We study the formation of a room temperature magnon Bose-Einstein condensate (BEC) in nanoscopic systems and demonstrate that its lifetime is influenced by the spatial confinement. We predict how dipolar interactions and nonlinear magnon scattering assist in the generation of a metastable magnon BEC in energy-quantized nanoscopic devices. We verify our prediction by a full numerical simulation of the Landau-Lifshitz-Gilbert equation and demonstrate the generation of magnon BEC in confined insulating magnets of yttrium iron garnet. We directly map out the nonlinear magnon scattering processes behind this phase transition to show how fast quantized thermalization channels allow the BEC formation in confined structures. Based on our results, we discuss a new mechanism to manipulate the BEC lifetime in nanoscaled systems. Our study greatly extends the freedom to study the dynamics of magnon BEC in realistic systems and to design integrated circuits for BEC-based applications at room temperature.
We propose inducing Bose-Einstein condensation of magnons in a magnetic insulator by a heat flow oriented toward its boundary. At a critical heat flux, the oversaturated thermal gas of magnons accumulated at the boundary precipitates the condensate, which then grows gradually as the thermal bias is dialed up further. The thermal magnons thus pumped by the magnonic bulk (spin) Seebeck effect must generally overcome both the local Gilbert damping associated with the coherent magnetic dynamics as well as the radiative spin-wave losses toward the magnetic bulk, in order to achieve the threshold of…
We explore routes to realize electrically driven Bose-Einstein condensation of magnons in insulating antiferromagnets. Even in insulating antiferromagnets, the localized spins can strongly couple to itinerant spins in adjacent metals via spin-transfer torque and spin pumping. We describe the formation of steady-state magnon condensates controlled by a spin accumulation polarized along the staggered field in an adjacent normal metal. Two types of magnons exist in antiferromagnets, which carry opposite magnetic moments. Consequently, and in contrast to ferromagnets, Bose-Einstein condensation ca…
We show that the formation of a magnon condensate in thin ferromagnetic films can be explained within the framework of a classical stochastic non-Markovian Landau-Lifshitz-Gilbert equation where the properties of the random magnetic field and the dissipation are determined by the underlying phonon dynamics. We have numerically solved this equation for a tangentially magnetized yttrium-iron garnet film in the presence of a parallel parametric pumping field. We obtain a complete description of all stages of the nonequilibrium time evolution of the magnon gas which is in excellent agreement with …
Spintronics is the science and technology of electric control over spin currents in solid-state-based devices. Recent advances have demonstrated a coupling between electronic spin currents in non-magnetic metals and magnons in magnetic insulators. The coupling is due to spin transfer and spin pumping at interfaces between the normal metals and magnetic insulators. In this Chapter, we review these developments and the prospects they raise for electric control of quasi-equilibrium magnon Bose-Einstein condensates and spin superfluidity.
