Soliton pair dynamics in patterned ferromagnetic ellipses

1. Soliton pair dynamics in patterned ferromagnetic ellipses Kristen Buchanan, Pierre Roy,* Frank Fradin, Konstantin Guslienko, Marcos Grimsditch, Sam Bader, and Val Novosad *Uppsala University, Sweden Acknowledgements L. Ocola, R. Divan, J. Pearson NSERC of Canada for a postdoctoral fellowship Argonne - U.S. DOE Contract No. W-31-109-ENG-38 Swedish Research Council (P. R.) Magnetic Films Group Materials Science Division

2. (Permalloy) 60 50 40 Dot thickness L, (nm) 30 20 10 0 0 10 20 30 40 50 60 Dot Diameter 2R, (nm) Magnetic Vortex State Vortex in a nanomagnet • Flux closure state with central core • Topological soliton Magnetic state (magnetically-soft nanodots) depends on: • Geometry: L and R • Material: A and Ms Polarization p = ± 1 Chirality c = ± 1 Vorticity (topological charge) Guslienko and Novosad, J. Appl. Phys. 96, 4451, 2004.

3. Spin Excitations of a Magnetic Vortex Low-frequency eigenmodes, sub-GHz range • Translation (gyrotropic) modes High-frequency spin-waves, GHz range • Radial modes • Azimuthal modes ** Magnetostatic interactions dominate in sub-micron and micron-size dots ** Vortex Pair Dynamics in elliptic dots Dynamic vortex interactions in: • Tri-layer F/N/F dots • Dense 2D dot arrays (theory/simulation) Single vortex dynamics: • Cylindrical • Square/rectangular • Elliptical

4. Vortex core trajectory - Polarization dictates direction Vortex Dynamics: Translational Mode Simulations of the vortex translational mode Shifted vortex core position Energy Theory/simulations: Guslienko et al., J. Appl. Phys. 91, 8037, 2002 Experiment: Park et al., Phys. Rev. B67, 020403 (R), 2003. Choe et al., Science304, 420, 2004. Novosad et al., Phys Rev. B72, 024455, 2005.

5. Mz Elliptical Dots: Remanent State 2 mm • Magnetic force microscopy/micromagnetic simulations 1 mm 40 nm Py H H Static reversal of ellipses: Vavassori et al., Phys. Rev. B 69, 214404 (2004)

6. Vortex Dynamics Experiment Goal: Explore dynamic vortex interactions of vortex pairs confined in elliptical magnetic dots Method: Microwave Reflection

7. Single Vortex Dynamics for an Ellipse n is Frequency a/b ~ 2 2b = 1 mm 2a = 2 mm Thickness L= 40 nm

8. Experimental Mode Map: Vortex Pair H // hrf H // hrf H  hrf H  hrf 3 x 1.5 mm2 ellipse, L = 40 nm

9. y x H H Vortex Pair Modes <Mx>  cos(wt+f) <My>  sin(wt+f) <Mx> = 0 <My> = 0 <Mx>  cos(wt+f) <My> = 0 <Mx> = 0 <My>  sin(wt+f) • Same frequency • “Splitting”! Notation: i = in-phase o = out-of-phase equilibrium

10. Micromagnetic Simulations – Single Vortex Py dot L= 40 nm 2a = 1 mm, 2b = 2 mm Ms = 700 emu/cm3 A = 1.3 merg/cm no anisotropy Damping a = 0.008 Gyromagnetic ratio: g/2p = 2.94 MHz/Oe LLG, Scheinfein OOMMF, NIST 134 MHz Single translational mode frequency

11. Dynamics of Interacting Solitons (o,o) (o,i) hr.f. red/blue represent My

12. Micromagnetic Simulations: Mode Map 1.5 x 0.75 mm2 ellipse, L = 40 nm

13. 1) Landau-Lifshitz Gilbert equation M(r):magnetization distribution W :energy Heff :effective magnetic field 2) Representation in terms of core position X G : gyrovector G : gyroconstant G=2MsL/ L : dot thickness Ms: saturation magnetization  : gyromagnetic ratio Vortex core trajectory Thiele et al., Phys. Rev. Lett, 30, 230, 1973 Applied to circular dots: Guslienko et al., J. Appl. Phys. 91, 8037, 2002 Vortex Dynamics: Theory Shifted vortex core Energy

14. Gyrovectors: X1, p1 Assume energy form: X2, p2 Eigenfrequencies: Prediction: True for simulations! Vortex Pair Dynamics: Theory Equations of motion of the vortex cores:

15. Motion patterns match simulations! Vortex Core Motion: Eigenvectors

16. Conclusions • First experimental data on magnetic vortex pair dynamics • Core Polarizations: • Negligible static effect • Very important for dynamics • Excitation direction • Mode map • Theory/simulations agree on • Frequency product invariance • Core motion patterns • Buchanan et al., Nature Physics (in press)

17. Competing Energies Exchange Nanomagnetism Competition between different energies at the nanoscale will determine the fundamental properties of nanomagnets Magnetocrystalline Magnetostatic Zeeman

18. 1 mm Fabrication • Top Down: Lithography Develop Spin Coat Expose Metallization Lift-off http://chem.ch.huji.ac.il/~porath/NST2/Lecture%204/Lecture%204%20-%20e-Beam%20Lithography%202003.pdf

19. (Permalloy) 60 50 40 Dot thickness L, (nm) 30 L 20 10 2R 0 0 10 20 30 40 50 60 Dot Diameter 2R, (nm) Phase Diagram for Nanodots Magnetic phase diagram for magnetically-soft nanodots • Magnetic state depends on: • Geometry: L and R • Material: A and Ms Guslienko and Novosad, J. Appl. Phys. 96, 4451, 2004.

20. Magnetic Vortex State Outline • Vortex state – unique dynamic excitations • Vortex pair dynamics in elliptical dots Vortex in a nanomagnet - nonlocalized soliton Flux closure state with central core Polarization p = ± 1 Chirality c = ± 1 Vorticity q = 1

21. X1, p1 X2, p2 Vortex Pair Dynamics: Theory Equations of motion of the vortex cores Gyrovectors: Dot energy for shifted vortices at positions Xj Assume energy form: