Temperature dependence of linewidth in nano-contact based spin torque oscillators: effect of multiple oscillatory modes

We discuss the effect of mode transitions on the current (I) and temperature (T) dependent linewidth (\Delta f) in nanocontact based spin torque oscillators (STOs). At constant I, \Delta f exhibits an anomalous temperature dependence near the mode transitions; \Delta f may either increase or decrease with T depending on the position w.r.t. the mode transition. We show that the behavior of \Delta f as a function of I can be fitted by the single mode analytical theory of STOs, even though there are two modes present near the mode transition, if the nonlinear amplification is determined directly from the experiment. Using a recently developed theory of two coupled modes, we show that the linewidth near mode transition can be described by an "effective" single-oscillator theory with an enhanced nonlinear amplification that carries additional temperature dependence, which thus qualitatively explain the experimental results.