Spin Current and Spin Seebeck Effect

Transcription

1 at Rome, Italy (September 18, 2013) Spin Current and Spin Seebeck Effect Sadamichi Maekawa Advanced Science Research Center (ASRC), Japan Atomic Energy Agency (JAEA) at Tokai and CREST-JST. Co-workers: Theory: H. Adachi and Y. Ohnuma (ASRC, JAEA), Experiment: K. Uchida and E. Saitoh (IMR, Tohoku University)

2 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, (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).

3 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, (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).

4 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

5 Spin-wave (magnon) spin current

6 Spin Hall Effect / Inverse SHE Conversion between charge and spin current Charge curent Spin current Spin current Charge current

7 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, (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).

8 Spin current generation by FMR (Spin pumping) : Spin Hall effect J c = Θ H σ J s Spin Pumping; Tserkovnyak, Brataas (2002) 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)

9 Electric and thermal generation of spin current: Pt Spin accumula8on : s Exchange coupling at the interface : J sd Interface exchange interaction (Jsd) Between normal metal (Pt) and ferromagnet H sd = J sd S A (r i ) s(r i ) +J sd S B (r j ) s(r j ) r i interface r j interface

10 Theoretical modeling of FMR spin pumping Bloch eq. (s: spin accumulation) d 2 s = J sd m s + ( D s dt N ) ( s m) 0 Nonmagnetic metal (N) J sd Microwave: h Ferromagnet (F) d m = Jsd s m + ( H dt 0 +h 1 ) m+ m d dt m Landau-Lifshitz-Gilbert eq. (m: localized moment) Response to h1

11 Linear response (busy slide, but important)!! Bloch eq.: t s = J sd m s + (D N 2 Γ)(s s 0 m) (s 0 = χ N J sd ) LLG eq.: t m = J sd s m +γ(h 0 + h 1 ) m +αm t m 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)x F (ω)γh 1 + (ω) m (ω) = X F (ω)γh 1 (ω) χ N (ω): spin susceptibility of N X 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) X F (ω) 2 < γh + 1 (ω)γh 1 ( ω) > This is the general expression valid for any types of spin pumping!

12 Acoustic spin pumping: Start from general expression of spin pumping (derived at the beginning) J in s = (J 2 sd / A contact ) dω Im χ N (ω) X F (ω) 2 < γh + 1 (ω)γh 1 ( ω) > E mag ph = g m p ( u)(m 2 m) h 1 = g m p ( u) 2 m J sd Pt electron For details, see Adachi et al., Rep. Prog. Phys. (2013) J in s = (J 2 sd / A contact )B(g m p K 0 u K0 ) 2 magnon Phonon YIG Piezoelectric actuator B = dω Im χ N (ω)im X F (ω) X F (ω) 2 * $ coth ω ν ' & % 2T ( ) coth $ ω '-, & % 2T )/ + (. Because magnons are OFF resonance with phonons, any phonon frequencies are allowed to excite magnons. Analogue to the phonon-drag spin Seebeck effect

13 Acoustic spin pumping (m x,y -square coupling) Uchida et al., Nature Mater. 10, 737(2012) Single-ion (spin-orbit) magnetostriction is important f~3.5mhz : magnons are OFF resonance with phonons Volume (exchange) magnetostriction is important E mag ph = g m p ( u)(m 2 m) ~ g m p ( u)(m + 2 m + c.c.)

14 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, (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).

15 K. Uchida et al.: Nature 455, 778 (2008) Pt: spin detector (4 mm x100 µm x10 nm) NiFe: thermo-spin generator (4 mm x6 mm x20 nm) spin Hall effect: E SHE = D ISHE J s σ magnitude & polarization of J s Lower T end Higher T end

16 No conduction electrons in YIG spin-wave mediated spin current! K. Uchida et al.: Nature Mater. 9, 894 (2010).

17 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 J c = Θ H σ J s Transverse SSE device Magnon spin current

18 H. Adachi et al.: Phys.Rev. B83, (2011)). N (Fluctuation-Dissipation theorem) F (c.f., J. Xiao et al.: Phys. Rev. B81, (2010))

19 (H. Adachi et al.: Phys.Rev. B83, (2011)). Spin diffusion eq.: LLG eq.: Injected spin current: " J s pump " J s back

20 H. Adachi et al.: Phys.Rev. B83, (2011)). N (Fluctuation-Dissipation theorem) F (c.f., J. Xiao et al.: Phys. Rev. B81, (2010))

21 Local non-equilibrium (Field theoretical calculation of Green s function) To get the non-equiliburium condition, we need heat flow!

22 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

23 Magnon Magnon Dynamics gives rise to the non-equilibrium! Field theoretical calculation of the Green function

24 Heat transport Q: In ferromagnetic insulators, Q = Q(magnon) + Q (phonon)

25 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.

26 Phonon-drag spin Seebeck effect Uchida et al., Nature Mater. 10, 737(2012) Only phonons in the nonmagnetic substrate can sense gradt!

27

28 Importance of phonons YIG GaMnAs T. Ota et al., (submitted). Pronounced peak consistent with our prediction!

29 In Summary: Spin Seebeck Effect 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, A variety of spin Seebeck devices!