  We study the auto-oscillating magnetodynamics in orthogonal spin torque
nano-oscillators (STNOs) as a function of the out-of-plane (OOP) magnetic field
angle. In perpendicular fields and at OOP field angles down to approximately 50
degrees we observe the nucleation of a droplet. However, for field angles below
50 degrees, experiments indicate that the droplet gives way to propagating spin
waves, in agreement with our micromagnetic simulations. Theoretical
calculations show that the physical mechanism behind these observations is the
sign changing of spin-wave nonlinearity (SWN) by angle. In addition, we show
that the presence of a strong perpendicular magnetic anisotropy (PMA) free
layer in the system reverses the angular dependence of the SWN and dynamics in
STNOs with respect to the known behavior determined for the in-plane magnetic
anisotropy free layer. Our results are of fundamental interest in understanding
the rich dynamics of nanoscale solitons and spin-wave dynamics in STNOs.
