1 and (Dated: October 5, 2018) I. A. Einstein Zur Quantentheorie der Strahlung C. H. Townes T. H. Maiman X [1] [2, 3] [4] (THz=10 12 Hz
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1 1 and (Dated: October 5, 2018) I. A. Einstein Zur Quantentheorie der Strahlung C. H. Townes T. H. Maiman X [1] [2, 3] [4] (THz=10 12 Hz) [5] THz ( ) THz [6] [7, 8] ( ) THz (10 15 ) (10 12 ) 1 h-fujita@issp.u-tokyo.ac.jp masahiro.sato.phys@vc.ibaraki.ac.jp [9, 10] Floquet [11 13] [14] [15] [16] Laguerre-Gaussian (LG) 1992 Allen [17] [18, 19] spiral phase plate holography 1 (STED) [20] [21] STED [24, 25] [26 28] ( ) [29 32] 1 UVSOR 2 3 Whispering Gallery Mode YIG Whispering Gallery Mode [22, 23]
2 2 II. Maxwell ( ) : + ω2 E( r) c = 0. E( r) 2 ω 3 c e p 4 E( r) = e p ϕ( r) ϕ( r) Helmholz ( + k 2 ) ϕ( r) = 0 (1) k = ω/c z (ρ, ϕ, z) ρ ϕ = 2 ρ ρ ρ ρ 2 ϕ z 2 T + 2 z 2 k z ϕ( r) = u( r)e ikz : ( T + 2ik ) 2 + z z 2 u( r) = 0. (2) u(ρ, ϕ, z) z u( r) z exp(ikz) : 2 u z 2 2 u x 2, 2 u y 2, k u z. (3) (z = 0) LG : ( ρ ) ( ) m E(ρ, ϕ, z = 0) e p L m 2ρ 2 p e imϕ e ρ2 w w 2. (5) w L m p (x) Laguerre e imϕ m 0 z 2 p, m p Laguerre m e imϕ z L z = iħ / ϕ ħm [18] ħm ( ) [33, 34] m () (5) m E ±ħ e p = ˆx ± iŷ ħm w 2 (2) Helmholz ( T + 2ik ) u( r) = 0 (4) z 2 p 0, m (Laguerre- Gaussian (LG) modes) LG p m(ρ, ϕ, z) 4 e p = ˆx, ŷ ˆx, ŷ x, y FIG. 1. (a) (b) ( ) 1 p, m (m = 0)
3 3 (m 0) e imϕ topological beam dounut beam p Laguerre m 0 (p + 1) 2m [35, 36] ( ) ( ) III. MnSi Dzyaloshinskii-Moriya (DM) H DM = r, r D r r ( m r m r ) (6) m r r Dzyaloshinskii-Moriya (DM) D r r [37] m r = 1 DM DM 2 (ferromagnetics) (ferroelectrics) [29 32] 5 () [38 40] H z H chi = J r r + r r m r m r D r r ( m r m r ) H z r m z r (7) J(> 0) DM D r r = D e r r e r r r r Heisenberg () π/2 DM () Zeeman () 3 6 DM ( ) [Fig. 2 (a)] 1 [41 43] [Fig. 2 (b)] 2 [Fig. 2 (c)] [Fig. 2 (a)] ( ) N SK = 1 ( m r m r 4π x m ) r dxdy = Z (8) y (x, y) 2 2 N SK = ±
![4 N SK N SK 7 (7) DM sgn(n SK ) DM D/J DM [40, 44] (7) () 21 [47, 48] [49 53] (1) (2) ( ) 2 IV. FIG.](/docs-images/103/157706352/images/4-0.jpg "2. (a): (7) (H z ) (b): 1 (c): (a) (b) 2 1980 0 [45, 46] 7 N SK (GHz=10 9 Hz) THz [44] THz GHz 3")
4 4 N SK N SK 7 (7) DM sgn(n SK ) DM D/J DM [40, 44] (7) () 21 [47, 48] [49 53] (1) (2) ( ) 2 IV. FIG. 2. (a): (7) (H z ) (b): 1 (c): (a) (b) [45, 46] 7 N SK (GHz=10 9 Hz) THz [44] THz GHz 3 [54]
![5 () THz THz [55] THz GHz THz X [51] ( ) [56, 57] 2 (Fig. 3) [58] FIG. 3. (a): +z (N SK = 1) (b): z (N SK = +1) (c): (a) (b) (N SK = 1 1 = 0) ( ) Landau-Lifshitz-Gilbert(LLG) ( ) A.](/docs-images/103/157706352/images/5-0.jpg "Heisenberg DM k = 0 [59 61] THz [62] ( ) DM H z H = J r r m r m r H z r m z r r B r (t) m r.")
5 5 () THz THz [55] THz GHz THz X [51] ( ) [56, 57] 2 (Fig. 3) [58] FIG. 3. (a): +z (N SK = 1) (b): z (N SK = +1) (c): (a) (b) (N SK = 1 1 = 0) ( ) Landau-Lifshitz-Gilbert(LLG) ( ) A. Heisenberg DM k = 0 [59 61] THz [62] ( ) DM H z H = J r r m r m r H z r m z r r B r (t) m r. (9) (7) B r (t) Zeeman t (9) 2 ( ρ ) m m w L p B r (t) = B 0 e p [ max r ( ρ w ( ) 2ρ 2 w e ρ2 2 w 2 t2 imϕ iωt e σ 2 ( 2ρ 2 ) m L m p w 2 ) e ρ2 w 2 ]. (10) B 0 σ (+z) m r Landau-Lifshitz-Gilbert(LLG) [40] LLG Gilbert damping α LLG d M r dt ( = γm r H ) M M + α r r M r d M r dt, (11) M r = ħγ m r γ g g µ B γ = gµ B /ħ LLG
6 M ( r H M r ) α p ω σ w m ω J t σ ħ/j (9) THz ( a ) w = 7.5a (a ) w LLG [25] Figure 4 +z e p = ˆx m x m 8 (e) χ s 3 r 1,2,3 3 m r1 ( m r2 m r3 ) χ s χ s DC χ s [63, 64] 4(e) 9 (ω J, H z ) ħm [25] THz Zeeman [65, 66] 8 [30] [25] 9 1 THz χ s FIG. 4. (a)-(c): m x ω/j = H z /J = 0.3 B 0/J = Fig. 5, 6 (d): (a)-(c) (e): m = 0, ±1 B. THz [54] Zeeman : H = H chi r 6 B r (t) m r. (12) H chi (7) D/J = 0.15, H z /J = z ω = 0.075J e p = ˆx + iŷ DM ( ) ħm Figure 5
![7 ħm sgn(m)(m + 1) (m = 1 1 ) 5 1 1 1 m [25] 5 [67] FIG. 5. (ω/j = 0.075, B 0/J = 0.15) (D/J = 0.15, H z /J = 0.015) ħm ( e p = ˆx + iŷ) tj/ħ = 1 0.1-1 Gilbert damping α = 0.1 C.](/docs-images/103/157706352/images/7-0.jpg "( )THz [45] ( X ) [68 70] 10 100 T ( r) [69] T ( r) u(ρ, ϕ, 0) 2 [FIG.1 (a)] LLG LLG (11) LLG stochastic LLG (sllg) : d M r dt ( = γm r H ) M + M h T ( r,t) + α r r M r d M r dt.")
7 7 ħm sgn(m)(m + 1) (m = 1 1 ) m [25] 5 [67] FIG. 5. (ω/j = 0.075, B 0/J = 0.15) (D/J = 0.15, H z /J = 0.015) ħm ( e p = ˆx + iŷ) tj/ħ = Gilbert damping α = 0.1 C. ( )THz [45] ( X ) [68 70] T ( r) [69] T ( r) u(ρ, ϕ, 0) 2 [FIG.1 (a)] LLG LLG (11) LLG stochastic LLG (sllg) : d M r dt ( = γm r H ) M + M h T ( r,t) + α r r M r d M r dt. (13) h T ( r,t) t r h i T ( r,t) hj T ( r,t ) = σ h ( r, t)δ ij δ(t t )δ r, r (14) σ h ( r, t) T ( r, t) : σ h ( r, t) = 2k B T ( r, t)α/(γ 2 ħ). (15)
![8 (13) [71] Heun Figure 6](/docs-images/103/157706352/images/8-0.jpg "p = 0, 1() (m = 5) T 0 w 20 J FIG. 6.")
![(a): (p = 0) [51] (b): (p = 0) (c): 2 (p = 1) 2 (4π-vortex [56, 57]) (a)-(c) Gilbert damping α = 0.](/docs-images/103/157706352/images/8-2.jpg "1 tj/ħ = 1 0.1-1 [FIG.6 (a)] [51] [FIG.6 (b)(c)] p [56, 57] ( ) Figure 7 p = 0, m = 5 FIG. 7. (a)-(c): H z /J = 0.")
8 8 (13) [71] Heun Figure 6 p = 0, 1() (m = 5) T 0 w 20 J FIG. 6. (a): (p = 0) [51] (b): (p = 0) (c): 2 (p = 1) 2 (4π-vortex [56, 57]) (a)-(c) Gilbert damping α = 0.1 tj/ħ = [FIG.6 (a)] [51] [FIG.6 (b)(c)] p [56, 57] ( ) Figure 7 p = 0, m = 5 FIG. 7. (a)-(c): H z /J = 0.01, , (D/J = 0.15) 20 (a)-(c) 10a (d): Fig. 6 (a)-(c) t = 0 t 0 J/ħ = 500 α = 0.1 spiral phase plate (EUV) X ( [24])
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/Magnetics Jpn. Vol. 10, No. 4, 2015 How to Write, Delete, and Drive Skyrmions M. Mochizuki, College of Science and Engineering, Aoyama Gakuin Univers
/Magnetics Jpn. Vol. 10, No. 4, 2015 How to Write, Delete, and Drive Skyrmions M. Mochizuki, College of Science and Engineering, Aoyama Gakuin University, PRESTO, Japan Science and Technology Agency Tel:
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![1 1.1 hν A(k,ε)[ k ρ(ω)] [1] A(k,ε) ε k μ f(ε) 1/[1 + exp( ε μ k B T )] A(k,ε)f(ε) ρ(ε)f(ε) A(k,ε)(1 f(ε)) ρ(ε)(1 f(ε)) A(k,ε) σ(ω) χ(q,ω) k B T ev k](/thumbs/92/109354346.jpg "1 1.1 hν A(k,ε)[ k ρ(ω)] [1] A(k,ε) ε k μ f(ε) 1/[1 + exp( ε μ k B T )] A(k,ε)f(ε) ρ(ε)f(ε) A(k,ε)(1 f(ε)) ρ(ε)(1 f(ε)) A(k,ε) σ(ω) χ(q,ω) k B T ev k")
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磁性物理学 - 遷移金属化合物磁性のスピンゆらぎ理論
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遍歴電子磁性とスピン揺らぎ理論 - 京都大学大学院理学研究科 集中講義
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5 H Boltzmann Einstein Brown 5.1 Onsager [ ] Tr Tr Tr = dγ (5.1) A(p, q) Â 0 = Tr Âe βĥ0 Tr e βĥ0 = dγ e βh 0(p,q) A(p, q) dγ e βh 0(p,q) (5.2) e βĥ0
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