Soliton pair dynamics in patterned ferromagnetic ellipses
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Soliton pair dynamics in patterned ferromagnetic ellipses l.jpg

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


Magnetic vortex state l.jpg

(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.


Spin excitations of a magnetic vortex l.jpg
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


Vortex dynamics translational mode l.jpg

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.


Elliptical dots remanent state l.jpg

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)


Vortex dynamics experiment l.jpg
Vortex Dynamics Experiment

Goal: Explore dynamic vortex interactions of vortex pairs confined in elliptical magnetic dots

Method: Microwave Reflection


Single vortex dynamics for an ellipse l.jpg
Single Vortex Dynamics for an Ellipse

n is Frequency

a/b ~ 2

2b = 1 mm

2a = 2 mm

Thickness L= 40 nm


Experimental mode map vortex pair l.jpg
Experimental Mode Map: Vortex Pair

H // hrf

H // hrf

H  hrf

H  hrf

3 x 1.5 mm2 ellipse, L = 40 nm


Vortex pair modes l.jpg

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


Micromagnetic simulations single vortex l.jpg
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


Dynamics of interacting solitons l.jpg
Dynamics of Interacting Solitons

(o,o)

(o,i)

hr.f.

red/blue represent My


Micromagnetic simulations mode map l.jpg
Micromagnetic Simulations: Mode Map

1.5 x 0.75 mm2 ellipse, L = 40 nm


Vortex dynamics theory l.jpg

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


Vortex pair dynamics theory l.jpg

Gyrovectors:

X1, p1

Assume energy form:

X2, p2

Eigenfrequencies:

Prediction:

True for simulations!

Vortex Pair Dynamics: Theory

Equations of motion of the vortex cores:


Vortex core motion eigenvectors l.jpg

Motion patterns match simulations!

Vortex Core Motion: Eigenvectors


Conclusions l.jpg
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)


Competing energies l.jpg
Competing Energies

Exchange

Nanomagnetism

Competition between different energies at the nanoscale will determine the fundamental properties of nanomagnets

Magnetocrystalline

Magnetostatic

Zeeman


Fabrication l.jpg

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


Phase diagram for nanodots l.jpg

(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.


Magnetic vortex state20 l.jpg
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


Vortex pair dynamics theory21 l.jpg

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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