Determination of the Interfacial Dzyaloshinskii-Moriya Interaction (idmi) in the Inversion Symmetry Broken Systems

Transcription

1 Determination of the Interfacial Dzyaloshinskii-Moriya Interaction (idmi) in the Inversion Symmetry Broken Systems 27 Nov Chun-Yeol You Dept. of Physics, Inha University, Korea

2 Collaborators Dongsoo Han June-Seo Kim Henk J.M. Swagten Samples MOKE measurement Jaehun Cho, Namhui Kim, Chun-Yeol You BLS measurement Idea Analytic Eq. Simulations Cho et al. Nat. Comm. 6, 7635 (2015) 27 Nov KMS 2

3 Introduction of DMI Contents DMI measurement with Brillouin Light Scattering (BLS) Pt/Co(t Co )/AlOx Effect of Ta buffer layer, Ta/Pt/Co/AlOx DMI in HM 1 /CoFeB/HM 2 systems 27 Nov KMS 3

4 DMI (Dzyaloshinskii-Moriya Interaction) Most general expression for two sites exchange energy S 1 E S A S ex i ij j i j A J I A A S A ij ij ij ij Antisymmetric exchange interaction (DMI) E S A S D S S A A ex i ij j ij i j i j i j Dzyaloshinskii (1958): purely symmetry Moriya (1960) : microscopic mechanism A A A 2 A 1 A A A 2 ij ij ij ij ij ij 27 Nov KMS 4

5 E J S S 27 Nov KMS ex ij i j i j What s the role of DMI? E DMI Dij Si S j EC (exchange coupling) prefers aligned spins DMI prefers perpendicular spin configurations They compete each other, spiral spin configuration! Domain walls (DW) with different chirality have different energies due to the DMI i j Walker breakdown is suppressed Formation of Skyrmion (small, stable, and easy to move) 5

6 Skyrmion for future logic devices Skyrmion is topologically stable and small object Easily moving with small field or current Broad ground state energy of skyrmions 27 Nov KMS 6

7 Topologically protected Skyrmion Topologically same objects, easily deformed Topologically different objects 27 Nov KMS 7

8 Topologically Protected 1D Skyrmion Topologically Protected!! 27 Nov KMS 8

9 DW motion & Walker Breakdown After Walker breakdown, DW precesses & energy loss 27 Nov KMS 9

10 DMI acts as effective field in DW Eq. of motion of DW [S. Emori, Nat. Mat. 12, 611 (2013)] dx H 2 0 K 1 0Hz 1 bj sin 2 dt d H SHE H y cos DMI x 2 2 DMI prefers Neel wall H H sin H 2 0 K 1 0Hz bj sin 2 dt 2 H H cos 2 2 H H sin 0 0 SHE y DMI x 27 Nov KMS 10

11 DW motion with DMI I DMI plays crucial role in the DW dynamics DMI prefers Neel type DW Walker breakdown is suppressed High DW velocity A. Thiaville et al. EPL 100, (2012) 27 Nov KMS 11

12 DW motion with DMI II SHE, DMI, STT are mixed DW moves current or electron directions 27 Nov KMS 12

13 Requirements for DMI Spin-Orbit Coupling (SOC): Origin of anisotropy, magnetostriction, MO effects, AMR, ferromagentic Hall effect, damping. E SO 1 1 2mc 2 2 r V r L S Inversion Symmetry Breaking 27 Nov KMS 13

14 Example of Symmetries Inversion Symmetry 27 Nov KMS 14

15 Inversion Symmetry Breaking 27 Nov KMS 15

16 Dzyaloshinskii-Moriya Interaction E D S S DMI ij i j i j 27 Nov KMS 16

17 J. H. Moon et al. PRB 88, (2013). Non-Reciprocal Spin Wave dispersion with DMI 27 Nov KMS DMI add extra linear term in SW dispersion relations Shift of SWD Different SW velocity for k 17

18 Spin Wave Dispersion (SWD) Relation Band diagram of the SW From SWD, we can determine SW excitation energy FMR: Ferromagnetic resonance (zero k-vector) BLS: Brillouin Light Scattering (non-zero k-vector) = / J Nov KMS k x a

