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Soliton pair dynamics in patterned ferromagnetic ellipses

Office of Science Laboratory. Operated by The University of Chicago ... Magnetic Films Group. Materials Science Division. Acknowledgements. L. Ocola, R. Divan, J. ...

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Soliton pair dynamics in patterned ferromagnetic ellipses

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  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:

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