Highlights of ReC-SDSW center's recent works OUTLINE

Transcription

1 Highlights of ReC-SDSW center's recent works Since 22 Spinics Lab. Since April, Introduction OUTLINE 2. Nontrivial dynamic properties of magnetic vortex - Phase diagram of vortex dynamic response - Low-amplitude vortex translation mode linear versus nonlinear gyrotropic motion 2 elementary eigenmodes - Vortex core switching Mechanism: how VC reversal takes place Dynamic origin - Universal criterion Critical velocity of vortex core switching 3. Conceptual design of Vortex based MRAM (VRAM) 4. Conclusion

2 Introduction Magnetic vortex states in continuous magnetic thin films Out-of-plane M components S.-K. Kim et al., Appl. Phys. Lett. 86, 5254 (25) - the cover of the January 31, 25 issue 33 nm thick Fe In-plane M components Vector magnetization imaging using STXM (Scanning transmission x-ray microscope) in at ALS, Berkeley by S.-K. Kim and J. B. Kortright 4

3 Magnetic vortex as a ground state in nanodots Experimental observation of magnetic vortex cores MFM image (Py) T. Shinjo et al., Science 289, 93 (2). Vortex structure -In-plane curling magnetization -Out-of-plane M at the core Dot thickness L, (nm) SP-STM image (Fe island) A. Wachowiak et al., Science 298, 577 (22) (Permalloy) Singledomain Vortex Dot Diameter 2R, (nm) K. Metlov et al., JMMM , (22) Rich static vortex states: Information carriers Different in-plane direction Four equivalent vortex states Different core orientation C=1, p=1 Up core C=-1, p=1 6 C=1, p=-1 Down core C=-1, p=-1 Information carrier Magnetic vortex states can be applicable to nonvolatile information storage devices. CCW CW

4 Nontrivial dynamic properties of magnetic vortex: Phase diagram of vortex dynamic response 7 Response of a single vortex in a disk to oscillating field Micromagnetic Simulations Geometry and dimensions H = Asin(2 π ν t) y z (nm) 1 nm H y 15 y (nm) -15 x (nm) t linearly oscillating harmonic fields Exchange constant A 1.3 x 1-11 J/m Anisotropy constant K J/m 3 Saturation Magnetization M s 86 x 1-3 A/m Cell size 2 x 2 x 1 nm 3 Damping Constant.1 Eigenfrequency v : 33 MHz Static vortex annihilation field A s : 5 Oe M Temperature K H 5 Oe 8

5 Phase diagram of the vortex dynamic response I. Low-amplitude gyrotropic motion II. Periodic V-AV pair creation and annihilation III. Giant-amplitude gyrotropic motion IV. Non-periodic V-AV multi-pairs creation and annihilation V. Instant dynamic saturation The different dynamic regimes of the MVs in response to the driving field versus A and ν K.-S Lee, S.-K. Kim et al, Phys. Rev. B 76, (27). 9 Nontrivial dynamic properties of magnetic vortex: Low-amplitude vortex translation mode 1

6 Low-amplitude vortex translation mode H(t).6 L = 1 nm t A/A s.4 z y x 2R = 3 nm ν ν Region I: The VC rotates around the dot center in an elliptical or more complicated orbit K.-S. Lee and S.-K. Kim, Appl. Phys. Lett 91, (27) 11 Governing equation of the gyrotropic motion Representation in terms of core position X M( r, t) = M( r X( t)) ( X) dx ˆ dx W G D + = dt dt X A soliton on a potential wall p=1 p=-1 Vortex core trajectory Solution for circular dots: Guslienko et al., J. Appl. Phys. 91, 837 (22) Appl. Phys. Lett. 89, 2251 (26) General approach: Thiele et al., Phys. Rev. Lett, 3, 23 (1973) Vortex dynamics in 2D magnets: D.L. Huber, Phys. Rev. B 26, 3758 (1982) 12

7 Vortex core trajectories under oscillating magnetic fields Micromagnetic simulation Numerical sol. of Thiele s Eq. ( νν, A As ) = (.6,.7) ( 1.,.1 ) ( 1.5,.2) (.6,.7 ) ( 1.,.1 ) ( 1.5,.2) Transient FFT power (a. u.) Steady Frequency (GHz) Frequency (GHz) Sharp peaks Broad peak at v = ν The steady-state motions responding to the driving field of a frequency v The initial transient motion associated the VC resonant excitation in the given dot. The simulation results and numerical solutions are in quite well agreement, in both the steady and initial transient states. K.-S. Lee and S.-K. Kim, Appl. Phys. Lett 91, (27) 13 t = ~ 1 ns ~ 1 8 ~ 1 Nonlinear gyrotropic motion [ ν ( GHz), A( Oe) ] = [.1, 3] Inverse FFTs Δf Δf ( νν, A A ) = (.3,.6) 1 = 5~15(MHz) 2 = 25~35 Δf 3 = 475~525 Δf = 4~475 FFT power (a. u.) s Δf 1 Δf 2 Δf Δf Frequency (GHz) Δf 1 + Δf 2 Δf 1 + Δf 2 + Δf 3 Δf 1 + Δf 2 + Δf 3 + Δf Peaks at ν = 1 MHz and 3ν, 5ν The steady-state motions as the nonlinear responses to the driving field of a frequency v The broad peak at 44 MHz The initial transient motion caused by the vortex eigenmotion, which is shifted from ν = 33 (for the linear case) to 44 MHz due to the significant nonlinearity To analytically interpret nonlinear motions using Thiele s equation of motion, 14 ( ) G X D ˆ X + W X X= κ 2 β 4 W( X) = W() + X + X μ [ zˆ H] X 2 4 For β/κ = m -2, not only the trajectories but also the frequency spectra obtained from the numerical solutions are in best agreement with those from the simulations. K.-S. Lee and S.-K. Kim, Appl. Phys. Lett 91, (27)

8 Elementary circular modes Superposition of two circular eigenmotions Superposition of two circular fields H(t) H x H y H y H CCW H CW ω H H Lin H ω H H CCW H ω H H Linear H CCW H CW H CW H Lin H CW ω H ω H HCCW VC position under H L VC position under H CCW VC position under H CW The application of linearly oscillating field is equivalent to the application of both the pure circularly rotating fields of HCCW and HCW simultaneously, with the same amplitude and with equal frequency. K.-S. Lee and S.-K. Kim, Phys. Rev. B 78, 1445 (28) 15 R CW R CCW Elementary eigenmodes in the gyrotropic motions ( X) dx ˆ dx W G D + = dt dt X ( X ) μ[ ˆ () t ] W, t = W() + κ X /2+ W H WH = z H X 2 μ = πrlm ξc ξ = 2/3 s For any polarized harmonic oscillating magnetic field D G κ 1 iω μ G D X + = κ X 1 H H = H exp( iω t) X= X exp( iω t) H H A dynamic susceptibility tensor ˆχ X defined as X ˆχ H = X ˆ χ ( ) χ χ μ iωg iωd κ χ χ ( iωd κ) ( ωg) iωd+ κ iωg + xx xy X,L ω = = 2 2 yx yy Through the diagonalization X χ H,CCW CCW,CCW = X,CW χ H CW,CW X X = χ H = χ H CCW CCW CCW CW CW CW Clock-wise (CW) and counter-clock-wise (CCW) circular eigenmotions with respect to pure circularrotating-field eigenvectors are the elementary eigenmodes of the gyrotropic motion of a magnetic vortex in soft magnetic circular nanodots. K.-S. Lee and S.-K. Kim, Phys. Rev. B 78, 1445 (28) 16

