Dynamical modes in a vertical nanocontact-based spin Hall nano-oscillator

Abstract

Spin-torque nano-oscillators (STNOs) with high nonlinear tunability can serve as nanoscale spin-wave emitters for high-speed magnon-based logic circuits and neural networks for promising new energy-efficiency computing. Although various STNOs have been modeled theoretically and characterized experimentally, there is a sustained effort to improve their coherence and nonlinear tunability. By using numerical simulation, here we explore the evolution rule of spectral characteristics and nonlinearities of the emitted coherent spin waves in a type of spin Hall nano-oscillator (SHNO) with a perpendicular magnetic anisotropy (PMA) coefficient ${K}_{u}$, which is based on a vertical nanocontact fabricated on an extended heavy metal/ferromagnet bilayer. There exist three distinct dynamic regimes with varying ${K}_{u}$. At the easy-plane anisotropy-dominated in-plane magnetized regime, the SHNO exhibits coexistence of the nonlinear self-localized spin-wave bullet mode with a significantly negative nonlinearity coefficient $\ensuremath{\aleph}$ and a secondary high-frequency quasilinear edge mode at higher current density. The latter excitation is supported by the energy transfer from the former via nonlinear coupling rather than the injected spin currents located in the center nanogap of the device. When the easy-plane shape anisotropy is effectively compensated by PMA, only a single quasipropagating spin-wave mode with a near-zero $\ensuremath{\aleph}$ is excited at lower current density, consistent with minimization of nonlinear damping due to the suppression of nonlinear mode coupling. For the out-of-plane magnetized SHNOs with ${K}_{u}$ above the demagnetization energy, a well-defined propagating spin-wave mode with a positive $\ensuremath{\aleph}$, characterized by a significant frequency blueshift and a rightward elongated spatial profile perpendicular to the in-plane component of the applied magnetic field, is observed. This detailed evolution diagram of auto-oscillating dynamics on the PMA coefficient ${K}_{u}$ provides a practical approach to selectively excite dynamical modes and optimize the spectral characteristics of the SHNO for applications in microwave technology and spin-wave logic.