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

2. 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)

3. Background – A Typical Simulation
Time(scaled units) Mz

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

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

7. 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 +

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

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

10. Realistic Models – Computational Details
6x6x90 computational lattice -> 3240 sites
10 nm x 10 nm x 150 nm Fe nanopillar
dt = 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

11. Cumulative Distribution Function of the Lifetime t – All Runs

12. Phase Plot of the Total Magnetization
Faster Mode
Slower Mode

13. Phase Plot of the Total Energy
Faster Mode
Slower Mode

14. Two Distributions
Fast
Slow

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

16. Thermalization
T = 0K
T = 20K

17. Quench/Relax vs Slow Mode
Q/R
Slow

18. 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

19. Projective Dynamics
Slower mode
Faster mode

20. Location of Extrema

21. 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)