soliton pair dynamics in patterned ferromagnetic ellipses

21
A U.S. Department of Energy Office of Science Laboratory Operated by The University of Chicago Argonne National Laboratory Office of Science U.S. Department of Energy Soliton pair dynamics in patterned ferromagnetic ellipses Kristen Buchanan , Pierre Roy,* Frank Fradin, Konstantin Guslienko, Marcos Grimsditch, Sam Bader, and Val Novosad Magnetic Films Group Materials Science Division 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.) *Uppsala University, Sweden

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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 - PowerPoint PPT Presentation

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Page 1: Soliton pair dynamics in patterned ferromagnetic ellipses

A U.S. Department of EnergyOffice of Science LaboratoryOperated by The University of Chicago

Argonne National Laboratory

Office of ScienceU.S. Department of Energy

Soliton pair dynamics in patterned

ferromagnetic ellipsesKristen Buchanan, Pierre Roy,* Frank Fradin,

Konstantin Guslienko, Marcos Grimsditch, Sam Bader, and Val Novosad

Magnetic Films GroupMaterials Science Division

AcknowledgementsL. Ocola, R. Divan, J. PearsonNSERC of Canada for a postdoctoral fellowshipArgonne - U.S. DOE Contract No. W-31-109-ENG-38Swedish Research Council (P. R.)

*Uppsala University, Sweden

Page 2: Soliton pair dynamics in patterned ferromagnetic ellipses

2

Pioneering Science andTechnology

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of Energy

Magnetic Vortex State

Magnetic state Magnetic state ((magnetically-soft nanodots) depends on: ) depends on:

• Geometry: L and RGeometry: L and R

• Material: A and MsMaterial: A and Ms

Guslienko and Novosad, J. Appl. Phys. 96, 4451, 2004.

00

10

20

30

40

50

60

Do

t th

ickn

ess

L, (

nm

)

10 20 30 40 50 60

Dot Diameter 2R, (nm)

(Permalloy)

Polarization p = ± 1

Chirality c = ± 1

Vorticity (topological charge)

Vortex in a nanomagnet

• Flux closure state with central core

• Topological soliton

Page 3: Soliton pair dynamics in patterned ferromagnetic ellipses

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Spin Excitations of a Magnetic Vortex

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

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

• Azimuthal modes

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

modes

Single vortex dynamics:

• Cylindrical

• Square/rectangular

• Elliptical

Vortex Pair Dynamics

in elliptic dots

Dynamic vortex interactions in:

• Tri-layer F/N/F dots

• Dense 2D dot arrays(theory/simulation)

Page 4: Soliton pair dynamics in patterned ferromagnetic ellipses

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Vortex Dynamics: Translational Mode

Vortex core trajectory- Polarization dictates direction

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.

Shifted vortex core position

Energ

y

0.1 0.2 0.30.0

0.5

1.0

1.5

R 100 nm 150 nm 200 nm 250 nmEi

genf

requ

ency

(GH

z)

Dot aspect ratio =L/R

2 2 2 4 2 6 2 8 3 0 3 2

-0.05

0.00

0.05

0.10

M/M

s

Time (ns)0 108642

0 Oe100 Oe

Simulations of the vortex translational mode

Page 5: Soliton pair dynamics in patterned ferromagnetic ellipses

5

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Elliptical Dots: Remanent State

• Magnetic force microscopy/micromagnetic simulations 2

m

1 m

40 nm Py

H

H

Static reversal of ellipses: Vavassori et al., Phys. Rev. B 69, 214404 (2004)

Mz

Page 6: Soliton pair dynamics in patterned ferromagnetic ellipses

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Vortex Dynamics Experiment

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

Method: Microwave Reflection

Page 7: Soliton pair dynamics in patterned ferromagnetic ellipses

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Single Vortex Dynamics for an Ellipse

100 200 300

0

20

R

eal I

mpe

danc

e D

eriv

ativ

e(a

rb. u

nits

)

(MHz)

0.05 0.10

100

200

300

(M

Hz)

Vertical Aspect Ratio, = 2L/(a+b)

experiment simulations theory

2b = 1 m

2a = 2 m

Thickness L= 40 nm

is Frequency

100 200 300

0

20

single pair

R

eal I

mpe

danc

e D

eriv

ativ

e(a

rb. u

nits

)

(MHz)

a/b ~ 2

Page 8: Soliton pair dynamics in patterned ferromagnetic ellipses

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Experimental Mode Map: Vortex Pair

3 x 1.5 m2 ellipse, L = 40 nm

-50 0 50 1000

50

100

150

200

p1p

2 = +1

p1p

2 = -1

HH

(M

Hz)

H (Oe)

H // hrf

H // hrf

H hrf

H hrf

Page 9: Soliton pair dynamics in patterned ferromagnetic ellipses

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Vortex Pair Modes

• Same frequency

• “Splitting”!Notation:

i = in-phaseo = out-of-phase

<Mx> = 0<My> = 0

<Mx> cos(t+)<My> sin(t+)

<Mx> = 0<My> sin(t+)

<Mx> cos(t+)<My> = 0

x

y

equilibrium

HH

Page 10: Soliton pair dynamics in patterned ferromagnetic ellipses

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Micromagnetic Simulations – Single Vortex

