/Magnetics Jpn. Vol. 10, No. 4, 2015 How to Write, Delete, and Drive Skyrmions M. Mochizuki, College of Science and Engineering, Aoyama Gakuin Univers

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1 /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: , Fax: , Skyrmions were originally proposed by British physicist Tony Skyrme in the 1960s as topological solitons to account for the stability of baryons in particle physics. Realization of skyrmions as vortex-like swirling spin textures was discovered in ferromagnets with chiral crystal symmetry, in which ferromagnetic-exchange interactions favoring parallel spin alignment and Dzyaloshinskii Moriya interactions favoring rotational spin alignment strongly compete. Subsequent studies have revealed that skyrmions possess numerous advantageous properties for application to information carriers in high-density and low-energy-consuming magnetic memories and logic devices. These properties are: (1) topologically protected stability, (2) small nanometric size, (3) rather high transition temperatures, and (4) ultralow fields or electric currents to drive their motion. This article first introduces fundamental properties of skyrmions and skyrmionic materials and then presents recent attempts and ideas on writing, deleting, and driving skyrmions towards establishing their functions in memory devices. Key words: skyrmion, chiral magnet, Dzyaloshinskii Moriya interaction, magnetic memory, spin transfer torque, spintronics A/m 2 2 MRAM 3, 4 2. skyrmion, 1960 Tony Skyrme Fig. 1(a) Fig. 1(b) MnSi Fe1 xcoxsi, FeGe B20 Fig. 1(c) Fig. 1(d) 2012 Cu2OSeO3 8 B20 Cu2OSeO3 Fig. 1(e) Fig. 1(f) P213 Dzyaloshinskii (DM) 192 Copyright 2015 by The Magnetics Society of Japan

Fig. 1 (a) Original hedgehog-type skyrmion. (b) Lorentz-TEM image of vortex-type skyrmion in Fe0.5Co0.5Si as projection of hedgehog skyrmion onto two-dimensional plane.

9, 10 =-J m m -D m m i j i j+γ < i, j> i, γ=ex, ey -gμμh m B 0 z i iz γ (J 0) DM γ ( ex, ey) P213 DM 11 DM J/D 5 nm 100 nm B20 Cu2OSeO3 Fig. 2(a) (1) Fig.

2 Fig. 1 (a) Original hedgehog-type skyrmion. (b) Lorentz-TEM image of vortex-type skyrmion in Fe0.5Co0.5Si as projection of hedgehog skyrmion onto two-dimensional plane. 7 (c) and (d) Magnetization configurations for (c) Bloch-type skyrmion, and (d) Néel-type skyrmion. (e) and (f) Chiral crystal structures of (e) B20 compound (MnSi) and (f) Cu2OSeO3. 9, 10 =-J m m -D m m i j i j+γ < i, j> i, γ=ex, ey -gμμh m B 0 z i iz γ (J 0) DM γ ( ex, ey) P213 DM 11 DM J/D 5 nm 100 nm B20 Cu2OSeO3 Fig. 2(a) (1) Fig. 2 (a) Skymion crystal composed of hexagonally packed skyrmions. (b) Conical spin structure. (c) (f) Experimental phase diagrams in plane of temperature and magnetic field for (c) bulk MnSi, 6 (d) bulk Cu2OSeO3, 8 (e) thin-film MnSi, 12 and (f) thin-film Cu2OSeO3 8 samples. 6, 7 Fig. 2(b) 0,1 Fig. 2(c) Fig. 2(d) 6, , 12, 13 Fig. 2(e) Fig. 2(f) Fig. 2(b) DM DM Fig. 1(c) Fig. 1(d) Copyright 2015 by The Magnetics Society of Japan 193

360 180 2 Fig. 1(c) Fig. 1(d) B20 Cu2OSeO3 11 2 4, 14 2 d r n n n =4 πq ( Q= ± 1) (2) x y n n(r) r Q 4π Q 1 Q 1 0 5 100 FeGe 13 10 5 10 6 A/m 2 10 1 100 1 15, 16 Fig. 3(a) Fig.

3 Fig. 1(c) Fig. 1(d) B20 Cu2OSeO , 14 2 d r n n n =4 πq ( Q= ± 1) (2) x y n n(r) r Q 4π Q 1 Q FeGe A/m , 16 Fig. 3(a) Fig. 3 Schematics for (a) skyrmion-train memory and (b) skyrmion-mram. 4 Fig. 3(b) 1 1 MRAM MRAM 3. Fig. 4(a) A/m DM 194 Copyright 2015 by The Magnetics Society of Japan

4 Fig. 4 (a) Skyrmion creation by electric-current injection to stripline-shaped thin-film sample with small rectangular notch. 17 (b) (d) Schematics of skyrmion creations by (b) laser irradiation, (c) application of magnetic-field, and (d) application of electric field MRAM 19 Fig. 4(b) 20, 21 DM 1 1 Fig. 4(c) Fig. 4(d) MnSi Fe1 xcoxsi, MnGe 2012 Cu2OSeO3 8 DM Cu2OSeO3 Copyright 2015 by The Magnetics Society of Japan 195

Fig. 5 Dynamical processes for skyrmion annihilation by (a) electric-current injection via collision against the sample edge, 17 and (b) microwave irradiation via intensely exciting the spin-wave

6 (a) Simulated trajectory of a moving skyrmion, which moves to avoid magnetic impurities by winding its trajectory.

5 Fig. 5 Dynamical processes for skyrmion annihilation by (a) electric-current injection via collision against the sample edge, 17 and (b) microwave irradiation via intensely exciting the spin-wave mode of the skyrmion crystal Figs. 4(a) (d) Fig. 5(a) A/m 2 22, 23 Fig. 5(b) Fig. 6 (a) Simulated trajectory of a moving skyrmion, which moves to avoid magnetic impurities by winding its trajectory. 24 (b) (d) Schematics of driven skyrmion motions: (b) translational motion of multiferroic skyrmion in presence of electric-field gradient, (c) translational motion induced by diffusive flows of thermally activated magnons in the presence of temperature gradient, (d) rotational motion associated with the topological magnon Hall effect in the presence of radial temperature gradient under irradiation of light or electron beam A/m A/m 2 24 Fig. 6(a) 196 Copyright 2015 by The Magnetics Society of Japan

6 m(r) LLG 3 dm eff a dm pa =-γ m B + m + ( j ) m dt m dt 2em 3 pa β - [ m ( j ) m] 2 (3) 2em Gilbert j (A/m 2 ) β p a Thiele 25, 26 LLG G ( v-v ) + ( βv-αv ) +F =0 (4) s d s d pin vs vd α β Gilbert Fpin G (0, 0, G) (2) G Dij 2 ˆ ˆ ( ij, ) =( xx, ),( yy, ), ij = d r iω jω= (5) 0 otherwise. α β G (4) G 4π 4π G ( vs-vd ) ~-F pin (6) Fpin (Fpin~0) vd vs (5) ( βvs -αvd ) ~-Fpin (7) vd Fig. 6(b) Fig. 6(c) Fig. 6(d) Copyright 2015 by The Magnetics Society of Japan 197

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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

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 1 and 2 1 2 (Dated: October 5, 2018) I. A. Einstein Zur Quantentheorie der Strahlung 100 1917 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