Spin-wave emission with current-controlled frequency by a PMA-based spin-Hall oscillator

TL;DR

This work addresses the need for tunable, long-range spin-wave sources suitable for magnonic neuromorphic networks by leveraging a low-damping Ga:YIG with dominant PMA to realize an in-plane spin-Hall oscillator. The authors combine current-controlled spin-orbit torques with a positive nonlinear frequency shift to enable resonant spin-wave emission, confirmed by Brillouin light scattering and micromagnetic simulations. They demonstrate a broad auto-oscillation bandwidth (~1.6 GHz) and long-range spin-wave emission (>10 μm), arising from a two-mode system linked to edge regions of reduced PMA and transitioning to single-mode operation at higher currents. The results establish Ga:YIG as a promising platform for interconnected SHOs in magnonic circuits, with design rules for controlling mode structure via microstructure and strain effects.

Abstract

Spin-torque and spin-Hall oscillators (SHOs) have emerged as promising candidates for building blocks in neuromorphic computing due to their ability to synchronize mutually, a process that can be mediated by propagating spin waves. We demonstrate a SHO that takes advantage of a low-damping magnetic garnet with dominant perpendicular magnetic anisotropy (PMA), namely gallium-substituted yttrium-iron-garnet (Ga:YIG). In-plane magnetized Ga:YIG allows for the operation at a high efficiency level while also enabling resonant spin-wave emission. A nonlinear self-localization of the excitation is avoided by exploiting the positive nonlinear frequency shift, which facilitates a current-controlled frequency of the emitted spin waves. Via micro-focused Brillouin light scattering spectroscopy, we investigate the properties of the local auto-oscillation and its spin-wave emission. Multiple modes are excited and compete internally, with two propagating modes detected up to distances larger than \SI{10}{\micro\meter}. Their frequencies combine to an extended frequency bandwidth of approximately \SI{1.6}{\giga\hertz}. The experimentally observed two-mode system and its transition to a single mode at higher currents are reproduced via micromagnetic simulations, which account for spatial variation of the PMA arising due to the microstructures on Ga:YIG. Our results propose a promising platform for hosting SHOs, interconnected via propagating spin waves with particular relevance to neuromorphic computing.

Figures (5)

• Figure 1: Experimental setup and Ga:YIG characteristics (a) Colorized SEM micrograph of the microstructure and a schematic of the applied BLS microscope. (b) Schematic illustration of the device layout with a frequency landscape for both nonlinear shift directions below. (c) Angle of the static magnetization $\theta_\mathrm{M}$ as a function of the external field $\upmu_0H_\mathrm{ext}$. (d) Nonlinear self-shift coefficient $N$ of the FMR mode as a function of $\upmu_0H_\mathrm{ext}$. (e) Calculated dispersion relation $f(k)$ for a Ga:YIG film in the linear case at $\upmu_0H_\mathrm{ext} =$ 87mT, with two exemplarily included nonlinear auto-oscillation frequencies $\tilde{\omega_0}$. The calculations from (c)-(e) are presented in the Supplementary material, Sec. 1 and the material parameters are taken from Sec. 2.
• Figure 2: Thermal mode spectrum (a) Thermal BLS spectrum as a function of $\upmu_\mathrm{0}H_\mathrm{ext}$, measured on the bare Ga:YIG waveguide and on Ga:YIG/Pt. The gray dashed line represents the field value $\upmu_\mathrm{0}H_\mathrm{app} = 77.5mT$. (b) Thermal BLS spectrum on Ga:YIG and Ga:YIG/Pt at $\upmu_\mathrm{0}H_\mathrm{app}$ as a function of the measurement position $y$. The BLS spectrum of each position is normalized to the respective maximum.
• Figure 3: Auto-oscillation (a) BLS spectrum, obtained through averaging across the Pt pad region, as a function of the current $I_\mathrm{DC}$. The data is normalized to the thermal intensity maximum at $I_\mathrm{DC}=0mA$. The spectral intensity maxima for each current value were fitted by a Gaussian, with the extracted frequency and intensity depicted as a function of $I_\mathrm{DC}$ in (b) and (c), respectively.
• Figure 4: Spin-wave emission (a) BLS spectra obtained at $x = -2.89µm$ for several currents $I_\mathrm{DC}$, normalized to the maximum value without a current applied. (b) Extracted frequencies of the edge and fundamental mode as a function of $I_\mathrm{DC}$ for two measurement positions (indicated in the pictogram). (c) BLS spectrum of the edge mode as a function of $I_\mathrm{DC}$ that is obtained in a distance of 11.5µm to the Pt pad.
• Figure 5: Micromagnetic studyvansteenkiste.mumax.2014Aithericon(a) Schematic illustration of the simulation setup. Towards the waveguide ends (darker blue region), the damping is smoothly increased to avoid reflections and mimic an infinite system. More detailed simulation parameters are given in the Supplementary material, Sec. 5A. (b) Normalized Fourier spectra $\mathcal{F}(m_y(t))$ as a function of the current density $j$, obtained within the injection area and in a distance of 1.5µm for three edge widths $w_\mathrm{edge}$. All of them are normalized to the maximum value observed within the entire simulation series. The gray dashed line represent the current density values used for (c). (c)$\mathcal{F}(m_y(t))$ as a function of the position $y$ on the injector for two current densities.