19 From Kittel Classical spin wave theory U 2J S p S p N p1 1 st excited state (b) 1 for classical spin, the ground energy U U JS U 0 2 JNS 2 If we let all spin share the reversal (c), we get much lower energy. Spin Wave 27 Nov KMS 19

20 SPEELS (Spin polarized electron energy loss spectroscopy) q~ 1 nm -1 Zero-magnetic field High quality samples 27 Nov KMS 20

21 FMR with antenna Complicate pattern, Rather poor signal for thin FM Better frequency resolution Osaka, Korea Univ., KIST, etc. D. S. Kim, JKPS (2015) 27 Nov KMS 21

22 DMI measurement by asymmetry DW motion Isotropic domain-wall motion H z =10 mt 10-3 H x H DMI v (m/s) H z H x (mt) 100 um 100 um When we apply the H x, asymmetry domain wall motion appears. Asymmetry in v with respect H x. There is inversion symmetry with respect to the axis H X. This axis appears due to the induced field by DMI, H DMI. Provide the simple and direct method for the quantification of DMI. 27 Nov KMS 22 S.-G. Je et al., Phys. Rev. B 88, (2013) 1 H z

23 Measurement system & analysis Measurement Analysis 200 um 27 Nov KMS 23 K.-W. Moon et al., Arxiv (2014): Magnetic Bubblecade Memory 2

24 Brillouin Light Scattering (BLS) I Schematics and geometry of BLS (a) anti-stokes k x q s q i (b) Stokes k x Scattering of photon by magnon Scattering wave-vector can be determined by input phonon Excited SW energy can be detected MOKE & SW is the origin of BLS q 4 sin ~ nm 1 in ~ 1 60 nm x y z 27 Nov KMS 24

25 MOKE (Magneto-Optical Kerr Effect) it k r it k r 1 1 E ˆ 0 0 ˆ ˆ ˆ ˆ linear E e x E e x iy x iy 2 2 LP = RCP + LCP = + Ellipitcally P = + n RCP n LCP SK Hynix, STT-MRAM (2015) 25

26 MOKE, BLS, (Raman) Spin Waves Acts as grating with wavelength Sound waves Different n for Right/Left Circular Polarized Light SK Hynix, STT-MRAM (2015) 26

27 Brillouin Light Scattering (BLS) II Intensity [Arb. unit] Frequency [GHz] DE-mode 1st-Bulk mode Nov KMS Frequency shfit [GHz] Applied magnetic field [koe] M, H, K, A, k 0 s ext u ex x 27

28 What we can do with BLS? Various SW energy includes M s, K u, and A ex dependent terms Determine M s, K u, and A ex with field or k-vector For DMI M, H, K, A, k Dk 0 s ext u ex x 27 Nov KMS 28

29 BLS spectra for Magnetic Properties Frequency (GHz) Applied magnetic field (T) 1.0 nm 1.1 nm 1.2 nm 1.3 nm K* t Co (mj/m 2 ) nm K t Co (nm) t K 1 2 M t 2K 2 eff FM V 0 S FM U f 0 = γ 2π H[H + μ 0M S 2K u M s ], M s = 1.1 T K U = 0.54 mj/m 2 27 Nov KMS 29

30 Theory for spin waves with idm interaction f D f f 0 M H K A k p k 0,,,, DE s ext U ex x x M s 2 D f f k f k k M D 0 x M s DE x DE x x s k f D k 0 x M s f M s :saturated magnetization H ext : applied magnetic field K u :anisotropy energy A ex :exchange stiffness constant k x :wavenumber of spin waves : gyromagnetic ratio D :DM energy density p :polarity of DM energy density 27 Nov KMS 30

31 BLS schematic and spectrum Sample structure AlOx cap 2 nm CoFeB (Co) wedge Pt 4 nm SiO 2 substrate x BLS inensity (a.u.) Stokes f = 1.99 GHz Frequency (GHz) anti-stokes z Co 48 Fe y 32 B 20 Wedge shape nm Co Wedge shape nm Strong Point of BLS!!! 27 Nov KMS 31

32 Result of the Field dependence Frequency (GHz) Stokes anti-stokes Δf = 2.18 GHz f (GHz) t Co = 1.2 nm Magnetic field (T) Magnetic field (T) f 2 D M s k k x M s m/(a s) x nm 1100 kam D 1.13 mj/m Nov KMS 32

