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
1. 1..1 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, 017 017
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 4 3.3 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 0 0 1 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
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 3. 3.1 Ω H SR γs Ω /γ B Ω Ω /γ 0 Ω 100 Hz nt g 6 g 10 7 g 1 g 3. 100 Gd 4 Vol. 7, No. 9, 017 017
3 khz ΔM Ω ΔH 8 * 1 Gd khz 1 khz 1 mm G 3 Gd g g Gd Tb Dy.00 0.08 1.53 0.17 1.15 0.3 4 9 g 3.3 3 3 NMR NMR 10 1 * 1 4 Gd Tb Dy 9 g g g 5 NMR a, b NMR c 7.356 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
6 115 In 9 Si 5 c 7.356 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 4. 4.1 13 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 14 4. Pt Ω H SR S Ω B Ω Ω /γ F H SR γs B Ω 6 Vol. 7, No. 9, 017 017
v r, t v 0 dr dr v r, t dt dt dt H =-S ω 10 SV, 16 ω v 4..1 8 16 17 18 4.. 19 9 Hg ω 8 9 Hg 5. 7 017
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, 393 1976. 3 K. Hashimoto, N. Iizuka, and T. Kimura, Phys. Rev. D 91, 086003 015. 4 C. G. de Oliveira and J. Tiomno, Nuovo Cimento 4, 67 196. 5 F. W. Hehl and W.-T. Ni, Phys. Rev. D 4, 045 1990. 6 S. J. Barnett, Phys. Rev. 6, 39 1915. 7 A. Einstein and W. J. de Haas, Verh. Dtsch. Phys. Ges. 17, 15 1915. 8 M. Ono et al., Phys. Rev. B 9, 17444 015. 9 Y. Ogata et al., Appl. Phys. Lett. 110, 07409 017. 10 H. Chudo et al., Appl. Phys. Express 7, 063004 014. 11 H. Chudo et al., J. Phys. Soc. Jpn. 84, 043601 015. 1 K. Harii et al., Jpn. J. Appl. Phys. 54, 05030 015. 13 J. Sinova et al., Rev. Mod. Phys. 87, 113 015. 14 M. Matsuo, J. Ieda, E. Saitoh and S. Maekawa, Phys. Rev. Lett. 106, 076601 011. 15 L. I. Schiff, Proc. Natl. Acad. Sci. U.S.A. 5, 391 1939. 16 M. Matsuo et al., Phys, Rev. B 87, 18040 R 013. 17 D. Kobayashi et al., Phys. Rev. Lett. 119, 0770 017. 18 M. Hamada, T. Yokoyama, and S. Murakami, Phys. Rev. B 9, 060409 R 015. 19 R. Takahashi et al., Nat. Phys. 1, 5 016. 017 3 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, 017 017