Electrons and holes residing on the opposing sides of an insulating barrier and experiencing an attractive Coulomb interaction can spontaneously form a coherent state known as an indirect exciton condensate. We study a trilayer system where the barrier is an antiferromagnetic insulator. The electrons and holes here additionally interact via interfacial coupling to the antiferromagnetic magnons. We show that by employing magnetically uncompensated interfaces, we can design the magnon-mediated interaction to be attractive or repulsive by varying the thickness of the antiferromagnetic insulator b…
We demonstrate how a magnon chemical potential is generated in parametric parallel pumping. We study how a time-periodic magnetic field of this pumping affects magnon properties of a ferrimagnet in a nonequilibrium steady state. We show that the magnon distribution function of our nonequilibrium steady state becomes the Bose distribution function with $μ=ω_{\textrm{p}}/2$, where $μ$ is the magnon chemical potential and $ω_{\textrm{p}}$ is the pumping frequency. This result is distinct from the absence of the magnon chemical potential in the standard theory and can qualitatively explain its gen…
Thermalization of a parametrically driven magnon gas leading to the formation of a Bose-Einstein condensate at the bottom of a spin-wave spectrum was studied by time- and wavevector-resolved Brillouin light scattering spectroscopy. It has been found that the condensation is preceded by the conversion of initially pumped magnons into a second group of frequency degenerated magnons, which appear due to parametrically stimulated scattering of the initial magnons to a short-wavelength spectral region. In contrast to the first magnon group, which wavevectors are orthogonal to the wavevectors of the…
We report the mean field model of nonequilibrium polariton condensation in annular effective non-Hermitian potential traps, stemming from incoherent optically induced excitonic reservoirs of annular shape. We solve the linearized extended Gross-Pitaevskii equation in the approximation of two delta-function effective shell potentials for complex spectra of trapped polariton modes and calculate corresponding condensation threshold optical pumping powers. The exhaustive map of condensate quantum number transitions in the multi-dimensional space of trap parameters, including a cascade of topologic…
We propose a stabilizing mechanism for the Bose-Einstein condensation (BEC) of interacting magnons in ferrimagnets and ferromagnets. By studying the effects of the magnon-magnon interaction on the stability of the magnon BEC in a ferrimagnet and two ferromagnets, we show that the magnon BEC remains stable even in the presence of the magnon-magnon interaction in the ferrimagnet and ferromagnet with a sublattice structure, whereas it becomes unstable in the ferromagnet without a sublattice structure. This indicates that the existence of a sublattice structure is the key to stabilizing the BEC of…
The formation of a Bose condensate of magnons in a perpendicularly magnetized film of yttrium iron garnet under radio-frequency pumping in a strip line is studied experimentally. The characteristics of nonlinear magnetic resonance and the spatial distribution of the Bose condensate of magnons in the magnetic field gradient are investigated. In these experiments, the Bosonic system of magnons behaves similarly to the Bose condensate of magnons in the antiferromagnetic superfluid 3He-B, which was studied in detail earlier. Magnonic BEC forms a coherently precessing state with the properties of m…
The quanta of magnetic excitations - magnons - are known for their unique ability to undergo Bose-Einstein condensation at room temperature. This fascinating phenomenon reveals itself as a spontaneous formation of a macroscopic coherent state under the influence of incoherent stimuli. Spin currents have been predicted to offer electronic control of magnon Bose-Einstein condensates, but this phenomenon has not been experimentally evidenced up to now. Here we experimentally show that current-driven Bose-Einstein condensation can be achieved in nanometer-thick films of magnetic insulators with ta…
We clarify the condition for the occurrence of magnon Bose-Einstein condensation (BEC) in spin pumping systems without using external pumping magnetic fields. The Goldstone model is generalized and the stability of the vacuum is closely investigated. By applying the generalized Goldstone model to spin pumping systems, the condition for the experimental realization of the stable magnon BEC in spin pumping systems is theoretically proposed.
We propose a mechanism for destabilizing or stabilizing Bose-Einstein condensation (BEC) of interacting magnons in an antiferromagnet. We study how the interaction between magnons affects the magnon BEC in a two-sublattice antiferromagnet without and with an external magnetic field. We show that in the absence of the magnetic field the magnon BEC is destabilized by the attractive interband interaction, which is larger than the repulsive intraband interaction. We also show that in the presence of the magnetic field the magnon BEC is stabilized only if the magnetic field is large enough to make …
We investigate the process of condensation of exciton-polaritons in a one-dimensional nanowire, predicting spontaneous formation of domains of uncondensed excitons and condensed polaritons. We demonstrate a universal scaling law for the density of domains, which results from the competition between characteristic timescales present in the system. However, we find that the system does not follow the standard Kibble-Żurek scenario of a nonequilibrium phase transition.
