Theory of microwave superradiance from a Bose-Einstein condensate of magnons

Abstract

We show that the nearly uniform mode generated by the confluence of Bose-Einstein condensate ͑BEC͒ magnon pairs produced by microwave radiation in a film of yttrium iron garnet ͑YIG͒ is a coherent magnon state. This state corresponds to a macroscopic precessing magnetization which emits a superradiant microwave signal as a result of the cooperative action of the spins. The theory explains quantitatively recent experimental observations of microwave emission from a BEC of magnons in a YIG film when the driving power exceeds a critical value.In a recent series of papers Demokritov et al. 1-3 reported the experimental observation of quasiequilibrium Bose-Einstein condensation ͑BEC͒ of magnons at room temperature in films of yttrium iron garnet ͑YIG͒ driven by microwave radiation. When magnetized in the plane these films have a dispersion relation ͑frequency k versus wave vector k͒ for magnons propagating along the field that exhibits a minimum frequency k0 =2f min at k 0 ϳ 10 5 cm −1 . Magnon pairs with opposite wave vectors pumped parametrically in large numbers by the microwave field are redistributed over the spectrum creating a hot magnon gas that remains decoupled from the lattice for some time due to the relatively slow spin-lattice relaxation. The experiments show that if the microwave power exceeds a certain threshold value the intensity of the light scattered by magnon with frequency k0 increases by orders of magnitude indicating the formation of a Bose-Einstein condensate. [1][2][3] We have shown 4 that the cooperative action in an interacting magnon gas in a YIG film creates a coherent magnon state at k0 when the magnon population exceeds a critical density. The coherent state corresponds to a macroscopic precessing magnetization providing theoretical support for the experimentally observed Bose-Einstein condensate of magnons. Since the wavelength of the associated spin wave is on the order of 10 −5 cm, the direct microwave radiation from the BEC is negligible. However, as observed by Dzyapko et al.,5 if the applied in-plane static field has a value such that the frequency of the k Ϸ 0 magnon is 0 =2 k0 , a microwave radiation is generated by k Ϸ 0 magnons created by pairs of BEC magnons k 0 ,−k 0 through a three-magnon confluent process. The k Ϸ 0 value is necessary for emission because the wave number of electromagnetic radiation with frequency of 1.5 GHz, as in the experiments, 5 is k =2 / f Ϸ 0.3 cm −1 . In this Rapid Communication we show that the k Ϸ 0 magnons created by the BEC are coherent magnons states, which correspond to a nearly uniform magnetization precessing with frequency 0 and generating a microwave signal. The microwave emitted by the collective action of the spins is identified with superradiance. We show that this process occurs when the driving microwave power exceeds a critical value and that the theoretical results for the emitted signal power agree very well with the experimental data. 5 The term superradiance was introduced by Dicke 6 in 1954 to designate the type of spontaneous ...

Dynamics of a Bose-Einstein condensate of excited magnons

“…Moreover, Φ(t) ensures the normalization of the probability distributions, and plays the role of the logarithm of a nonequilibrium partition function: Φ(t) = lnZ(t). It is verified that 4) and similarly for the other quantities, in complete analogy with the situation in equilibrium, meaning that F q (t) and the others in set (15) are the nonequilibrium thermodynamic variables said conjugated to the basic variables in set (16). Furthermore, it is verified that…”

“…It can be shown that 13) and the (acoustic) magnon dispersion relation is given by 14) and Refs. [4,67] presents recent studies on this dispersion relation in cases of thin films of YIG.…”

“…Some theoretical studies along certain approaches has been presented by several authors (see for example Refs. [3,4,5]); we proceed here to describe the phenomenon within a complete thermo-statistical description ensemble formalism.…”

Schwinger-Keldysh theory for Bose-Einstein condensation of photons in a dye-filled optical microcavity

“…Theoretically, a lot of progress has been made for BEC of magnons and exciton-polaritons [13][14][15][16][17][18][19]. Although the observation of Bose-Einstein condensation of photons is more recent, it has also motivated theoretical studies: Klaers et al predicted a regime of large fluctuations of the condensate number [20].…”

Bose–Einstein condensation of spin wave quanta at room temperature

“…Thus, the narrowing of the magnon distribution with respect to that determined by the classical Boltzmann statistics is more than six orders of magnitude! The detailed theory of BEC of interacting quasi-particles with a finite lifetime is still missing [12][13][14][15][16]. However, one can imagine that, owing to a finite lifetime of the particles, each quantum state is spread in frequency, the width of the spreading df being determined by the lifetime, t 0 : df ≈ (2pt 0 ) −1 .…”