Domain wall dynamics in nanostrips with disorder

DW dynamics in nanostrips: motivationsDW dynamics in a disordered nanostrip

Domain wall dynamics in disordered magneticnanostrips

B. Van de Wiele1, L. Laurson2, G. Durin3,4

1Dep. of Electrical Energy, Systems and Automation, Ghent Univ., Belgium2Dep. of Appl. Physics, Aalto Univ., Finland

3ISI Foundation, Torino, Italy4INRIM, Torino, Italy

talk@Jems - Parma - Sept. 12, 2012

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Outline

1 DW dynamics in nanostrips: motivationsDW for spintronics devicesRole of disorder in DW dynamics

2 DW dynamics in a disordered nanostripLandau-Lifshitz (LL) equation on permalloy stripsDynamics under applied magnetic fieldsDynamics under spin-polarized currents

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DW for spintronics devicesRole of disorder in DW dynamics

Tame the stochastic nature of DW dynamics

Racetrack memory (2008) Magnetologic memory (2005)

DW oscillator (2008)

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Disorder as rough wire edges

Turbolent DW motion:no Walker breakdown

Main conclusion...Roughness should rather be engeneered than avoided

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Disorder as fluctuation of magnetization

Main conclusion...Effective damping increasing with disorder content.

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Disorder enhances stochasticity of DW motion

Main conclusion...Dynamic DW pinning enhances stochasticity

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Landau-Lifshitz (LL) equation on permalloy stripsDynamics under applied magnetic fieldsDynamics under spin-polarized currents

The LL equation with random non-magnetic voids

The LL equation with the spin-transfer torque terms,

∂M∂t

= − γ

1 + α2 M×Heff (1)

− αγ

Ms(1 + α2)M× (M×Heff )

−bj

M2s (1 + α2)

M× (M× (j · ∇)M)

−bj

Ms(1 + α2)(ξ − α)M× (j · ∇)M,

where Heff is the effective magnetic field, γ is the gyromagneticratio, α is the Gilbert damping constant, ξ is the degree ofnon-adiabaticity, j is the current density, andbj = PµB/(eMs(1 + ξ2)), with P the polarization, µB the Bohrmagneton and e the electron charge.

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GPU-accelerated micromagnetic simulations

Mumax• Finite-difference discretization• Landau-Lifshitz formalism• Spin-transfer torque (Zhang-Li and Slonczewski)• Finite temperature• Space- and time-dependent input parameters• GPU speedup up to 100x compared to CPU• Optional periodic boundary conditions• Flexible Python input files• Cross-platform and Open Source

Visit url: http://code.google.com/p/mumax2/

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Simulation of DW dynamics in Permalloy nanostrips

Simulation parametersMaterial• thickness = 10 nm, width = 100 nm• lenght = 3.2 µm (field), lenght = 6.4 µm (currents)

Disorder as a distribution of voids• Size: 3.125 x 3.125 x 10 nm3 (1 cell columns)• Densities: 3125, 6250, 9375, 12500 voids/µm2

V-shapedtransverse DW

anti-vortex DW(core up)

anti-vortex DWs(core down) 9 / 14



Perfect vs disordered wires under magnetic fields

H

PERFECT DISORDERED

What’s new: Walker breakdown shifted,10 / 14



Perfect vs disordered wires under magnetic fields

H

PERFECT DISORDERED

What’s new: Walker breakdown shifted, DW core pinning10 / 14



DW velocity vs magnetic field

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Applied current, adiabatic ST, the results

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Applied current, non-adiabatic ST, the results

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Maps of contributions

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Domain wall dynamics in nanostrips with disorder

Technology

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