Soliton pair dynamics in patterned ferromagnetic ellipses

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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
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Magnetic Vortex State

• Magnetic state (magnetically-soft nanodots)
  depends on
• Geometry L and R
• Material A and Ms

• Vortex in a nanomagnet
• Flux closure state with central core
• Topological soliton

Polarization p 1 Chirality c 1 Vorticity
(topological charge)
Guslienko and Novosad, J. Appl. Phys. 96, 4451,
2004.
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Spin Excitations of a Magnetic Vortex

• High-frequency spin-waves, GHz range
• Radial modes
• Azimuthal modes

• Low-frequency eigenmodes,
• sub-GHz range
• Translation (gyrotropic) modes

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

• Magnetostatic interactions dominate in
  sub-micron and micron-size dots

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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. B 67, 020403 (R), 2003. Choe et al.,
Science 304, 420, 2004. Novosad et al., Phys Rev.
B 72, 024455, 2005.
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Elliptical Dots Remanent State

• Magnetic force microscopy/micromagnetic
  simulations

2 mm
1 mm
40 nm Py
H
H
Static reversal of ellipses Vavassori et al.,
Phys. Rev. B 69, 214404 (2004)
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Vortex Dynamics Experiment
Goal Explore dynamic vortex interactions of
vortex pairs confined in elliptical magnetic
dots Method Microwave Reflection
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Single Vortex Dynamics for an Ellipse
n is Frequency
a/b 2
2b 1 mm
2a 2 mm
Thickness L 40 nm
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Experimental Mode Map Vortex Pair
H // hrf
H // hrf H ? hrf
H ? hrf
3 x 1.5 mm2 ellipse, L 40 nm
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Vortex Pair Modes
ltMxgt ? cos(wtf) ltMygt ? sin(wtf)
ltMxgt 0 ltMygt 0
ltMxgt ? cos(wtf) ltMygt 0
ltMxgt 0 ltMygt ? sin(wtf)

• Same frequency

• Splitting!

Notation i in-phase o out-of-phase
equilibrium
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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
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Dynamics of Interacting Solitons
(o,o)
(o,i)
hr.f.
red/blue represent My
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Micromagnetic Simulations Mode Map
1.5 x 0.75 mm2 ellipse, L 40 nm
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Vortex Dynamics Theory
Shifted vortex core
Energy
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Vortex Pair Dynamics Theory
Equations of motion of the vortex cores
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Vortex Core Motion Eigenvectors
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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)

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

• Top Down Lithography

Develop
Spin Coat
Expose
Metallization
Lift-off
http//chem.ch.huji.ac.il/porath/NST2/Lecture204
/Lecture20420-20e-Beam20Lithography202003.pdf
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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.
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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
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Vortex Pair Dynamics Theory
Equations of motion of the vortex cores
Gyrovectors
Dot energy for shifted vortices at positions Xj
Assume energy form