# Presentation: 096020

## Soliton pair dynamics in patterned ferromagnetic ellipses

**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

## Magnetic Vortex State

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

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

- Polarization p = ± 1
- Chirality c = ± 1
- Vorticity (topological charge)

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

## 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)

## Vortex Dynamics: Translational Mode

**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***

- Energy

**Simulations of the vortex translational mode**

## 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)

## 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

- 2*b* = 1 m

- 2*a* = 2 m

- Thickness *L*= 40 nm

-  is Frequency

- a/b ~ 2

## Experimental Mode Map: Vortex Pair

- 3 x 1.5 m2 ellipse, *L* = 40 nm

**H // h****rf**

**H // h****rf**
**H ******** h****rf**

**H ******** h****rf**

## Vortex Pair Modes

**Same frequency**

**“****Splitting”!**

_**Notation:**_
**	****i = in-phase**
**	****o = out-of-phase**

- <Mx> = 0
- <My> = 0

- <Mx>  cos(*t*+)
- <My>  sin(*t*+)

- <Mx> = 0
- <My>  sin(*t*+)

- <Mx>  cos(*t*+)
- <My> = 0

- equilibrium

## Micromagnetic Simulations – Single Vortex

_**Py dot**_
- L= 40 nm
- 2a = 1 m, 2b = 2 m
- Ms = 700 emu/cm3
- A = 1.3 erg/cm
- no anisotropy
- Damping  = 0.008
- Gyromagnetic ratio:
-   = 2.94 MHz/Oe
- LLG, Scheinfein
- OOMMF, NIST

**134 MHz**

**Single translational mode frequency**

## Dynamics of Interacting Solitons

- red/blue represent My

**(o,o)**

**(o,i)**

**h****r.f.**

## Micromagnetic Simulations: Mode Map

- 1.5 x 0.75 m2 ellipse, *L* = 40 nm

## Vortex Dynamics: Theory

*Shifted vortex*
*core*

- Energy

## Vortex Pair Dynamics: Theory

**Vortex Pair Dynamics: Theory**

**Equations of motion of the vortex cores:**

## Vortex Core Motion: Eigenvectors

## 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

***Exchange***** **

***Magnetostatic***

***Zeeman***

_**Nanomagnetism**_** **
- Competition between different energies at the nanoscale will determine the fundamental properties of nanomagnets

***Magnetocrystalline***

## Fabrication

**Top Down: Lithography**

- 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

## 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 State

**Vortex in a nanomagnet  - ****nonlocalized soliton**
**Flux 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**

## Vortex Pair Dynamics: Theory

**Vortex Pair Dynamics: Theory**

**Dot energy for shifted vortices at positions X****j**

**Equations of motion of the vortex cores**

- Gyrovectors:

**Assume energy form:**