O. Dzyapko

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.

Controlled enhancement of spin-current emission by three-magnon splitting

Spin currents--the flow of angular momentum without the simultaneous transfer of electrical charge--play an enabling role in the field of spintronics. Unlike the charge current, the spin current is not a conservative quantity within the conduction carrier system. This is due to the presence of the spin-orbit interaction that couples the spin of the carriers to angular momentum in the lattice. This spin-lattice coupling acts also as the source of damping in magnetic materials, where the precessing magnetic moment experiences a torque towards its equilibrium orientation; the excess angular momentum in the magnetic subsystem flows into the lattice. Here we show that this flow can be reversed by the three-magnon splitting process and experimentally achieve the enhancement of the spin current emitted by the interacting spin waves. This mechanism triggers angular momentum transfer from the lattice to the magnetic subsystem and modifies the spin-current emission. The finding illustrates the importance of magnon-magnon interactions for developing spin-current based electronics.

Spatially non-uniform ground state and quantized vortices in a two-component Bose-Einstein condensate of magnons

A gas of magnons in magnetic films differs from all other known systems demonstrating Bose-Einstein condensation (BEC), since it possesses two energetically degenerate lowest-energy quantum states with non-zero wave vectors ±kBEC. Therefore, BEC in this system results in a spontaneously formed two-component Bose-Einstein condensate described by a linear combination of two spatially non-uniform wave-functions ∝exp(±ikBECz), while condensates found in other physical systems are characterized by spatially uniform wave-functions. Here we report a study of BEC of magnons with sub-micrometer spatial resolution. We experimentally confirm the existence of the two wave-functions and show that their interference results in a non-uniform ground state of the condensate with the density oscillating in space. Additionally, we observe stable topological defects in the condensate. By comparing the experimental results with predictions of a theoretical model based on the Ginzburg-Landau equation, we identify these defects as quantized vortices.

Spin pumping by parametrically excited short-wavelength spin waves

We use both parallel and perpendicular parametric pumping techniques to excite short-wavelength spin waves in an yttrium iron garnet film and study the spin current generation from spin waves excited by these pumping methods with the help of the inverse spin-Hall effect in the adjacent Pt layer. We observed clear spin current generations for these pumping techniques and find that the efficiency is nearly independent of the magnitude and the direction of the wave vectors of excited spin waves. These experimental results are important for future spintronic devices operated by short-wavelength spin waves.

Ginzburg-Landau model of Bose-Einstein condensation of magnons

We introduce a system of phenomenological equations for Bose-Einstein condensates of magnons in the one-dimensional setting. The nonlinearly coupled equations, written for amplitudes of the right- and left-traveling waves, combine basic features of the Gross-Pitaevskii and complex Ginzburg-Landau models. They include localized source terms to represent the microwave magnon-pumping field. With the source represented by the delta functions, we find analytical solutions for symmetric localized states of the magnon condensates. We also predict the existence of asymmetric states with unequal amplitudes of the two components. Numerical simulations demonstrate that all analytically found solutions are stable. With the delta-function terms replaced by broader sources, the simulations reveal a transition from the single-peak stationary symmetric states to multipeak ones, generated by the modulational instability of extended nonlinear-wave patterns. In the simulations, symmetric initial conditions always converge to symmetric stationary patterns. On the other hand, asymmetric inputs may generate nonstationary asymmetric localized solutions, in the form of traveling or standing waves. Comparison with experimental results demonstrates that the phenomenological equations provide for a reasonably good model for the description of the spatiotemporal dynamics of magnon condensates.

Bose-Einstein Condensation of Magnons under Incoherent Pumping

Bose-Einstein condensation in a gas of magnons pumped by an incoherent pumping source is experimentally studied at room temperature. We demonstrate that the condensation can be achieved in a gas of bosons under conditions of incoherent pumping. The critical transition point is shown to be almost independent of the frequency spectrum of the pumping source and is solely determined by the density of magnons. The electromagnetic power radiated by the magnon condensate is found to scale quadratically with the pumping power. The obtained results are in a good agreement with the theory of Bose-Einstein condensation of quasiequilibrium magnons.

Quantum coherence due to Bose-Einstein condensation of parametrically driven magnons

The room-temperature kinetics and thermodynamics of the magnon gas driven by microwave pumping has been investigated by means of the Brillouin light scattering (BLS) technique. We show that for high enough pumping powers the quantum relaxation of the driven gas results in a quasi-equilibrium state described by the Bose–Einstein statistics with a nonzero chemical potential. Further increase of the pumping power causes a Bose–Einstein condensation in the magnon gas documented by an observation of the magnon accumulation at the lowest energy level. Using the sensitivity of the BLS to the coherence degree of the scattering magnons, we confirm the spontaneous emergence of coherence of the magnons accumulated at the bottom of the spectrum, if their density exceeds a critical value.

Monochromatic microwave radiation from the system of strongly excited magnons

A conversion of a broadband microwave energy accumulated by a system of strongly excited magnons into a monochromatic microwave is demonstrated. The mechanism is based on recently discovered room-temperature Bose–Einstein condensation of nonequilibrium magnons. A realization of an electronically tunable microwave generator pumped by an incoherent broadband sources and the achievable linewidth of the monochromatic radiation are discussed.

Direct observation of Bose–Einstein condensation in a parametrically driven gas of magnons

A gas of thermalized quasi-equilibrium magnons with a non-zero chemical potential created in a magnetic film using parametric pumping is studied. The value of the chemical potential of the gas is determined directly from the measured distribution of magnons over the spectrum. With increasing pumping power the value of the chemical potential increases. At high enough pumping powers it reaches the energy corresponding to the lowest magnon frequency. Under these conditions a very narrow peak of magnon population at the lowest magnon frequency appears. The measured width of the peak is five orders of magnitude smaller than that expected for the thermal distribution. We associate this effect with Bose–Einstein condensation of magnons.

Reconfigurable heat-induced spin wave lenses

We study the control and manipulation of propagating spin waves in yttrium iron garnet films using a local laser-induced heating. We show that, due to the refraction of spin waves in the thermal gradients, the heated region acts as a defocusing lens for Damon-Eshbach spin waves and as a focusing lens for backward volume waves enabling collimation of spin-wave beams in the latter case. In addition to the focusing/defocusing functionality, the local heating allows one to manipulate the propagation direction of the spin-wave beams and to efficiently suppress their diffraction spreading by utilizing caustic effects.