The feasibility of creating a Bose-Einstein condensate of magnons using a dense ensemble of nitrogen-vacancy spin defects in diamond is investigated. Through assessing a density-dependent spin exchange interaction strength and the magnetic phase transition temperature ($T_c$) using the Sherrington-Kirkpatrick model, the minimum temperature-dependent concentration for magnetic self-ordering is estimated. For a randomly dispersed spin ensemble, the calculated average exchange constant exceeds the average dipole interaction strengths for concentrations approximately greater than 70 ppm, while $T_…
An easy-plane ferromagnetic insulator in a uniform external magnetic field and in contact with a phonon bath and a normal metal bath is studied theoretically in the presence of dc spin current injection via the spin Hall effect in the metal. The Keldysh path integral formalism is used to model the magnon gas driven into a nonequilibrium steady state by mismatched bath temperatures and/or electrical injection, and we analyze the magnon system in the normal (uncondensed) state, but close to the instability to Bose-Einstein condensation (BEC), within the self-consistent Hartree-Fock approximation…
We develop a numerically exact scheme for resumming certain classes of Feynman diagrams in the self-consistent perturbation expansion for the electron and magnon self-energies in the nonequilibrium Green function formalism applied to a coupled electron-magnon (\mbox{e-m}) system which is driven out of equilibrium by the applied finite bias voltage. Our scheme operates with the electronic and magnonic GFs and the corresponding self-energies viewed as matrices in the Keldysh space, rather than conventionally extracting their retarded and lesser components. This is employed to understand the effe…
The fundamental phenomenon of Bose-Einstein Condensation (BEC) has been observed in different systems of real and quasi-particles. The condensation of real particles is achieved through a major reduction in temperature while for quasi-particles a mechanism of external injection of bosons by irradiation is required. Here, we present a novel and universal approach to enable BEC of quasi-particles and to corroborate it experimentally by using magnons as the Bose-particle model system. The critical point to this approach is the introduction of a disequilibrium of magnons with the phonon bath. Afte…
Semiconductor microcavity systems strongly coupled to quantum wells are now receiving a great deal of attention because of their ability to efficiently generate coherent light by the Bose-Einstein condensation (BEC) of an exciton-polariton gas. Since the exciton polaritons are composite quasi-bosonic particles, many fundamental features arise from their original constituents, i.e., electrons, holes and photons. As a result, not only equilibrium phases typified by the BEC but also nonequilibrium lasing phases can be achieved. In this contribution, we describe a framework which can treat such eq…
We show experimentally that the spin current generated by the spin Hall effect drives the magnon gas in a ferromagnet into a quasi-equilibrium state that can be described by the Bose-Einstein statistics. The magnon population function is characterized either by an increased effective chemical potential or by a reduced effective temperature, depending on the spin current polarization. In the former case, the chemical potential can closely approach, at large driving currents, the lowest-energy magnon state, indicating the possibility of spin current-driven Bose-Einstein condensation.
Two recent articles of the Munster University experimental team led by S.O. Demokritov displayed several important facts related to the Bose-Einstein condensation of magnons (BECM) under permanent pumping first discovered in 2006. They contradicted existing theories of this phenomenon, which predict the attractive interaction between magnons and strong spontaneous violation of the reflection symmetry. In this article, we show that these theories implicitly assumed all relaxation processes to be fast compared with the lifetime of the magnons, whereas one of them -- relaxation between two minima…
For dipole-carrying excitations observed in a high-quality resonator, strong-coupling modes can appear as composite bosons with the spontaneous formation of quantized vortices in the condensed phase of a polariton fluid. In exciton-polaritons, in particular, it leads to sustained trapping of the emitted photon. In this paper, we show that magnon-polaritons can be realized due to magnon condensation caused by magnetic dipole-dipole interaction. In a quasi-2D ferrite disk placed in a microwave cavity, one observes quantum confinement effects of magnetic-dipolar-mode (MDM) oscillations. These mod…
Bose-Einstein condensation of quasi-equilibrium magnons is one of few macroscopic quantum phenomena observed at room temperature. Since its discovery, it became an object of intense research, which led to the observation of many exciting phenomena such as quantized vortices, second sound, and Bogolyubov waves. However, for a long time it remained unclear, what physical mechanisms can be responsible for the spatial stability of the magnon condensate. Indeed, since magnons are believed to exhibit attractive interaction, it is generally expected that the magnon condensate should be unstable with …
Using one of the methods of quantum nonequilibrium statistical physics we have investigated the spin transport transverse to the normal metal/ferromagnetic insulator interface in hybrid nanostructures. An approximation of the effective parameters, when each of the interacting subsystems (electron spin, magnon, and phonon) is characterized by its own effective temperature have been considered. The generalized Bloch equations which describe the spin-wave current propagation in the dielectric have been derived. Finally, two sides of the spin transport "coin" have been revealed: the diffusive natu…
Bose-Einstain condensation occurs at an appropriate density of bosonic particles, depending on their mass and temperature. We were able to experimentally observe the transition from the spin wave regime to the magnon Bose-Einstein condensed state (mBEC) with increasing magnon density by a microwave pumping. We used optical methods to register the spatial distribution of the magnon density and phase. For the first time, a coherent state of stationary magnons was demonstrated far from the region of their excitation.
