Phase-binarized auto-oscillation modes in wide nanoconstriction spin Hall nano-oscillators

Nanoconstriction spin Hall nano-oscillators (SHNOs) are cutting-edge spintronic devices for gigahertz signal generation and neuromorphic computing, offering a CMOS-compatible nanoscale footprint, ultra-wide frequency tunability, and robust synchronization in large networks. Most previous studies have focused on constrictions narrower than 200 nm, where a single dominant spin-wave mode typically emerges. The auto-oscillation dynamics of wide constrictions remain largely unexplored. Here, using micromagnetic simulations, we demonstrate the coexistence of two independently tunable auto-oscillation modes in constrictions wider than 200 nm: a low-frequency in-phase mode and a high-frequency out-of-phase mode, both localized at opposite constriction edges. The out-of-phase mode arises from the interplay of exchange, magnetodipolar coupling, and the antisymmetric Oersted field component, producing strongly edge-localized oscillations with a nearly 180 ∘ phase difference. We develop an analytical two-mode framework that captures their hybridization and nonlinear competition. Their distinct subharmonic injection-locking responses enable phase-binarized states within a single wide SHNO, opening opportunities for multimode synchronization, unconventional computing, and complex phase locking in SHNO networks.