Modulation and phase-locking in nanocontact vortex oscillators

Abstract

We have conducted experiments to probe how the dynamics of nanocontact vortex oscillators can be modulated by an external signal. We explore the phase-locking properties in both the commensurate and chaotic regimes, where chaos appears to impede phase-locking while a more standard behavior is seen in the commensurate phase. These different regimes correspond to how the periodicity of the vortex core reversal relates to the frequency of core gyration around the nanocontact; a commensurate phase appears when the reversal rate is an integer fraction of the gyration frequency, while a chaotic state appears when this ratio is irrational. External modulation where the power spectral density exhibits rich features, appears due to the modulation between the external source frequency, gyration frequency, and core reversal frequency. We explain these features with firstor second-order modulation between the three frequencies. Phase-locking is also visible between the external source frequency and internal vortex modes (gyration and core reversal modes). arXiv:1906.08492v1 [cond-mat.mes-hall]

Nanocontact vortex oscillators based on Co$_2$MnGe pseudo-spin valves

“…This is achieved by applying a large DC current, here 9 or 10 mA which is toward the upper limit before sample degradation, while sweeping an inplane magnetic field. Simulations have shown previously [23][24][25][26] that as the magnetization reverses, a domain wall sweeps through the free layer and as it crosses the nanocontact region, a vortex is nucleated through the competition between the current-induced Oersted field and spin-transfer torques. Some simulations show nucleation of two vortices in Heusler compound samples.…”

“…As in previous studies of nanocontact vortex oscillators [23][24][25][26], it is necessary to nucleate a vortex (nominally in the free magnetic layer) as this state is not necessarily the ground state of the magnetization. This is achieved by applying a large DC current, here 9 or 10 mA which is toward the upper limit before sample degradation, while sweeping an inplane magnetic field.…”

“…In Fig. 5, we present color maps of the current-dependence of these power spectra, exhibiting a richer behavior than permalloy standard nanocontact oscillators [25]. The color map represents a density plot in which the power spectra are shown as a function of applied current by assigning a color value to the amplitude of the peaks shown in in Fig.…”

“…A unique feature of nanocontact vortex oscillators is the onset of periodic core reversal above a critical current [23][24][25][26]. This reversal occurs concurrently with the steady-state gyration around the nanocontact, giving rise to self-phase-locked and chaotic states.…”

Application of Reservoir Computing for the Modeling of Nano-Contact Vortex Oscillator

“…The current distribution and the Oersted field it generates were previously calculated with COMSOL [43], before being injected as a parameter in Mumax3. A precise description of the procedure used to realize these simulations can be found in the Supplementary Section in [15] and in [44]. The extracted M x (t) and M y (t) correspond to the time evolution of the average magnetization along the x and y directions, respectively.…”