Origin of Magnetization Auto-Oscillations in Constriction-Based Spin Hall Nano-Oscillators

Abstract

We use micromagnetic simulations to map out and compare, the linear and auto-oscillating modes in constriction-based spin Hall nano-oscillators as a function of applied magnetic field with varying magnitude and out-of-plane angle. We demonstrate that for all possible applied field configurations the auto-oscillations emerge from the localized linear modes of the constriction. For field directions tending towards the plane, these modes are of the so-called "edge" type, i.e. localized at the opposite sides of the constriction. When the magnetization direction instead approaches the film normal, the modes transform to the so-called "bulk" type, i.e. localized inside the constriction with substantially increased precession volume, consistent with the re-distribution of the magnetic charges from the sides to the top and bottom surfaces of the constriction. In general, the threshold current of the corresponding auto-oscillations increases with the applied field strength and decreases with its outof-plane angle, consistent with the behavior of the internal field and in good agreement with a macrospin model. A quantitative agreement is then achieved by taking into account the strongly non-uniform character of the system via a mean-field approximation. Both the Oe field and the spin transfer torque from the drive current increase the localization and decrease the frequency of the observed mode. Furthermore, the anti-symmetric Oe field breaks the lateral symmetry, favoring the localized mode at one of the two constriction edges, in particular for large out-of-plane field angles where the threshold current is significantly increased and the edge demagnetization is suppressed.

Two-dimensional mutually synchronized spin Hall nano-oscillator arrays for neuromorphic computing

“…At all larger dimensions, neither the 6x6 nor the 8x8 array showed complete mutual synchronization (see Supplementary material 2). Similarly, the 10x10 arrays did not show complete mutual synchronization at any dimension.As discussed in Ref (43),. the auto-oscillating regions can be expanded by increasing the out-of-plane angle of the applied field.…”

Spin-Hall Nano-Oscillator Simulations

“…A. COMSOL Distributions @ I = 1.2mA A 100nm NC width geometry was constructed to verify the COMSOL methodology against previous results [14] before the following current density and Oersted field distributions were calculated. Fig.…”

“…Lambda here determines the degree of angular dependency of the generated Spin Orbit Torque on the relative orientation between the magnetisation direction and spin polarisation direction [14]. Here we set this to 1 to remove any angular dependency from the simulation.…”

Spin-orbit torque–driven propagating spin waves

“…The rich non-linear magneto-dynamics in patterned magnetic thin films can be analytically described by a single non-linearity coefficient, N , the magnitude and sign of which determine the strength and nature of magnon-magnon interactions, with positive and negative values signifying magnon repulsion and attraction, respectively. 37,44,45 As spin transfer torque and SOT can generate very high SW amplitudes, the sign and magnitude of N leads to dinstinctly different behavior of the autooscillations. A negative non-linearity makes the auto-oscillation frequency decrease with amplitude, eventually moving it into the magnonic band gap, where it first leads to SW self-localization, and can further promote the nucleation of magnetodynamical solitons such as SW bullets [46][47][48] in easy-plane magnetic films and magnetic droplets 49,50 in films with very large PMA.…”