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## Homework Statement

Hi there, thanks in advance for any help!

I have a first order DE: [tex] \frac{\partial \vec{m}}{\partial t} = -\vec{m} \times \vec{h}_{eff} + \alpha \vec{m} \times \frac{\partial \vec{m}}{\partial t}[/tex] (a scaled Landau-Lifshitz-Gilbert equation)

where m is a magnetism vector, alpha is a damping factor and h is an effective uniform magnetic field.

I'm trying to numerically integrate it with the Euler method to get a precession of the spin vector around the h vector.

So far I've integrated the first term but the second, damping term I can't see how to translate into code.. (in C++)

So essentially what I've done is assumed the magnetic field to be aligned in the z-direction, and written

Code:

```
for(i=1 ; i<=tmax ; i++) {
mx = mx + h * -my;
my = my + h * mx;
t = t + h;
```

Considering the x-component first, presumably the derivative in the damping term has to be put down as m_x as well, but what direction is the other m vector to be taken in?

Sorry if that's not very well asked, but thanks a lot for any help!

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