A. N. Slavin

Nonlinear Auto-Oscillator Theory of Microwave Generation by Spin-Polarized Current

This paper formulates a general analytic approach to the theory of microwave generation in magnetic nano-structures driven by spin-polarized current and reviews analytic results obtained in this theory. The proposed approach is based on the universal model of an auto-oscillator with negative damping and nonlinear frequency shift. It is demonstrated that this universal model, when applied to the case of a spin-torque oscillator (STO) based on a current-driven magnetic nano-pillar or nano-contact, gives adequate description of most of the experimentally observed properties of STO. In particular, the model describes the power and frequency of the generated microwave signal as functions of the bias current and magnetic field, predicts the magnitude and properties of the generation linewidth, and explains the STO behavior under the influence of periodic and stochastic external signals: frequency modulation, phase-locking to external signals, mutual phase-locking in an array of STO, broadening of the generation linewidth near the generation threshold, etc. The proposed nonlinear auto-oscillator theory is rather general and can be used not only for the development of practical nano-sized STO, but, also, for the description of nonlinear auto-oscillating systems of any physical nature.

Bose–Einstein condensation of quasi-equilibrium magnons at room temperature under pumping

Bose–Einstein condensation is one of the most fascinating phenomena predicted by quantum mechanics. It involves the formation of a collective quantum state composed of identical particles with integer angular momentum (bosons), if the particle density exceeds a critical value. To achieve Bose–Einstein condensation, one can either decrease the temperature or increase the density of bosons. It has been predicted that a quasi-equilibrium system of bosons could undergo Bose–Einstein condensation even at relatively high temperatures, if the flow rate of energy pumped into the system exceeds a critical value. Here we report the observation of Bose–Einstein condensation in a gas of magnons at room temperature. Magnons are the quanta of magnetic excitations in a magnetically ordered ensemble of magnetic moments. In thermal equilibrium, they can be described by Bose–Einstein statistics with zero chemical potential and a temperature-dependent density. In the experiments presented here, we show that by using a technique of microwave pumping it is possible to excite additional magnons and to create a gas of quasi-equilibrium magnons with a non-zero chemical potential. With increasing pumping intensity, the chemical potential reaches the energy of the lowest magnon state, and a Bose condensate of magnons is formed.

Magnetic nano-oscillator driven by pure spin current

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.

Electric field tunable ferrite-ferroelectric hybrid wave microwave resonators: Experiment and theory

The electric field tuning characteristics of a combined microwave resonator based on ferrite-ferroelectric layered structure have been studied in a wide range of bias magnetic fields. The combined ferrite-ferroelectric resonator was composed of two rectangular resonators fabricated from a ceramic barium strontium titanate (BST) slab and a single-crystal yttrium iron garnet (YIG) film. The in-plane dimensions for the YIG and BST resonators were chosen to be equal in order to maximize the electromagnetic coupling between their main modes and reduce spurious influence of their higher order modes. A tuning range of 100MHz for the resonator frequency was realized at 5GHz through the variation of magnetic permeability and dielectric permittivity of the YIG-BST structure. A theory for the hybrid wave excitations, based on a coupled-mode approach, has been developed and provides good description of the data.

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 quasilinear 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 auto-oscillator, gives a good description of experimentally measured angular and temperature dependences of the linewidth.

Ferrite-ferroelectric layered structures for electrically and magnetically tunable microwave resonators

It is demonstrated experimentally that a layered structure consisting of ferrite and ferroelectric thin films can be used as an electrically and magnetically tunable microwave resonator. The dual tunability is realized through the application of a bias electric field to the ferroelectric layer (thus changing its dielectric constant), and a bias magnetic field to the ferrite layer. The resonator having central frequency f0≅5GHz and bandwidth Δf=3.5MHz demonstrated a broadband (∼300Δf) tunability through the variation of the bias magnetic field, and a narrow-band (∼2Δf) tunability through the variation of the bias electric field.

A frequency-controlled magnetic vortex memory

Using the ultra low damping NiMnSb half-Heusler alloy patterned into vortex-state magnetic nano-dots, we demonstrate a new concept of non-volatile memory controlled by the frequency. A perpendicular bias magnetic field is used to split the frequency of the vortex core gyrotropic rotation into two distinct frequencies, depending on the sign of the vortex core polarity

Spin-wave spectra of perpendicularly magnetized circular submicron dot arrays

p=\pm1

Bistability of vortex core dynamics in a single perpendicularly magnetized nanodisk.

inside the dot. A magnetic resonance force microscope and microwave pulses applied at one of these two resonant frequencies allow for local and deterministic addressing of binary information (core polarity).

Boundary conditions for magnetization in magnetic nanoelements

Dynamic microwave properties of arrays of circular Ni and Ni81Fe19 dots were studied by X-band ferromagnetic resonance (FMR) technique. All of the dots had the same radius 0.5μm, thickness 50–70nm, and were arranged into rectangular or square array with different interdot separations. In the case of perpendicular magnetization multiple (up to 8) sharp resonance peaks were observed below the main FMR peak, and the relative positions of these peaks were independent of the interdot separations. Quantitative description of the observed multiresonance FMR spectra is given using the dipole-exchange spin wave dispersion equation for a perpendicularly magnetized film where in-plane wave vector is quantized due to the finite dot radius, and the inhomogenetiy of the intradot static demagnetization field in the nonellipsoidal dot is taken into account.