Bias dependence of perpendicular spin torque and of free and fixed layer   eigenmodes in MgO-based nanopillars
  We have measured the bias voltage and field dependence of eigenmode frequencies in a magnetic tunnel junction with MgO barrier. We show that both free layer (FL) and reference layer (RL) modes are excited, and that a cross-over between these modes is observed by varying external field and bias voltage. The bias voltage dependence of the FL and RL modes are shown to be dramatically different. The bias dependence of the FL modes is linear in bias voltage, whereas that of the RL mode is strongly quadratic. Using modeling and micromagnetic simulations, we show that the linear bias dependence of FL frequencies is primarily due to a linear dependence of the perpendicular spin torque on bias voltage, whereas the quadratic dependence of the RL on bias voltage is dominated by the reduction of exchange bias due to Joule heating, and is not attributable to a quadratic dependence of the perpendicular spin torque on bias voltage. 
P. K. Muduli, O. G. Heinonen and Johan {\AA}kerman
cond-mat.mtrl-sci