Generation linewidth of an auto-oscillator with a nonlinear frequency shift: Spin-torque nano-oscillator

It is shown that the generation linewidth of an auto-oscillator with a nonlinear frequency shift (i.e. an auto-oscillator in which frequency depends on the oscillation amplitude) is substantially larger than the linewidth of a conventional quasi-linear auto-oscillator due to the renormalization of the phase noise caused by the nonlinearity of the oscillation frequency. The developed theory, when applied to a spin-torque nano-contact auto-oscillator, predicts a minimum of the generation linewidth when the nano-contact is magnetized at a critical angle to its plane, corresponding to the minimum nonlinear frequency shift, in good agreement with recent experiments.Comment: 4 pages, 2 figure

Temperature dependence of nonlinear auto-oscillator linewidths: Application to spin-torque nano-oscillators

The temperature dependence of the generation linewidth for an auto-oscillator with a nonlinear frequency shift is calculated. It is shown that the frequency nonlinearity creates a finite correlation time, tau, for the phase fluctuations. In the low-temperature limit in which the spectral linewidth is smaller than 1/tau, the line shape is approximately Lorentzian and the linewidth is linear in temperature. In the opposite high-temperature limit in which the linewidth is larger than 1/tau, the nonlinearity leads to an apparent "inhomogeneous broadening" of the line, which becomes Gaussian in shape and has a square-root dependence on temperature. The results are illustrated for the spin-torque nano-oscillator.Comment: 4 pages, 1 figur

Generation of spin-wave dark solitons with phase engineering

We generate experimentally spin-wave envelope dark solitons from rectangular high-frequency dark input pulses with externally introduced phase shifts in yttrium-iron garnet magnetic fims. We observe the generation of both odd and even numbers of magnetic dark solitons when the external phase shift varies. The experimental results are in a good qualitative agreement with the theory of the dark-soliton generation in magnetic films developed earlier [Phys. Rev. Lett. 82, 2583 (1999)].Comment: 6 pages, including 7 figures, submitted to Phys. Rev.

Lineshape distortion in a nonlinear auto-oscillator near generation threshold: Application to spin-torque nano-oscillators

The lineshape in an auto-oscillator with a large nonlinear frequency shift in the presence of thermal noise is calculated. Near the generation threshold, this lineshape becomes strongly non-Lorentzian, broadened, and asymmetric. A Lorentzian lineshape is recovered far below and far above threshold, which suggests that lineshape distortions provide a signature of the generation threshold. The theory developed adequately describes the observed behavior of a strongly nonlinear spin-torque nano-oscillator.Comment: 4 pages, 3 figure

THz-Frequency Spin-Hall Auto-Oscillator Based on a Canted Antiferromagnet

We propose a design of a THz-frequency signal generator based on a layered structure consisting of a current-driven platinum (Pt) layer and a layer of an antiferromagnet (AFM) with easy-plane anisotropy, where the magnetization vectors of the AFM sublattices are canted inside the easy plane by the Dzyaloshinskii-Moriya interaction (DMI). The DC electric current flowing in the Pt layer creates, due to the spin-Hall effect, a perpendicular spin current that, being injected in the AFM layer, tilts the DMI-canted AFM sublattices out of the easy plane, thus exposing them to the action of a strong internal exchange magnetic field of the AFM. The sublattice magnetizations, along with the small net magnetization vector $\textbf{m}_{\rm DMI}$ of the canted AFM, start to rotate about the hard anisotropy axis of the AFM with the THz frequency proportional to the injected spin current and the AFM exchange field. The rotation of the small net magnetization $\textbf{m}_{\rm DMI}$ results in the THz-frequency dipolar radiation that can be directly received by an adjacent (e.g. dielectric) resonator. We demonstrate theoretically that the radiation frequencies in the range $f=0.05-2$~THz are possible at the experimentally reachable magnitudes of the driving current density, and evaluate the power of the signal radiated into different types of resonators, showing that this power increases with the increase of frequency $f$, and that it could exceed 1~$\mu$W at $f \sim 0.5$~THz for a typical dielectric resonator of the electric permittivity $\varepsilon \sim 10$ and quality factor $Q \sim 750$

Detection of spin waves in permalloy using planar Hall effect

Rectification of microwave oscillations of magnetization in a permalloy film is realized using planar Hall effect. Two different rectified signals are obtained: a signal from the linearly excited uniform magnetization precession at the frequency of the external pumping and a signal from the pairs of contra-propagating short-wavelength spin waves parametrically generated at a half of the pumping frequency. The second, most unusual, rectified signal is caused by the uniform component of the dynamic magnetization created due to the interference of the phase correlated pairs of parametric spin waves

Non-resonant wave front reversal of spin waves used for microwave signal processing

It is demonstrated that non-resonant wave front reversal (WFR) of spin-wave pulses caused by pulsed parametric pumping can be effectively used for microwave signal processing. When the frequency band of signal amplification by pumping is narrower than the spectral width of the signal, the non-resonant WFR can be used for the analysis of the signal spectrum. In the opposite case the non-resonant WFR can be used for active (with amplification) filtering of the input signal.Comment: 4 pages, 3 figure

Stochastic theory of spin-transfer oscillator linewidths

We present a stochastic theory of linewidths for magnetization oscillations in spin-valve structures driven by spin-polarized currents. Starting from a nonlinear oscillator model derived from spin-wave theory, we derive Langevin equations for amplitude and phase fluctuations due to the presence of thermal noise. We find that the spectral linewidths are inversely proportional to the spin-wave intensities with a lower bound that is determined purely by modulations in the oscillation frequencies. Reasonable quantitative agreement with recent experimental results from spin-valve nanopillars is demonstrated.Comment: Submitted to Physical Review