Vortex dynamics in an equilateral triangular arrangement of three magnetic disks

1. Vortex dynamics in an equilateral triangular arrangement of three magnetic disks PEEM image X. M. Cheng,1,2 D. J. Keavney2, D. J. Clarke3, 4,O. Tchernyshyov3, M. Mahoney1, and A. Melikyan5 1 Department of Physics, Bryn Mawr College 2 Advanced Photon Source, Argonne National Laboratory 3 Department of Physics and Astronomy, Johns Hopkins University 4Department of Physics and Astronomy, University of California 5Materials Science Division, Argonne National Laboratory • Motivation • Time-resolved X-ray Photoemission Electron Microscopy (TR-PEEM) • Experimental results of vortex gyration in the tri-disk system • Theoretical calculation of frequency shift due to dipolar interaction • Summary

2. 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 D=5µm Chirality: CW CCW CW CCW Polarity: up(+1) up(+1) down (-1) down (-1) R=2 µm S.B.Choe et al., Science 304, 420 (2004). J. Raabe et al., PRL 94, 217204 (2005). X. M. Cheng et al, PRB, 79, 172411 (2009) K. Guslienko et al., JAP 91 8037 (2002), PRL 96, 067205 (2006).

3. X-ray Photoemission Electron Microscopy (X-PEEM) X-ray Magnetic Circular Dichroism (XMCD) Fe PEEM FeNi disk 25º y x Brightness ~ M · k ~ Mx

4. 90 ps PEEM Optics 50Ω Advanced Photon Source Argonne National Lab I0(t) Pulse Generator Pump-probe time-resolved X-ray Photoemission Electron Microscopy • 100 nm Spatial Resolution • 90 ps Temporal Resolution I0(t) 153 ns 24-bunch mode: Dt B(t) FeNi disks B Au Waveguide 10μm J(t) Radius=2 µm

5. B y x 2 B (mT) 0 Vortex core motion in an isolated disk at 2mT excitation Radius=2µm k Brightness ~ Mx f=71 MHz, In agreement with theoretical prediction K. Guslienko et al., JAP 91 8037 (2002), PRL 96, 067205 (2006)

6. Vortex core motion in tri-disk system with D=4.5 µm Disk Spacing D=4.5 µm Radius=2µm

7. Vortex core motion in tri-disk system with D=5.0 µm Disk Spacing D=5.0 µm Radius=2µm

8. Calculated frequency shift due to the dipolar interaction z y x ω/ω0 ω/ω0 k2/k k2/k

9. Comparison between tri-disk system with different spacing

10. Summary • Elliptical vortex core trajectories in tri-disk systems imaged by TR-PEEM • Shift in frequency of vortex core motion observed and calculated • The observed frequency shift in the 5 µm spaced tri-disk may result from slight difference in disk shape • The observed frequency shift the 4.5 µm spaced tri-disk might be due to the interaction among disks

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12. B Vortex Core Motion at 2mT excitation

13. B 1 mT 2 mT Vortex Core Motion at 4mT excitation 4 mT

14. Micromagnetic Simulation: Vortex Core Trajectories 1mT 2mT 4mT • Vortex motion following a single pulse:Circular regardless of field magnitude • Free core circulation limit:~0.2 R • Initial core displacement<0.2RCircular core trajectory • Initial core displacement>0.2R Transient domain state, • Randomization of core polarity • Cancellation of x component of vortex motion Images average over 108 pulses

15. Summary of Vortex Dynamics • Vortex core polarity reversed by non-resonant in-plane magnetic field • A narrow window exists for predictable core reversal above this field regime randomization of core polarity observed • Transient domain state observed in both experiments and simulations • Imaged core trajectory changed from circular to more elliptical as excitation field increases • A critical core displacement exists at ~20% of the disk radius • <0.2R Circular core trajectory • >0.2R Transient domain state, • Randomization of core polarity • Cancellation of x component of core motion