# Magnetization dynamics including spin-torque

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

Magnetization reversal applet
Stoner-Wohlfarth astroid applet
Basic magnetization dynamics 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 total magnetic field consisting of the effective field and the spin-torque field which can not be written as the variational derivative of a free-energy functional. The free energy of entering the effective field includes the external magnetic field, a uniaxial anisotropy. In addition a random field with Gaussian distributions for each component is included. is the gyromagnetic ratio. The scalar function g is given by , with P the polarizing factor for the spin polarized current.

Here are some hints:

• The simulation starts with settings that lead to a spin-torque driven oscillation, where the torque due to damping and the spin-torque cancel each other - in order to find these solutions it can be helpful to plot the sum of those two torques (shown in orange).
• The other surface that can be interest is the total torque surface (shown in green) - zeros in this surface indicate magnetization orientations with zero net torque, which can be stable solutions.
• Try to change the spin-torque field pre-factor ASL to the following values: -10, 0, 10, -100 [Oe] and take a look at the total torque and sum of damping torque and spin-torque surfaces in each case.
• Now change the orientation of the polarizer with respect to the external magnetic field and try similar cases.
• You can also take a look at the energy as a function of time - try turning of the spin torque completely, then turn of the damping as well.
• The effective field torque contains all torque contributions caused by the effective field, i.e. it does not including the damping and the spin-torque.

Other tips:

• Make sure to hit "ENTER" after changing values - only after you hit enter will the changes affect the simulation, to indicate this the value is highlighted in yellow until you do so.
• The (normalized) magnitude of the strength of the total torque is shown as a green surface, however keep in mind that torque is a vector quantity.
• The (normalized) magnitude of the strength of the damping torque plus the spin-torque is shown as an orange surface, however as before keep in mind that torque is a vector quantity.
• 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

## References

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