9 The vortex core motion under CCW and CW rotating fields χ CCW,CW Both and δ H CCW,CW show strong resonance effects at ωh / ωd = 1. Asymmetric resonance effect between two rotating eigenmodes: There is resonance effect for only one eigenmode, and nonresonance for the other eigenmode. The mode showing the resonance effect switches according to p X = χ H CCW CCW CCW χ = 2 R / H CCW(CW) CCW(CW),CCW(CW) XCW = χcwhcw δccw,cw = χccw,cw arg( ) 17 The variation of χ CCW,CW with ωh depends only on P not C. The variation of δ H CCW,CW with ωh depends on both P and C. / ωd / ωd K.-S. Lee and S.-K. Kim, Phys. Rev. B 78, 1445 (28) The vortex core motion under CCW and CW rotating fields v : Resonance frequency : 3 MHz H CCW ω H H ω H CW H ω H H Lin H Giant asymmetry of the resonance effect between the CCW and CW circular eigenmotions: Resonance effect for only one of the two eigenmodes, and nonresonance for the other eigenmode, depending on the core orientation From technological point of view, the CCW and CW circular fields are very effective means to switch VC orientation selectively, with low power consumption and the circular fields can be made by currents flowing along the two different electrodes orthogonally crossing on a vortex. S.-K. Kim et al. Appl. Phys. Lett. 92, 2259 (28), (the cover of the January 14 issue) 18

10 Nontrivial dynamic properties of magnetic vortex: Vortex core switching 19 Vortex-core reversal mechanism: how it takes place Vortex core motion Oscillating field H = y 9 5sin(2π t) Deformation (entire V structure) Py V-AV pair creation (opposite core polarization) V AV annihilation V (original) + AV (new) Strong SW radiation Vortex core reversal V (new) K.-S Lee, S.-K. Kim et al, Phys. Rev. B 76, (27). 2

11 Summary of VC Switching Dynamics Vortex core switching What we found from simulations are as follows: This dynamic process is mediated by the creation and annihilation of the V-AV pairs in a nanodot. This switching is a pure dynamic process, which is driven by external oscillating fields, not by overcoming energy barrier. This core switching is allowed to occur on the 1 ps time scale. A gyrotropic field induced by the vortex motion acts as the physical origin of the VC dynamical reversal K.-S Lee, S.-K. Kim et al, Phys. Rev. B 76, (27). 21 Origin of dynamic vortex core switching : Why Py H = 5( Oe)sin(2 π ν t) y 2nm ν = ν = 58MHz R = 15nm H H The gyrofield (the kinetic part of the effective field) h = 1 g / m M s The kinetic part of the Lagrangian density g = h z M s γ 1 = γ ( ) n m m 1+ m n ( m m ) z ( m + p) 2 z Velocity Gyrofiled Deformation The dynamic core profile deformation up to the VC reversal is caused by the effective Zeeman energy, w ( t) = M h ( t) m ( t) Z which is indeed the driving force of the process. K. Y. Guslienko, K.-S. Lee, and S.-K. Kim, Phys. Rev. Lett. 1, 2723 (28) 22 s z z

12 Nontrivial dynamic properties of magnetic vortex: Universal criterion 23 Vortex-core reversal criterion : the critical velocity I = 7.2sin(2 π ν t) ( ma) ν = 3MHz x 2nm Py R = 3nm R = 3nm Whenever the VC velocity reaches its critical value, the VC orientation is switched to its opposite direction. Constant current density At resonant frequency S.-K. Kim et al., Appl. Phys. Lett. 91, 8256 (27). 24

13 Summary of vortex-core reversal criterion (m/s) υ [R (nm), L (nm)] =[15, 2] - There is a critical field corresponding to the critical velocity, required for the VC switching. [ Ω, H (Oe)] [.8, 72] [1., 15] [1., 2] [1., 24] [1., 3] [1.4, 94] t (ns) -Thecritical velocity is the governing parameter and does not depend on the driving force parameters as well as the size and shape of a given dot. VC reversal always occurs when the VC velocity reaches its critical value (~ 33 ±37 m/s) which does not depend on the ac current parameters. This critical velocity can serve as the universal criterion of the VC reversal. 25 K.-S Lee, S.-K. Kim et al, arxiv (28). Universality of the critical velocity Exchange stiffness Dimension Saturation magnetization Gyromagnetic ratio 6 [R (nm), L (nm)] =[15, 2] υ C (m/s) 4 2 γ R (nm) L/R M s /M s,py ( A A ) ex ex, Py This critical velocity can be expressed as υ = ηγ C A ex 12 [R (nm), L (nm)] =[15, 2] γ γ Py η = 1.66 ± K.-S Lee, S.-K. Kim et al, arxiv (28).

