  Spin Hall nano-oscillators (SHNOs) are promising candidates for new microwave
oscillators with high durability due to a small driving current. However,
conventional SHNOs with an in-plane precession (IPP) mode require a bias field
for stable oscillations which is not favored in certain applications such as
neuromorphic computing. Here, we propose and theoretically analyze a
bias-field-free SHNO with an in-plane hard axis and an out-of-plane precession
(OPP) mode by solving the Landau-Lifshitz-Gilbert (LLG) equation analytically
and numerically. We derive formulas for driving currents and precession
frequency, and show that they are in good agreement with numerical simulation
results. We show that our proposed SHNOs can be driven by much smaller bias
current than conventional spin torque nano-oscillators.
