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a Responsivities of rectification devices vs frequency. Blue and orange rectangular regions refer to bolometers and magnetic tunnel junctions (MTJs), respectively. Red point represents our result. b, c Schematic of spin bolometer (b) without and (c) with applied microwaves. Red and black arrows represent the magnetizations of the ferromagnetic free and pinned layers, respectively.
a Perpendicular magnetic field dependence of the ferromagnetic resonance frequency measured by the spin-torque diode technique. The dashed lines indicate linear fitting. b Bias-voltage dependence of perpendicular magnetic anisotropy. The open and filled circles represent the voltage sweep directions. The dashed red line is the fitting curve of a second-order polynomial.
Moreover, the HCMA value can be enhanced by the improvement of thermal design as discussed by Okuno30. By contrast, enhancement of spin-transfer torque requires a decrease in the magnetization or thickness of the ferromagnetic layer; this induces deterioration in MTJs. Therefore, utilization of HCMA is promising for further enhancement of responsivity.
HCMA is also useful for enhancement of dynamic range. Although the dynamic range is limited by the noise equivalent voltage, it can be improved by increasing the ferromagnetic thickness. However, spin-transfer torque and VCMA decrease significantly when this is done. HCMA decreases only slightly because the increase in the temperature of the ferromagnetic layer is mainly affected by the MgO layer through which the heat flows, rather than the FeB layer. Therefore, HCMA is the appropriate spin torque for improving dynamic range (see Supplementary Note 5).
With the advent of pure-spin-current sources, spin-based electronic (spintronic) devices no longer require electrical charge transfer, opening new possibilities for both conducting and insulating spintronic systems. Pure spin currents have been used to suppress noise caused by thermal fluctuations in magnetic nanodevices, amplify propagating magnetization waves, and to reduce the dynamic damping in magnetic films. However, generation of coherent auto-oscillations by pure spin currents has not been achieved so far. Here we demonstrate the generation of single-mode coherent auto-oscillations in a device that combines local injection of a pure spin current with enhanced spin-wave radiation losses. Counterintuitively, radiation losses enable excitation of auto-oscillation, suppressing the nonlinear processes that prevent auto-oscillation by redistributing the energy between different modes. Our devices exhibit auto-oscillations at moderate current densities, at a microwave frequency tunable over a wide range. These findings suggest a new route for the implementation of nanoscale microwave sources for next-generation integrated electronics.
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 the applied magnetic field with a 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 edges of the constriction. By contrast, when the magnetization direction 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 redistribution of the magnetic charges from the edges 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 out-of-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 nonuniform character of the system via a mean-field approximation. Both the Oersted (Oe) field and the spin-transfer torque from the drive current increase the localization and decrease the frequency of the observed mode. Furthermore, the antisymmetric Oe field breaks the lateral symmetry, favoring the localized mode at one of the two constriction edges, particularly for large out-of-plane field angles where the threshold current is significantly increased and the edge demagnetization is suppressed.
Auto-oscillation threshold current vs applied field strength and out-of-plane angle as estimated (a) using micromagnetic simulations, (b) a macrospin model given by Eqs. (4) and (5), and (c) a mean-field model given by Eqs. (7) and (6). (d) The efficiency of pure-spin-current injection vs applied field geometry.
Spatial profiles of the auto-oscillations calculated for a field applied at θ0=70 and (a) without any Oe field or STT, (b) with STT, (c) with an Oe field, and (d) with both an Oe field and STT. (e) Contribution of the demagnetizing field and the Oe field to the depth of the spin-wave wells vs the applied field strength. (f) Contribution of the STT and Oe field to the frequency of the edge mode vs the applied field strength.
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