  The nonlinear frequency shift coefficient, which represents the strength of
the transformation of amplitude fluctuations into phase fluctuations of an
oscillator, is measured for MgO-based spin-torque oscillators by analyzing the
current dependence of the power spectrum. We have observed that linewidth
against inverse normalized power plots show linear behavior below and above the
oscillation threshold as predicted by the analytical theories for spin-torque
oscillators. The magnitude of the coefficient is determined from the ratio of
the linear slopes. Small magnitude of the coefficient has been obtained for the
device exhibiting narrow linewidth at high bias current.
