It looks like your material_automated.mat has a relatively small α, i.e.:
material[1]:damping-constant = 0.006
Have you tried increasing the α value to see if it dampens out the oscillations in the magnetization? Have you also tried turning off the temperature pulses or setting temperature to 0, or turning off the magnetic field pulses to see if one of them perhaps could be significantly contributing to the oscillations?
The applet at (1) is rudimentary compared to VAMPIRE, but maybe it can help illustrate how a small α near zero can be more oscillatory in magnetization than that for a higher constant:
Kind Regards,
Gavin
VAMPIRE user