0 5 10

-0.02

0.00

0.02

0.04

My/M

s

Time (ns)

simulation sine fit

-50 0 50

-50

0

50

y (n

m)

x (nm)

Py dotL= 40 nm2a = 1 m, 2b = 2 m

Ms = 700 emu/cm3

A = 1.3 erg/cmno anisotropyDamping = 0.008Gyromagnetic ratio: = 2.94 MHz/Oe

LLG, ScheinfeinOOMMF, NIST

134 MHz

Single translational mode frequency

Page 11: Soliton pair dynamics in patterned ferromagnetic ellipses

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Dynamics of Interacting Solitons

red/blue represent My100 200 300

0

20

Rea

l Im

pede

nce

Der

ivat

ive

(arb

. uni

ts)

(MHz)

single pair

(o,o)

(o,i)

hr.f.

Page 12: Soliton pair dynamics in patterned ferromagnetic ellipses

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Micromagnetic Simulations: Mode Map

-50 0 50 1000

100

200

300

x x

x x

x x

x x

x x

x x

H H

Freq

uenc

y, M

Hz

H, Oe

p1p

2 = +1

p1p

2 = -1

1.5 x 0.75 m2 ellipse, L = 40 nm

Page 13: Soliton pair dynamics in patterned ferromagnetic ellipses

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Vortex Dynamics: Theory

Vortex coretrajectory

Shifted vortex core

Energ

y

Dampingt eff

HMM

1

M

rMH

W

eff

1) Landau-Lifshitz Gilbert equation

M(r): magnetization distributionW : energy Heff : effective magnetic field

0

X

XXG

W

dt

d

Applied to circular dots: Guslienko et al., J. Appl. Phys. 91, 8037, 2002

2) Representation in terms of core position X

Thiele et al., Phys. Rev. Lett, 30, 230, 1973

G : gyrovector

G : gyroconstant G=2MsL/L : dot thicknessMs : saturation magnetization

: gyromagnetic ratio

zG ˆGp))((),( tt XrMrM

Page 14: Soliton pair dynamics in patterned ferromagnetic ellipses

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X1, p1

X2, p2

Vortex Pair Dynamics: Theory

0

,

1

2111

X

XXXG

W

dt

d 0

,

2

2122

X

XXXG

W

dt

d

21int21121 ,, XXXXXX WWWW

Equations of motion of the vortex cores: Gyrovectors: zG ˆjj Gp

21212

22

122

2121 2

1

2

1, YYXXYYXXW yxyx XX

Assume energy form:

yyxxG 1

2,1 yyxxG

12,1

Eigenfrequencies:

Prediction: 2121 True for simulations!

Page 15: Soliton pair dynamics in patterned ferromagnetic ellipses

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Vortex Core Motion: Eigenvectors

Motion patterns match simulations!

1

1

1

1

xx

xx

i

i

2

2

1

1

xx

xx

i

i

1

1

1

1

xx

xx

i

i

2

2

1

1

xx

xx

i

i

1

2 1

2

2

2

1

1

Y

X

Y

X

iii YX ,X

Page 16: Soliton pair dynamics in patterned ferromagnetic ellipses

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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)

Page 17: Soliton pair dynamics in patterned ferromagnetic ellipses

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Competing Energies

Exchange

Magnetostatic

Zeeman

Nanomagnetism

Competition between different energies at the

nanoscale will determine the fundamental properties of

nanomagnetsMagnetocrystalline

Page 18: Soliton pair dynamics in patterned ferromagnetic ellipses

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Fabrication• Top Down: Lithography

1 m

Spin Coat Expose

Metallization Lift-off

http://chem.ch.huji.ac.il/~porath/NST2/Lecture%204/Lecture%204%20-%20e-Beam%20Lithography%202003.pdf

Develop

Page 19: Soliton pair dynamics in patterned ferromagnetic ellipses

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Phase Diagram for Nanodots

Magnetic phase diagram for magnetically-soft nanodots

LL

2R2R

Magnetic state depends on: Magnetic state depends on: • Geometry: L and RGeometry: L and R• Material: A and MMaterial: A and Mss

Guslienko and Novosad, J. Appl. Phys. 96, 4451, 2004.

00

10

20

30

40

50

60

Do

t th

ickn

ess

L, (

nm

)

10 20 30 40 50 60

Dot Diameter 2R, (nm)

(Permalloy)

Page 20: Soliton pair dynamics in patterned ferromagnetic ellipses

20

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Magnetic Vortex State

Vortex in a nanomagnet - nonlocalized solitonFlux closure state with central core

Polarization p = ± 1

Chirality c = ± 1

Vorticity q = 1

Outline• Vortex state – unique dynamic

excitations

• Vortex pair dynamics in elliptical dots

Page 21: Soliton pair dynamics in patterned ferromagnetic ellipses

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X1, p1

X2, p2

Vortex Pair Dynamics: Theory

Dot energy for shifted vortices at positions Xj

0

,

1

2111

X

XXXG

W

dt

d 0

,

2

2122

X

XXXG

W

dt

d

21int21121 ,, XXXXXX WWWW

21212

22

122

2121 2

1

2

1, YYXXYYXXW yxyx XX

Equations of motion of the vortex cores

Gyrovectors: zG ˆjj Gp

Assume energy form: