  We study the theoretical conditions to excite a stable self-oscillation in a
spin torque oscillator with an in-plane magnetized free layer and a
perpendicularly magnetized pinned layer in the presence of magnetic field
pointing in an arbitrary direction. The linearized Landau-Lifshitz-Gilbert
(LLG) equation is found to be inapplicable to evaluate the threshold between
the stable and self-oscillation states because the critical current density
estimated from the linearized equation is considerably larger than that found
in the numerical simulation. We derive a theoretical formula of the threshold
current density by focusing on the energy gain of the magnetization from the
spin torque during a time shorter than a precession period. A good agreement
between the derived formula and the numerical simulation is obtained. The
condition to stabilize the out-of-plane self-oscillation above the threshold is
also discussed.
