Micromagnetic Simulations of Systems with Shape-Induced Anisotropy

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Micromagnetic Simulations of Systems with
Shape-Induced Anisotropy

• S. Hill Thompson

Florida State University
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Manufactured Single-Domain Iron Nanopillars

• Grown by STM-assisted CVD 1

200 nm
40 nm
1 S. Wirth, M. Field, D. D. Awschalom, and S. von
Molnar, Phys. Rev. B 57, R14028 (1998) J. Appl.
Phys. 85, 5249 (1999)
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Background A Typical Simulation
Mz
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Metastable Decay
F
Saddle point
Free energy barrier
Metastable minimum
Mz
Free energy vs. Mz
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(No Transcript)
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Lattice
Dynamic equation, Landau-Lifshitz-Gilbert (LLG)
on a computational lattice
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Landau-Lifshitz-Gilbert (LLG)

• uniform magnetization density
• go electron gyromagnetic ratio, 1.67x107 Hz/Oe
• a phenomenological damping parameter, 0.1
• total local field at

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Rescaling

• M M/Ms
• H H/Ms
• r r/le
• t ?oMst

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Dipole interactions
Handled by the Fast Multipole Method O(n2)
O(n)
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Realistic Models Computational Details

• 6x6x90 computational lattice -gt 3240 sites
• 10 nm x 10 nm x 150 nm Fe nanopillar
• dt 0.083 picoseconds usin first-order Euler
  integration
• Temperature 20 Kelvin
• Applied Field 3160 Oe at 75 degrees from the
  easy axis
• Fields dipole-dipole, thermal, exchange, Zeeman
• 3-4 days on IBM SP3 using 20 processors

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Cumulative Distribution Function of the Lifetime
t All Runs
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Phase Plot of the Total Magnetization
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Phase Plot of the Total Energy
Slower Mode
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Two Distributions
Fast
Slow
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Thermalization out of the T0K Metastable State
Quenched
Slower mode
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Thermalization
T 20K
T 0K
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Quench/Relax vs Slow Mode
Q/R
Slow
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Projective Dynamics
Number of visits, N
Same, N (G S)
Growth, G
Shrinkage, S
Mz
Growth Probability G/N Shrinkage Probability
S/N
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Projective Dynamics
Slower mode
Faster mode
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Location of Extrema
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Choosing the Correct Model
7x7x101 spins
1x1x17 spins
Stoner-Wohlfarth

• 1-D models are not sufficient, full 3-D models
  are necessary

Wirth, et al, J. Appl. Phys. 85, 5249 (1999). Li,
et al, J. Appl Phys, 93, 7912 (2003). Li, et al,
J. Appl. Phys. Lett 80, 4644 (2002)