  Experiments on spin torque oscillators commonly observe multi-mode signals.
Recent theoretical works have ascribed the multi-mode signal generation to
coupling between energy-separated spin wave modes. Here, we analyze in detail
the dynamics generated by such mode coupling. We show analytically that the
mode-hopping dynamics broaden the generation linewidth and makes it generally
well described by a Voigt lineshape. Furthermore, we show that the mode-hopping
contribution to the linewidth can dominate in which case it provides a direct
measure of the mode-hopping rate. Due to the thermal drive of mode-hopping
events, the mode-hopping rate also provides information on the energy barrier
separating modes and temperature-dependent linewidth broadening. Our results
are in good agreement with experiments, revealing the physical mechanism behind
the linewidth broadening in multi-mode spin torque oscillators.