33 Result of SW Dispersion relations f (GHz) Pt(4 nm)/co(0.5 nm)/pt(4 nm) k x (nm -1 ) t Co (nm)= D f DE f0 p k M s x 27 Nov KMS 33

34 Thickness dependence 54 3 t FM (nm) 2 Pt/CoFeB/AlOx Pt/Co/AlOx 1 f (GHz) interface t FM -1 (nm -1 ) 27 Nov KMS 34

35 idm energy density of Pt/Co/AlO x IDM energy density (mj m -2 ) t Co (nm) Field dependence (D H ) Dispersion relation (D k ) 2 BLS limit 1 f 2 Df k M D x 2 M k D max s 1.24 t Co = 1.0 nm 2 x s t Co -1 (nm -1 ) 27 Nov KMS 35

36 idm energy density Pt/CoFeB/AlOx IDM energy density (mj m -2-2 ) ) BLS limit t CoFeB CoFeB (nm) Field dependence (D H ) t CoFeB CoFeB (nm -1-1 ) 1 D D max f M 2 k 0.84 t CoFeB = 1.6 nm 2 x s 27 Nov KMS 36

37 Is it real DMI? f (GHz) Pt(4 nm)/co(0.5 nm)/pt(4 nm) t Co =1.10 nm t Co =1.20 nm t Co =1.50 nm t Co =1.60 nm k x (nm -1 ) No meaningful results for symmetric structure 27 Nov KMS 37

38 Another possible origin of f, I Different anisotropies of two interfaces First Evidence: k-dep. measurement 0 Dk Insulator FM HM substrate Interface 1 Interface 2 f M, H, K, K, A, k, s ext v s ex 2 2 H k M sk tfm M s 2A 2 2 2K s H k KV 4 M s 1 k tfm / 2 2 M s M s t FM 1/2 2A 2 sin, 27 Nov KMS 38

39 Another possible origin of f, II Second Evidence: f f sin 0 a Δf = 1.71 GHz b Intensity k H = 90 o k H = 0 o Δf = 0.11 GHz f (GHz) k H -1.0 H k = -90 o Frequency Shift (GHz) Δf = GHz ( o ) 27 Nov KMS

40 Another possible origin of f, III Third Evidence: D k = D H IDM energy density (mj m -2 ) t Co (nm) Field dependence (D H ) Dispersion relation (D k ) IMA 0.2 BLS limit t Co -1 (nm -1 ) PMA 1 27 Nov KMS 40

41 Interface DMI, thickness dep. Pt/Co/AlOx Pt/CoFeB/AlOx IDM energy density (mj m -2 ) a t Co (nm) IMA 0.2 BLS limit t Co -1 (nm -1 ) PMA b Field dependence (D H ) Dispersion relation (D k ) Field dependence (D H ) IDM energy density (mj m -2 ) IMA t CoFeB (nm) 0.2 BLS limit t CoFeB -1 (nm -1 ) 27 Nov KMS 41

42 Effect of Ta buffer layer APL 107, (2015) Pt/Co/AlOx Ta/Pt/Co/AlOx M s 1.10 (MA/m) 1.42 (MA/m) K s 0.56 (mj/m 2 ) 1.10 (mj/m 2 ) 27 Nov KMS 42

43 Enhanced DMI with Ta buffer layer f (GHz) With a Tantalum buffer layer Without a Tantalum buffer layer t Co -1 (nm -1 ) 2 D f ky M s idm energy density (mj/m 2 ) Ta/Pt/Co/AlO x (D H ) 0.4 Ta/Pt/Co/AlO x (D k ) Pt/Co/AlO x (D H ) t Co -1 (nm -1 ) M s f D 2 k y Pt/Co/AlOx Ta/Pt/Co/AlOx D max (mj/m 2 ) 1.24 ± ± Nov KMS D tco=1.4 nm (mj/m 2 ) 0.98 ± ±

44 Conclusions Field dep. & k-dep. measurements Well defined k-vector and k dep. dispersion relations Monolayer sensitivity Local detection Relatively small limitation of the sample structure Good roughness, moderate anisotropy field, etc. BLS is wonderful for DMI 27 Nov KMS 44