a L = Ψ éiγ c pa qaa mc ù êë ( - )- úû Ψ 1 Ψ 4 γ a a 0, 1,, 3 {γ a, γ b } η ab æi O ö æo ö β, σ = ço I α = è - ø çèσ O ø γ 0 x iβ γ i x iβα i

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1 解説 4 matsuo.mamoru jaea.go.jp 4 eizi imr.tohoku.ac.jp 4 maekawa.sadamichi jaea.go.jp i ii iii i Gd Tb Dy g khz Pt ii iii Keywords vierbein 3 dreibein 4 vielbein torsion JST-ERATO 1 017

2 a L = Ψ éiγ c pa qaa mc ù êë ( - )- úû Ψ 1 Ψ 4 γ a a 0, 1,, 3 {γ a, γ b } η ab æi O ö æo ö β, σ = ço I α = è - ø çèσ O ø γ 0 x iβ γ i x iβα i I σ i η ab diag,,, q e A a U 1 m c 4 GeV ev H 0 βmc cα π qa 0 π p qa H 0 E qa 0 O cα π U exp iβo/mc H UH 0 U iħu t U H UH U iħu t U... 1/m é 1/ m q ù H ( ) 0 = β mc qa ê + π ë m + σ m ú + û B 0 3 1/m 1/ m qλ qλ H ( ) 0 = σ ( π E- E π)- div E 4 λ ħ /4m c zitterbewegung. vierbein 1 μ a L = Ψ éie aγ c pμ qaμ i Γμ mc ù êë ( - + )- úû Ψ 5 e μ a e μ aη ab e ν b Vol. 7, No. 9,

3 U 1 A a Ψ qψ γ a ΨA a j a qψ γ a Ψ 4 1 g μν γ μ x e μ a x γ a {γ μ x, γ ν x } g μν x U 1 ab Γ μ ω μ Σ ab ω ab μ e a λ μ δ λ ν Γ λ μν e νb Γ λ μν Σ ab 1/4 γ a, γ b 1 k Σ ij = æσ O ö ² ijk, i, j 1,, 3 ç çèo σ k ø ( = ) A μ j μ qψ γ μ Ψ ω ab μ j μ ab Ψ γ μ Σ ab Ψ Ω t x t, r x t, r dr dr Ω r dt dt dt d s dct dr g μν d x μ d x ν g 00 1 u g 0i g i0 u i g ij δ i, ij j 1,, 3 u Ω r/c e e 0 j 0 e i 0 u i e i j δ i j e α 0 δ α 0 η α i u i e α i δ α i γ 0 x iβ iγ i x iβ α i u i Γ 0 00 Γ 0 i0 Γ 0 ij Γ jk 0 Γ i 00 i ² ijk Ω j u k /c 0 u i Γ j i 0 ² ijk Ω k /c Γ 0 x γ i γ j ² ijk Ω l /4c i Σ Ω /c Γ i x 0 H βmc c α u π qa 0 Σ Ω 6 4, 5 v 1/iħ r, H cα Ω r cα Ω r Σ Ω Spin-rotation coupling c α u π cα π r π Ω H 0 βmc cα π qa 0 H H 0 r π Σ Ω r p Σ Ω J r p Σ U exp J Ωt /iħ H 0 dynamical phase iħu t U r p Ω r p Σ.4 E qa 0 Ω r π Σ O cα π U exp iβo/mc 1/m 3 017

4 é 1/ m q ù ( H ) β π = mc + + σ B + qa0-( r π + Σ) Ω 7 ê ë m m ú û Σ Ω 1/ m e H ( e ) = π æ ö ea0 m - - ç çè + ø - r π σ Ω σ m B 8 1/m 1/ m qλ qλ H ( e ) = σ ( π E - E π)- div E 9 E E Ω r B E Ω r B 14 E, B E rot, B rot E rot E Ω r B B rot B 15 E rot E H SR S Ω γ H SR γs Ω /γ B Ω Ω /γ H 0 r π S Ω Ω H SR γs Ω /γ B Ω Ω /γ 0 Ω 100 Hz nt g 6 g 10 7 g 1 g Gd 4 Vol. 7, No. 9,

5 3 khz ΔM Ω ΔH 8 * 1 Gd khz 1 khz 1 mm G 3 Gd g g Gd Tb Dy g NMR NMR 10 1 * 1 4 Gd Tb Dy 9 g g g 5 NMR a, b NMR c MHz 115 In NMR Ω 0 Ω 10 khz 1.17 mt NMR 5 a, b NMR B 0 H γ N I B 0 B N Ω I γ N B N Ω Ω /γ N 5 017

6 6 115 In 9 Si 5 c MHz 115 In NMR Ω 0 Ω 10 khz B N Ω 1.17 mt 6 InP 115 In Si 9 Si 115 In 9 Si H SO qλ / ħ σ π E E π v σ 1/iħ r, H SO qλ /m σ E 7 a B Ω E Ω Ω r B r ΩrB b H MSO E Ω Ω 0, 0, Ω B 0, 0, B E Ω E Ω r B E rot r r Ω B H MSO Ω qλ / ħ σ π E E π v σ 1/iħ r, H MSO Ω qλ /m σ E Ω E Ω Pt Ω H SR S Ω B Ω Ω /γ F H SR γs B Ω 6 Vol. 7, No. 9,

7 v r, t v 0 dr dr v r, t dt dt dt H =-S ω 10 SV, 16 ω v Hg ω 8 9 Hg

8 1 S. Maekawa, S. Valenzuela, E. Saitoh, and T. Kimura, ed., Spin Current Oxford Univ. Press, Oxford, 01. F. W. Hehl, P. von der Heyde, and G. D. Kerlick, Rev. Mod. Phys. 48, K. Hashimoto, N. Iizuka, and T. Kimura, Phys. Rev. D 91, C. G. de Oliveira and J. Tiomno, Nuovo Cimento 4, F. W. Hehl and W.-T. Ni, Phys. Rev. D 4, S. J. Barnett, Phys. Rev. 6, A. Einstein and W. J. de Haas, Verh. Dtsch. Phys. Ges. 17, M. Ono et al., Phys. Rev. B 9, Y. Ogata et al., Appl. Phys. Lett. 110, H. Chudo et al., Appl. Phys. Express 7, H. Chudo et al., J. Phys. Soc. Jpn. 84, K. Harii et al., Jpn. J. Appl. Phys. 54, J. Sinova et al., Rev. Mod. Phys. 87, M. Matsuo, J. Ieda, E. Saitoh and S. Maekawa, Phys. Rev. Lett. 106, L. I. Schiff, Proc. Natl. Acad. Sci. U.S.A. 5, M. Matsuo et al., Phys, Rev. B 87, R D. Kobayashi et al., Phys. Rev. Lett. 119, M. Hamada, T. Yokoyama, and S. Murakami, Phys. Rev. B 9, R R. Takahashi et al., Nat. Phys. 1, Spintronics in Non-Inertial Frames Mamoru Matsuo, Eiji Saitoh, and Sadamichi Maekawa abstract: We review the interconversion phenomena between spin and mechanical angular momentum in moving bodies. In non-inertial frames, spin-dependent inertial forces emerge, which enable the conversion from mechanical angular momentum into spins. In particular, this article focuses the recent results on spin manipulation and spincurrent generation from mechanical motion, including rigid rotation, elastic deformations and fluid motion. 8 Vol. 7, No. 9,

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