Micromagnetic Simulations of Systems with Shape-Induced Anisotropy S. Hill Thompson Florida State University

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)

Background – A Typical Simulation Time(scaled units) Mz

Metastable Decay Free energy vs. Mz Saddle point Free energy barrier Metastable minimum +Mz Free energy vs. Mz

Lattice Dynamic equation, Landau-Lifshitz-Gilbert (LLG) on a computational lattice

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 = z e d a n +

Rescaling M = M/Ms H = H/Ms r = r/le t = γoMst

Dipole interactions Handled by the Fast Multipole Method O(n2) O(n)

Realistic Models – Computational Details 6x6x90 computational lattice -> 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

Cumulative Distribution Function of the Lifetime t – All Runs

Phase Plot of the Total Magnetization Faster Mode Slower Mode

Phase Plot of the Total Energy Faster Mode Slower Mode

Two Distributions Fast Slow

Thermalization out of the T=0K Metastable State Quenched Slower mode

Thermalization T = 0K T = 20K

Quench/Relax vs Slow Mode Q/R Slow

Projective Dynamics Number of visits, N Growth Probability = G/N Same, N – (G + S) Shrinkage, S Growth, G Mz Growth Probability = G/N Shrinkage Probability = S/N

Projective Dynamics Slower mode Faster mode

Location of Extrema

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)