Micromagnetic simulations of linewidths and nonlinear frequency shift coefficient in spin torque nano-oscillators

The dependence of the linewidth on the temperature and the applied magnetic field angle is studied in spin torque nano-oscillators (STNOs) by means of full micromagnetic simulations. The analyzed spin valve is the experimental one by Sankey [Phys. Rev. Lett. 96, 227601 (2006)] and the magnetic parameters are given by magnetoresistance fitting. Linewidth behavior increases with the temperature, in agreement with the analytical predictions by Tiberkevich [Phys. Rev. B 78, 092401 (2008)], and its slope depends on the applied field angle. Also, the nonlinear frequency shift coefficient, which gives a measure of the nonlinearity degree of STNO and indicates the strength of the transformation of amplitude into phase fluctuations, is found. The understanding of the nonlinear frequency shift allows one to tune the generation frequency of the STNO, but, at the same time, creates an additional source of the phase noise, which leads to a significant broadening of the linewidth generation. Narrow linewidths (around 10 MHz at 0 K and 100 MHz at 300 K) are found in our shape-anisotropy nanopillars by applying close to in-plane magnetic field at an angle of 45° between in-plane easy and hard axes.