14 Phase diagram and switching time on vortex-core switching (nm koe) Ω= ω H ω D ω 2π the vortex eigenfrequency, 58 MHz for R = 15 nm, L = 2 nm D Critical velocity RH (nm koe) 12 6 [R (nm), L (nm)] [15, 2] [15, 3] Ω Ω [3, 2] [45, 2] H (Oe) υc = (1.66 ±.18) γ Aex H (koe) H (koe) ns 1 ns 2 ns 1.5 ns.2 ns.3 ns Δt g (ns) Ω 5 ps.1 ns K.-S Lee, S.-K. Kim et al, arxiv (28). Conceptual design of Vortex based MRAM (VRAM) 28

15 Conceptual design of VRAM versus STT-RAM 1 UP DOWN - Information storage (O) - Thermal stability : retention (O) - Endurance : repeatable writing (O) - Storage capacity : density(?) - Low power writing (?) - Cell selection reliability(?) - Low power reading(?) 29 Cell selection problem: rotating fields Cell Selection for Recording and Readout by the use of the CCW and CW rotational fields H CCW ω H = ω D ωh = ω D H CW 1 1 UP H CCW ωh = ω D DOWN ωh = ω D H CW UP UP DOWN DOWN DOWN UP S.-K. Kim et al. Appl. Phys. Lett. 92, 2259 (28), (the cover of the January 14 issue) 3

16 Summary/Conclusion The dynamic VC switching process via the creation and annihilation of the V-AV pairs in a nanodot. - A pure dynamic process, not by overcoming energy barrier. - M reversals occur on the 1 ps time scale. Universal criterion for ultrafast vortex-core switching -Critical velocity (~ 33 ± 37 m/s) - depending on exchange stiffness and gyromagnetic ratio - not depending on dimensions and shape The use of rotating fields is very promisingly advanced key technology The present work provides a further step toward the practical application of vortex states to information storage such as VRAM. 31 Result Highlight Simulations of a spin wave generator make the idea that future computing devices might use these magnetic phenomena more plausible. Spin waves propagate as oscillations in the orientation of the magnetic moments of atoms in a magnetic medium. Harnessing their wave-like behaviour could lead to new paradigms for logic devices. Sang-Koog Kim at Seoul National University in South Korea and his colleagues present a computer model of a 15-nanometre disc shooting spin waves into a magnetic wire. They predict that briefly applying an external field to the disc when the magnetic moments are in a whirlpoollike arrangement will create disturbances in their orientation (pictured) that spill into the wire. They also model how spin waves propagate in the wire, and how wires with different magnetic properties could filter out specific frequencies of spin wave. Phys. Rev. Lett. 98, 8725 (27) Nature Research Highlights, Vol 446 (1 March 27) page 5 32 Selected as the cover image for the January 14, 28 issue of Applied Physics Letters. S.-K. Kim et al., Appl. Phys. Lett. 92, 2259 (28)

17 Domain wall dynamics 33 Average velocities of domain walls versus H Region I : The steady motion of a single DW Region II : Oscillatory motion of DWs in periodic manner J.-Y. Lee, K.-S. Lee, S. Choi, K. Y. Guslienko, and S.-K. Kim, Phys. Rev. B, 76, (27). Region III : Chaotic DW motion with the appearance of multiple vortex and antivortex state 34 S.-K. Kim et al., Appl. Phys. Lett., 93, 5253 (28).