We study the nonequilibrium transport for the asymmetric and negative differential magnon tunneling driven by temperature bias. We demonstrate that the many-body magnon interaction that makes the magnonic spectrum temperature-dependent is the crucial factor for the emergence of rectification and negative differential spin Seebeck effects in magnon tunneling junctions. When magnonic junctions have temperature-dependent density of states, reversing the temperature bias is able to give asymmetric spin currents and increasing temperature bias could give an anomalously decreasing magnonic spin curr…
The concept of temperature in nonequilibrium thermodynamics is an outstanding theoretical issue. We propose an energy repartition principle that leads to a spectral (mode-dependent) temperature in steady-state nonequilibrium systems. The general concepts are illustrated by analytic solutions of the classical Heisenberg spin chain connected to Langevin heat reservoirs with arbitrary temperature profiles. Gradients of external magnetic fields are shown to localize spin waves in a Wannier-Zeemann fashion, while magnon interactions renormalize the spectral temperature. Our generic results are appl…
Ultrafast optical excitation of magnons in 2D antiferromagnetic semiconductors via spin torque mediated by unbound electron-hole pairs and excitons: Signatures in magnonic charge pumping
Department of Physics and Astronomy, University of Delaware（特拉华大学物理与天文学系）
We theoretically investigate spin transfer between a system of quasiequilibrated Bose-Einstein condensed magnons in an insulator in direct contact with a conductor. While charge transfer is prohibited across the interface, spin transport arises from the exchange coupling between insulator and conductor spins. In normal insulator phase, spin transport is governed solely by the presence of thermal and spin-diffusive gradients; the presence of Bose-Einstein condensation (BEC), meanwhile, gives rise to a temperature-independent condensate spin current. Depending on the thermodynamic bias of the sy…
Local temperature control of magnon frequency and direction of supercurrents in a magnon Bose-Einstein condensate
Rheinland-Pfälzische Technische Universität Kaiserslautern-Landau（莱茵兰-普法尔茨技术大学凯泽斯劳滕-兰道）；Weizmann Institute of Science（魏茨曼科学研究所）；Fraunhofer Institute for Industrial Mathematics ITWM（弗劳恩霍夫工业数学研究所）
With the aim to reveal universal features of hadronic matter and correlated Dirac insulators in strong AC-electric fields, we study the $\mathcal{N}=2$ supersymmetric QCD with a finite quark mass driven by a rotating electric field $\mathcal{E}_x+i\mathcal{E}_y= E e^{iΩt}$. The analysis is done in the holographically dual D3/D7 system in the co-rotating frame, effectively. The nonequilibrium phase diagram is determined from the threshold electric field at which the insulator phase breaks down to a conductive phase due to the AC version of the Schwinger mechanism. The external field induces a r…
Over the last decade, significant progresses have been achieved to create Bose-Einstein condensates (BEC) of magnetic excitations, i.e., magnons, at the room temperature, which is a novel quantum many-body system with a strong spin-spin correlation, and contains potential applications in magnonic spintronics. For quantum information science, the magnonic condensates can become an attractive source of quantum entanglement, which plays a central role in most of the quantum information processing tasks. Here we theoretically study the entanglement properties of a magnon gas above and below the co…
