Micromagnetics of single and double point contact spin torque   oscillators
  In this paper we numerically conduct micromagnetic modelling to optimize computational boundaries of magnetic thin-film elements applicable to single and double point contact spin torque nano-oscillators. Different boundary conditions have been introduced to compensate spin waves reflections at boundaries that are based on extended layers, absorbing boundaries, and focal point methods and are compared with a technique based on scattering theory. A surface roughness boundary model is presented which is modelled according to the Rayleigh criterion to minimize specular reflections at computational boundaries. It is shown that the surface roughness model disperses the reflected spin waves and improves the signal to background noise ratio. The model is tested in comparison to conventional approaches such as extended layer systems, variable damping constant and focal point methods for double point contacts. The surface roughness model gives solutions that are stable in time, in qualitative agreement with experiments and capable to reproduce phenomena such as phase locking in double point contacts. 
Gino Hrkac, Julian Dean, Alexander Goncharov, Simon Bance, Dan   Allwood, Thomas Schrefl, Dieter Suess and Josef Fidler