Presentation given at JEMS 2012 in Parma on domain wall dynamics in nanowires with disorder

1. DW dynamics in nanostrips: motivations
DW dynamics in a disordered nanostrip
Domain wall dynamics in disordered magnetic
nanostrips
B. Van de Wiele1 , L. Laurson2 , G. Durin3,4
1 Dep. of Electrical Energy, Systems and Automation, Ghent Univ., Belgium
2 Dep. of Appl. Physics, Aalto Univ., Finland
3 ISI Foundation, Torino, Italy
4 INRIM, Torino, Italy
talk@Jems - Parma - Sept. 12, 2012
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2. DW dynamics in nanostrips: motivations
DW dynamics in a disordered nanostrip
Outline
1 DW dynamics in nanostrips: motivations
DW for spintronics devices
Role of disorder in DW dynamics
2 DW dynamics in a disordered nanostrip
Landau-Lifshitz (LL) equation on permalloy strips
Dynamics under applied magnetic fields
Dynamics under spin-polarized currents
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3. DW dynamics in nanostrips: motivations DW for spintronics devices
DW dynamics in a disordered nanostrip Role 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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4. DW dynamics in nanostrips: motivations DW for spintronics devices
DW dynamics in a disordered nanostrip Role of disorder in DW dynamics
Disorder as rough wire edges
Turbolent DW motion:
no Walker breakdown
Main conclusion...
Roughness should rather be engeneered than avoided
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5. DW dynamics in nanostrips: motivations DW for spintronics devices
DW dynamics in a disordered nanostrip Role of disorder in DW dynamics
Disorder as fluctuation of magnetization
Main conclusion...
Effective damping increasing with disorder content.
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6. DW dynamics in nanostrips: motivations DW for spintronics devices
DW dynamics in a disordered nanostrip Role of disorder in DW dynamics
Disorder enhances stochasticity of DW motion
Main conclusion...
Dynamic DW pinning enhances stochasticity
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7. Landau-Lifshitz (LL) equation on permalloy strips
DW dynamics in nanostrips: motivations
Dynamics under applied magnetic fields
DW dynamics in a disordered nanostrip
Dynamics under spin-polarized currents
The LL equation with random non-magnetic voids
The LL equation with the spin-transfer torque terms,
∂M γ
= − M × Heff (1)
∂t 1 + α2
αγ
− M × (M × Heff )
Ms (1 + α2 )
bj
− 2 M × (M × (j · )M)
Ms (1 + α2 )
bj
− (ξ − α)M × (j · )M,
Ms (1 + α2 )
where Heff is the effective magnetic field, γ is the gyromagnetic
ratio, α is the Gilbert damping constant, ξ is the degree of
non-adiabaticity, j is the current density, and
bj = PµB /(eMs (1 + ξ 2 )), with P the polarization, µB the Bohr
magneton and e the electron charge.
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8. Landau-Lifshitz (LL) equation on permalloy strips
DW dynamics in nanostrips: motivations
Dynamics under applied magnetic fields
DW dynamics in a disordered nanostrip
Dynamics under spin-polarized currents
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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9. Landau-Lifshitz (LL) equation on permalloy strips
DW dynamics in nanostrips: motivations
Dynamics under applied magnetic fields
DW dynamics in a disordered nanostrip
Dynamics under spin-polarized currents
Simulation of DW dynamics in Permalloy nanostrips
Simulation parameters
Material
• 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-shaped anti-vortex DW anti-vortex DWs
transverse DW (core up) (core down) 9 / 14

10. Landau-Lifshitz (LL) equation on permalloy strips
DW dynamics in nanostrips: motivations
Dynamics under applied magnetic fields
DW dynamics in a disordered nanostrip
Dynamics under spin-polarized currents
Simulation of DW dynamics in Permalloy nanostrips
Simulation parameters
Material
• 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-shaped anti-vortex DW anti-vortex DWs
transverse DW (core up) (core down) 9 / 14

11. Landau-Lifshitz (LL) equation on permalloy strips
DW dynamics in nanostrips: motivations
Dynamics under applied magnetic fields
DW dynamics in a disordered nanostrip
Dynamics under spin-polarized currents
Perfect vs disordered wires under magnetic fields
PERFECT DISORDERED
H
What’s new: Walker breakdown shifted,
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12. Landau-Lifshitz (LL) equation on permalloy strips
DW dynamics in nanostrips: motivations
Dynamics under applied magnetic fields
DW dynamics in a disordered nanostrip
Dynamics under spin-polarized currents
Perfect vs disordered wires under magnetic fields
PERFECT DISORDERED
H
What’s new: Walker breakdown shifted,
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13. Landau-Lifshitz (LL) equation on permalloy strips
DW dynamics in nanostrips: motivations
Dynamics under applied magnetic fields
DW dynamics in a disordered nanostrip
Dynamics under spin-polarized currents
Perfect vs disordered wires under magnetic fields
PERFECT DISORDERED
H
What’s new: Walker breakdown shifted, DW core pinning
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14. Landau-Lifshitz (LL) equation on permalloy strips
DW dynamics in nanostrips: motivations
Dynamics under applied magnetic fields
DW dynamics in a disordered nanostrip
Dynamics under spin-polarized currents
DW velocity vs magnetic field
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15. Landau-Lifshitz (LL) equation on permalloy strips
DW dynamics in nanostrips: motivations
Dynamics under applied magnetic fields
DW dynamics in a disordered nanostrip
Dynamics under spin-polarized currents
DW velocity vs magnetic field
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16. Landau-Lifshitz (LL) equation on permalloy strips
DW dynamics in nanostrips: motivations
Dynamics under applied magnetic fields
DW dynamics in a disordered nanostrip
Dynamics under spin-polarized currents
Applied current, adiabatic ST, the results
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17. Landau-Lifshitz (LL) equation on permalloy strips
DW dynamics in nanostrips: motivations
Dynamics under applied magnetic fields
DW dynamics in a disordered nanostrip
Dynamics under spin-polarized currents
Applied current, non-adiabatic ST, the results
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18. Landau-Lifshitz (LL) equation on permalloy strips
DW dynamics in nanostrips: motivations
Dynamics under applied magnetic fields
DW dynamics in a disordered nanostrip
Dynamics under spin-polarized currents
Maps of contributions
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