ω )G F (ω )γ h 1 + (ω ) m (ω ) = G F (ω )γ h 1 (ω ) χ N (ω ): spin susceptibility of N G F (ω ): spin susceptibility of F 3) Substitute 2) into 1) and obtain the following result: J s in = J 2 sd A contact dω Im χ N (ω ) G F (ω ) 2 < γ h + 1 (ω )γ h 1 ( ω ) > This is the general expression valid for any types of spin pumping!

10 Model for spin injec.on by thermal magnons H. Adachi et al.: Phys.Rev. B83, (2011)). N (Fluctuation-Dissipation theorem) F (c.f., J. Xiao et al.: Phys. Rev. B81, (2010))

11 (Local) spin injec.on by thermal magnons (H. Adachi et al.: Phys.Rev. B83, (201 Spin diffusion eq.: t s = J sd m s + (D N 2 Γ)(s s 0 m) + l (s 0 = χ N S 0 J sd ) LLG eq.: t m = J sd s m + γ(h eff + h) m + αm t m Injected spin current: J s in < t s z >= J sd Im dω < s + (ω)m ( ω) > s + (ω ) = Γs 0 G F * ( ω )γ h + (ω ) + χ N * ( ω )l + (ω ) m (ω ) = G F (ω )γ h (ω ) + J sd G F (ω )χ N (ω )l (ω ) (a ± a x ± ia y ) J s in = J sd 1 dω ω Im χ N (ω )ImG F (ω ) Γs 0 < γ h + (ω )γ h ( ω ) > α J sd < l + (ω )l ( ω ) > é J pump s é J back s J s in = J s pump J s back

12 Local non-equilibrium J s in = A(T F T N ) 2 ( A J sd dω 1 ω Im χ (ω )ImG (ω ) N F ) To get the non-equiliburium condition, we need heat flow!

13 Spin Seebeck Effect and Spin Peltier Effect: i) Spin Seebeck Effect: Review Article, [K.Uchida, H.Adachi, T.Kikkawa, A.Kirihara, M.Ishida, S.Yorozu, S.Maekawa and E.Saitoh, Proc. IEEE 104, 1946 (2016)]. ii) Spin Peltier Effect: Y. Ohnuma, M.Matsuo and S.Maekawa: to be published in Phys. Rev. B (2017). Co-Workers: Theory: Y.Ohnuma (ASRC, JAEA), H.Adachi ( ASRC, JAEA Okayama U.), M.Matsuo (ASRC, JAEA). Experiment: E.Saitoh(Tohoku U.) and members in his group, K. Uchida (Tohoku U. NIMS, Tsukuba),

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17 Spin & heat injec.on Spin diffusion eq.: t s = ( J sd m + b) s + (D N 2 Γ)(s s 0 m) + l LLG eq.: t m = J sd s m + γ (H eff + h) m + αm t m b = δµ S z (s 0 = χ N S 0 J sd ) 1) Define the spin and heat current injected into N. From Bloch equation: From Heisenberg eqaution: J in Spin < t s z >= J sd Im dω < s + (ω )m ( ω ) > H. Adachi et al.: Phys.Rev. B 83, (2011). J Heat in < t H >= J sd Im dω!ω < s + (ω )m ( ω ) > 2) Linearize above two equations with respect to s and m. s + (ω ) = Γs 0 G F * (ω )γ h + (ω ) + χ N * (ω + δµ S )l + (ω ) m (ω ) = G F (ω )γ h (ω ) + J sd G F (ω )χ N (ω + δµ S )l (ω ) 3) Substitute 2) into 1) and obtain the following results: < γ h + (ω )γ h ( ω ) > J in Spin = J sd dω Im χ N (ω + δµ S )ImG F (ω ) Γs 0 ω é J s pump α J sd < l + (ω )l ( ω ) > ω + δµ S é J s back < γ h + (ω )γ h ( ω ) > J in Heat = J sd dω!ω Im χ N (ω + δµ S )ImG F (ω ) Γs 0 ω é J H pump α J sd < l + (ω )l ( ω ) > ω + δµ S é J H back

18 Model for spin injec.on by thermal magnons H. Adachi et al.: Phys.Rev. B83, (2011)). N (Fluctuation-Dissipation theorem) F (c.f., J. Xiao et al.: Phys. Rev. B81, (2010))

19 Expression of spin & heat current 4) Substitute the correlation of noises into 3) : J in 2 Spin = J eff J in 2 Heat = J eff dω Im χ N (ω + δµ S )ImG F (ω ) T + ΔT N ω dω!ω Im χ N (ω + δµ S )ImG F (ω ) T + ΔT N ω 5) Obtain the linear response theory as follows: T N ω + δµ S T N ω + δµ S J 2 eff := 2J 2 sd χ N αγk B ΔT := T F T N J in = J 2 Spin eff J in = J 2 Heat eff dω X ( ω )[ ωδt + T δµ ] N S dω!ω X ( ω )[ ωδt + T δµ ] N S X ( ω ) := Im χ N (ω + δµ S ) ImG F (ω ) ~ ω + δµ S ω 2 χ N 1 ( ) 2 1+ ω / Γ ( ) 2 + ( αω ) 2 ω ω 0

20 Spin Seebeck effect and spin Pel.er effect 6) From the fluctuation dissipation theorem, 3) reduce as follows: J Spin in J Heat in = L 11 L 12 L 21 L 22 δµ S ΔT / T L 12 = 2J 2 sd αγk B T F dωω Im χ N (ω + δµ S ) ImG F (ω ) ω + δµ S ω = L 21 Onsager s reciprocal relation Kelvin relation for interconversion of heat and spin currents J Spin in = S SSE ΔT J Heat in = Π SPE δµ S Π SPE = TS SSE

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22 ΔT = QYIG C v YIG ~ 20mK

23 Heat current

24 In conclusion: Heat vs. Electricity To get Electricity To get Heat Charge Seebeck effect Peltier effect Spin Spin Seebeck effect Uchida 2008 Spin Peltier effect Flipse 2014 Daimon 2016