18 Topological charges of magnetic solitions Region II : Oscillatory motion of DWs in periodic manner Antivortex wall nucleation Vortex wall nucleation TW polarization (V- or Λ- shape) determine polarization of any type of vortex or antivortex J.-Y. Lee, K.-S. Lee, S. Choi, K. Y. Guslienko, and S.-K. Kim, Phys. Rev. B, 76, (27). 35 Analytical solutions for DW dynamics Governing equation ˆ ˆ W ( X ) GX + DX = X 1 2 W ( X) = W () + κy λx H + μzˆ X H 2 General solution ( ) Bˆ = Gˆ Dˆ X λh xy w H ωd t () t = X ( ) t + Y( ) ( e 1) B xx B B xx 2 H w Y w H 2 H ωdt () t = + Y( ) e w w H 2 H w y κ > y κ < μ H κ x x J.-Y. Lee, K.-S Lee, S. Choi, K. Guslienko, and S.-K. Kim et al, arxiv (27). K. Guslienko, S.-K. Kim, and J.-Y. Lee et al, arxiv (27). 36

19 Enhancement of domain wall velocity The PMA underlayer significantly suppresses the typically observed velocity breakdown above the Walker critical field. The perpendicularly magnetized under layer plays a crucial role in the suppression of the velocity breakdown above the H w by introducing magnetostatic and exchange interactions, which prevents the nucleation of the cores of the VW or AVW. J. Y. Lee, K.-S. Lee and S.-K. Kim, Appl. Phys. Lett 91, (27) 37 Preventing the nucleation of the VWs or AVWs The oscillatory displacement versus time curve The oscillatory displacement versus time curve Model I Model II M x / M s -1 1 A clear steady motion of a single TW was observed, without any DW transformation. J. Y. Lee, K.-S. Lee and S.-K. Kim, Appl. Phys. Lett 91, (27) 38

20 List of publications 1. K.-S. Lee, B.-W. Kang, Y.-S. Yu, and S. -K. Kim, Appl. Phys. Lett. 85, 1568 (24). Vortex-antivortex pair driven magnetization reversal dynamics: Micromagnetic simulation evidence 2. S.-K. Kim, K.-S. Lee, B.-W. Kang, K.-J. Lee, and J. B. Kortright, Appl. Phys. Lett. 86, 5254 (25). Vortex-antivortex assisted magnetization dynamics in a semi-continuous thin-film model system studied by micromagnetic simulations Selected as the cover of the 31 Jan. 25 issue. 3. K.-S. Lee, S. K. Choi, and S.-K. Kim, Appl. Phys. Lett. 87, (25). Radiation of spin waves from magnetic vortex cores by their dynamic motion and annihilation processes Selected as the cover of the 7 Nov. 25 issue. 4. S.-K. Choi, K.-S. Lee, K. Y. Guslienko, and S.-K. Kim, Phys. Rev. Lett. 98, 8725 (27). Strong Radiation of Spin Waves by Core Reversal of a Magnetic Vortex and their Wave Behaviors in Magnetic Nanowire Waveguides Nature Research Highlights, Vol 446 (1 March 27) page 5. Selected for the Virtual Journal of Nanoscale Science & Technology [March 26, Volume 15, Issue 1]. 5. S.-K. Kim, Y.-S. Choi, K.-S. Lee, K. Y. Guslienko, and D.-E. Jeong, Appl. Phys. Lett. 91, 8256 (27). Electric-current-driven vortex-core reversal in soft magnetic nanodots Selected for the Virtual Journal of Nanoscale Science & Technology [Sep. 3, 27, Volume 16, Issue 1.] 6. K.-S. Lee and S.-K. Kim, Appl. Phys. Lett. 91, (27). Gyrotropic linear and nonlinear motions of a magnetic vortex core in soft magnetic nanodots 7. K.-S. Lee, K. Y. Guslienko, J.-Y. Lee, S.-K. Kim, Phys. Rev. B 76, (27). Ultrafast Vortex-Core Reversal Dynamics in Ferromagnetic Nanodots Selected for the Virtual Journal of Nanoscale Science & Technology [Nov. 19, 27, Volume 16, Issue 21]. Selected for the Virtual Journal of Ultrafast Science [Dec. 27, Volume 6, Issue 12]. 8. S.-K. Kim, K.-S. Lee, Y.-S. Yu, and Y.-S. Choi, Appl. Phys. Lett. 92, 2259 (28). Reliable low-power control of ultrafast vortex-core switching with the selectivity in arrays of vortex states by in-plane circular-rotational magneticfields and spin-polarized currents 9. K. Yu. Guslienko, K.-S. Lee, S.-K. Kim, Phys. Rev. Lett. 1, 2723 (28). Dynamic Origin of Vortex Core Switching in Soft Magnetic Nanodots Selected for the Virtual Journal of Nanoscale Science & Technology [Jan. 28, 28, Volume 17, Issue 4]. Professor Sang-Koog Kim Director of Research Center for Spin Dynamics & Spin-Wave Devices sangkoog@snu.ac.kr Research Center for Spin Dynamics & Spin-Wave Devices

