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Register a new userNon-Hermitian topology of one-dimensional spin-torque oscillator arrays
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Magnetic systems have been extensively studied both from a fundamental physics perspective and as building blocks for a variety of applications. Their topological properties, in particular those of excitations, remain relatively unexplored due to their inherently dissipative nature. The recent introduction of non-Hermitian topological classifications opens up new opportunities for engineering topological phases in dissipative systems. Here, we propose a magnonic realization of a non-Hermitian topological system. A crucial ingredient of our proposal is the injection of spin current into the magnetic system, which alters and can even change the sign of terms describing dissipation. We show that the magnetic dynamics of an array of spin-torque oscillators can be mapped onto a non-Hermitian Su-Schrieffer-Heeger model exhibiting topologically protected edge states. Using exact diagonalization of the linearized dynamics and numerical solutions of the non-linear equations of motion, we find that a topological magnonic phase can be accessed by tuning the spin current injected into the array. In the topologically nontrivial regime, a single spin-torque oscillator on the edge of the array is driven into auto-oscillation and emits a microwave signal, while the bulk oscillators remain inactive. Our findings have practical utility for memory devices and spintronics neural networks relying on spin-torque oscillators as constituent units.
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Spin Hall nano-oscillators (SHNOs) utilize pure spin currents to drive local regions of magnetic films and nanostructures into auto-oscillating precession. If such regions are placed in close proximity to each other they can interact and sometimes mutually synchronize, in pairs or in short linear chains. Here we demonstrate robust mutual synchronization of two-dimensional SHNO arrays ranging from 2 x 2 to 8 x 8 nano-constrictions, observed both electrically and using micro-Brillouin Light Scattering microscopy. The signal quality factor, $Q=f/Delta f$, increases linearly with number of mutually synchronized nano-constrictions ($N$), reaching 170,000 in the largest arrays. While the microwave peak power first increases as $N^2$, it eventually levels off, indicating a non-zero relative phase shift between nano-constrictions. Our demonstration will enable the use of SHNO arrays in two-dimensional oscillator networks for high-quality microwave signal generation and neuromorphic computing.
We investigate the spectral characteristics of spin torque oscillator (STO) excited by the spin Hall-induced spin current. We observe that the modest spin current injection triggers the conventional single peak oscillating behavior of STO. As the spin current is further increased to enter the non-linear regime, we find the transition of the spectrum from a single peak to multipeak structure whose frequency spacing is constant. This behavior can be primarily explained by the extremely broadened peak of the STO, which is accompanied by the frequency-dependent filtering by the transmission line. To explain the observation more quantitatively, we also discuss that the multipeak may reflect the characteristics of the intrinsic dynamics of STO in the non-linear regime.
A theoretical analysis is developed on spin-torque diode effect in nonlinear region. An analytical solution of the diode voltage generated from spin-torque oscillator by the rectification of an alternating current is derived. The diode voltage is revealed to depend nonlinearly on the phase difference between the oscillator and the alternating current. The validity of the analytical prediction is confirmed by numerical simulation of the Landau-Lifshitz-Gilbert equation. The results indicate that the spin-torque diode effect is useful to evaluate the phase of a spin-torque oscillator in forced synchronization state.
We numerically study reservoir computing on a spin-torque oscillator (STO) array, describing the magnetization dynamics of the STO array by a nonlinear oscillator model. The STOs exhibit synchronized oscillation due to coupling by magnetic dipolar fields. We show that reservoir computing can be performed using the synchronized oscillation state. The performance can be improved by increasing the number of STOs. The performance becomes highest at the boundary between the synchronized and disordered states. Using an STO array, we can achieve higher performance than that of an echo-state network with similar number of units. This result indicates that STO arrays are promising for hardware implementation of reservoir computing.
Spin torque and spin Hall effect nanooscillators generate high intensity spin wave auto oscillations on the nanoscale enabling novel microwave applications in spintronics, magnonics, and neuromorphic computing. For their operation, these devices require externally generated spin currents either from an additional ferromagnetic layer or a material with a high spin Hall angle. Here we demonstrate highly coherent field and current tunable microwave signals from nanoconstrictions in single 15 and 20 nm thick permalloy layers. Using a combination of spin torque ferromagnetic resonance measurements, scanning microBrillouin light scattering microscopy, and micromagnetic simulations, we identify the autooscillations as emanating from a localized edge mode of the nanoconstriction driven by spin orbit torques. Our results pave the way for greatly simplified designs of auto oscillating nanomagnetic systems only requiring a single ferromagnetic layer.
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