Download Magnetization Dynamics

MAGNETIZATION DYNAMICS
Roger Ellicock
This is a simple model of an object becoming magnetized as it cools in the presence
of an external field. In the movie, the field is constant in the z direction (up).
The object is represented as a cubic array of magnetic moments that feel a torque
from the external field. The magnetization is the vector sum of the moments. They evolve
according to the Landau-Lifshitz (LL) equation:
d
m
dt
= −γm × Heff + λm × (m × Heff)
where γ is the gyromagnetic ratio and λ is a damping factor. Heff
is an effective field that combines the external field with other
magnetic and quantum mechanical effects, although in this model
it is taken to be a constant for simplicity.
The first term causes the moment to precess around the
direction of the external field. The second term dampens the motion
and causes the moment vector to align with the field.
A moment vector moving
according to the LL equation.
http://wpage.unina.it/mdaquino/PhD_thesis/main/node28.html
The aligning effect is countered by random thermal fluctuations of the direction of
the moment vector. This is introduced into the equation by including in the field a randomly
oriented vector with magnitude proportional to temperature .
The object cools as the heat leaves the object according to the heat equation. In the
movie, the temperature is represented by the color of the moment vectors.
RUN WITH MAGNETIZATION_DYNAMICS.M, WITH FUNCTION LL.M