21 1. K.-S. Lee, Y.-S. Yu, Y.-S. Choi, D.-E. Jeong and S.-K. Kim, Appl. Phys. Lett. 92, (28). Oppositely rotating eigenmodes of spin-polarized current-driven vortex gyrotropic motions in elliptical nanodots Selected for the Virtual Journal of Nanoscale Science & Technology [June. 2, 28, Volume 17, Issue 22]. 11. K.-S. Lee and S.-K. Kim, Phys. Rev. B. 78, 1445 (28). Two Circular-Rotational Eigenmodes and their Giant Resonance Asymmetry in Vortex Gyrotropic Motions in Soft Magnetic Circular Nanodots 12. S.-K. Kim, K.-S. Lee, Y.-S. Choi, and Y.-S. Yu, IEEE Trans. Mag. (in press). Low-Power Selective Control of Ultrafast Vortex-Core Switching by Circularly Rotating Magnetic Fields: Circular-Rotational Eigenmodes [as a proceeding of the IEEE Internatinoal Magnetic Conference 28 (Intermag 28)]. 13. Y.-S. Choi, S.-K. Kim, K.-S. Lee, and Y.-S. Yu, Appl. Phys. Lett. 93, (28). Understanding eigenfrequency shifts observed in vortex gyrotropic motions in a magnetic nanodot driven by spin-polarized out-of-plane dc current Selected for the Virtual Journal of Nanoscale Science & Technology [Nov. 24, 28, Volume 18, Issue 21]. 14. J.-Y. Lee, K.-S. Lee, and S.-K. Kim, Appl. Phys. Lett. 91, (27). Remarkable enhancement of domain-wall velocity in magnetic nanostripes Selected for the Virtual Journal of Ultrafast Science [Oct. 27, Volume 6, Issue 1]. 15. J.-Y. Lee, K.-S. Lee, S.-K. Choi, K. Yu. Guslienko, and S.-K. Kim, Phys. Rev. B. 76, (27). Dynamic transformations of the internal structure of a moving domain wall in magnetic nanostripes Selected for the Virtual Journal of Nanoscale Science & Technology [Nov. 19, 27, Volume 16, Issue 21]. 16. S.-K. Kim, J.-Y. Lee, Y.-S. Choi, K. Yu. Guslienko, Appl. Phys. Lett. 93, 5253 (28). Underlying Mechanism of Domain-Wall Motions in Soft Magnetic Thin-Film Nanostripes Beyond the Velocity-Breakdown Regime Selected for the Virtual Journal of Nanoscale Science & Technology [Aug. 18, 28, Volume 18, Issue 7]. 17. K. Yu. Guslienko, J.-Y. Lee, and S.-K. Kim, IEEE Trans. Mag. (in press). Dynamics of domain walls in soft magnetic nanostripes: topological soliton approach Professor Sang-Koog Kim Director of Research Center for Spin Dynamics & Spin-Wave Devices sangkoog@snu.ac.kr Research Center for Spin Dynamics & Spin-Wave Devices