Vortex dynamics in an equilateral triangular arrangement of

Vortex dynamics in an equilateral triangular arrangement of three magnetic disks X. M. Cheng, 1, 2 D. J. Keavney 2, D. J. Clarke 3, 4, O. Tchernyshyov 3, M. Mahoney 1, and A. Melikyan 5 1 Department 2 Advanced of Physics, Bryn Mawr College Photon Source, Argonne National Laboratory PEEM image 3 Department of Physics and Astronomy, Johns Hopkins University 4 Department of Physics and Astronomy, University of California 5 Materials Science Division, Argonne National Laboratory q Motivation q Time-resolved X-ray Photoemission Electron Microscopy (TR-PEEM) q Experimental results of vortex gyration in the tri-disk system q Theoretical calculation of frequency shift due to dipolar interaction q Summary 10 APS March meeting, Portland, March 16, 2010

Magnetic Vortex Dynamics Vortex State: Magnetic vortices have been of great interest • Rich physics • Applications in memory devices • Study on interaction of adjacent vortices lacking D=4. 5µm Chirality: Polarity: CW CCW up(+1) down (-1) S. B. Choe et al. , Science 304, 420 (2004). X. M. Cheng et al, PRB, 79, 172411 (2009) D=5µm R=2 µm J. Raabe et al. , PRL 94, 217204 (2005). K. Guslienko et al. , JAP 91 8037 (2002), PRL 96, 067205 (2006). X. M. Cheng 10 APS March Meeting , March 16, 2010 2

X-ray Photoemission Electron Microscopy (X-PEEM) X-ray Magnetic Circular Dichroism (XMCD) Fe PEEM Fe. Ni disk 25º y x Brightness ~ M · k ~ Mx X. M. Cheng 10 APS March Meeting , March 16, 2010 3

Pump-probe time-resolved X-ray Photoemission Electron Microscopy I 0(t) 24 -bunch mode: 153 ns 90 ps § 100 nm Spatial Resolution § 90 ps Temporal Resolution Dt PEEM Optics B(t) 50Ω Advanced Photon Source Argonne National Lab I 0(t) Fe. Ni disks Au Waveguide B 10μm J(t) Pulse Generator Radius=2 µm X. M. Cheng 10 APS March Meeting , March 16, 2010 4

Vortex core motion in an isolated disk at 2 m. T excitation Radius=2µm B y x k B (m. T) Brightness ~ Mx 2 0 f=71 MHz, In agreement with theoretical prediction K. Guslienko et al. , JAP 91 8037 (2002), PRL 96, 067205 (2006) X. M. Cheng 10 APS March Meeting , March 16, 2010 5

Vortex core motion in tri-disk system with D=4. 5 µm Disk Spacing D=4. 5 µm Radius=2µm X. M. Cheng 10 APS March Meeting , March 16, 2010 6

Vortex core motion in tri-disk system with D=5. 0 µm Disk Spacing D=5. 0 µm Radius=2µm X. M. Cheng 10 APS March Meeting , March 16, 2010 7

Calculated frequency shift due to the dipolar interaction z y x ω/ω0 k 2/k X. M. Cheng 10 APS March Meeting , March 16, 2010 8

Comparison between tri-disk system with different spacing X. M. Cheng 10 APS March Meeting , March 16, 2010 9

Summary q Elliptical vortex core trajectories in tri-disk systems imaged by TR-PEEM q Shift in frequency of vortex core motion observed and calculated q The observed frequency shift in the 5 µm spaced tri-disk may result from slight difference in disk shape q The observed frequency shift the 4. 5 µm spaced tri-disk might be due to the interaction among disks X. M. Cheng 10 APS March Meeting , March 16, 2010 10

? X. M. Cheng 10 APS March Meeting , March 16, 2010 11

Vortex Core Motion at 2 m. T excitation B X. M. Cheng 10 APS March Meeting , March 16, 2010 12

Vortex Core Motion at 4 m. T excitation B 1 m. T 2 m. T 4 m. T X. M. Cheng 10 APS March Meeting , March 16, 2010 13

Micromagnetic Simulation: Vortex Core Trajectories 1 m. T 2 m. T 4 m. T Vortex motion following a single pulse: Circular regardless of field magnitude Free core circulation limit: ~0. 2 R • Initial core displacement<0. 2 R Circular core trajectory • Initial core displacement>0. 2 R Transient domain state, Randomization of core polarity 8 pulses Images average over 10 Cancellation of x component of vortex motion X. M. Cheng 10 APS March Meeting , March 16, 2010 14

Summary of Vortex Dynamics q Vortex core polarity reversed by non-resonant in-plane magnetic field q A narrow window exists for predictable core reversal above this field regime randomization of core polarity observed q Transient domain state observed in both experiments and simulations q Imaged core trajectory changed from circular to more elliptical as excitation field increases q A critical core displacement exists at ~20% of the disk radius <0. 2 R Circular core trajectory >0. 2 R Transient domain state, Randomization of core polarity Cancellation of x component of core motion X. M. Cheng 10 APS March Meeting , March 16, 2010 15