# Magnetization dynamics

The applet below calculates the time evolution of the magnetization of a single domain particle using the Landau-Lifshitz Gilbert equation including damping. The direction of the external magnetic field, the damping constant and the anisotropy of the particle can be changed while the simulation is running.

Magnetization reversal applet
Stoner-Wohlfarth astroid applet
Spin-torque applet.
Tim Mewes - Mainpage

## Simulation of the magnetization dynamics

The simulation solves the Landau-Lifshitz Gilbert equation:

by using a Runge-Kutta-Fehlberg 5(4) algorithm. Where is the unit magnetization vector, is the effective field which includes the external magnetic field and a uniaxial or four-fold anisotropy field, is the gyromagnetic ratio.
Try to change the external field by dragging the tip of the green vector, also try changing the damping constant and changing the anisotropy (including the sign).

Here are some more things to try:

• Set the external magnetic field to zero and the uniaxial anisotropy (K/Ms) to a negative value, take a look at the free energy surface - what does this tell you about the easy axis of the uniaxial anisotropy used in the simulation?
• Now set the anisotropy to a positive value - along which direction does the magnetization settle? Now turn on the external magnetic field for a short period of time and then turn it off again (or simply drag the magnetization to a new starting orientation). Try this a few times, take another look at the free energy surface.
• Without an anisotropy but with an external field present (H=(0 0 1)) let the magnetization settle for a while. Now reverse the external magnetic field (H=(0 0 -1)). After the magnetization settled again set the external magnetic field to H=(0 1 0) and let the magnetization go through roughly half a precession cycle pause the simulation and now set the external magnetic field to H=(0 0 1). Which approach can switch the magnetization faster?

Tips:

• The simulation runs faster when the unit sphere is not shown (it is transparent which tends to slow down things)
• When changing quantities by orders of magnitude make sure to change the time step accordingly
• You can drag both the field vector and the magnetization vector at their tips - the mouse pointer turns into a hand symbol
• The (normalized) energy surface is shown in red. To better understand this it is helpful to turn off the external magnetic first and change the sign of the anisotropy.

## Acknowledgements

This material is based upon work supported by the National Science Foundation under Grant No. 0804243. Any opinions, findings and conclusions or recomendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation (NSF).
Created with Easy Java Simulations

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