{'fraction_non_alphanumeric': 0.018596001859600187, 'fraction_numerical': 0.007438400743840074, 'mean_word_length': 5.166189111747851, 'pattern_counts': {'":': 0, '<': 0, '<?xml version=': 0, '>': 0, 'https://': 0, 'lorem ipsum': 0, 'www.': 0, 'xml': 0}, 'pii_count': 0, 'substrings_counts': 0, 'word_list_counts': {'cursed_substrings.json': 0, 'profanity_word_list.json': 0, 'sexual_word_list.json': 0, 'zh_pornsignals.json': 0}}
Bose–Einstein condensation and superfluidity of magnons in yttrium iron garnet films

A brief review of the theory of quasi-equilibrium Bose–Einstein condensation and superfluidity of magnons in a film of yttrium iron garnet is presented. The Bose–Einstein condensation of magnons in YIG film at room temperature under rf pumping was discovered in 2006 by the Münster experimental team led by Demokritov. There are two symmetric minima in the magnon spectrum of a ferromagnetic film, and therefore two condensates. In 2012 the same experimental group discovered the interference of these two condensates, thus proving their coherence. The reviewed theory that explains these experimental observations predicts that the reflection symmetry of the magnon gas is spontaneously violated at Bose–Einstein condensation in thick films. In thin films the condensate is symmetric at low magnetic field and transits to the non-symmetric state at higher field. Dipolar interaction energy depends on the phase of the condensate wave function. In quasi-equilibrium it traps the phase. All these features are due to the interaction between magnons Since the magnon condensate is coherent, a logical question is whether the condensate is superfluid. Two obstacles for superfluidity are the dominance of the normal magnon density over the condensate (approximately 100-fold) and the phase trapping. We show that the velocity of the superfluid part is by 5–7 decimal orders larger than that of the normal part at typical values of the field gradients. Thus, the spin current is mainly superfluid. The phase trapping violates the U(1) symmetry, reducing it to a discrete symmetry. Stationary superfluid flow is still possible, but it becomes inhomogeneous. In 1-d stationary flow at low kinetic energy the condensate phase over long intervals of length remains close to the trapped values and changes by 2π within comparatively short intervals (phase solitons). The current and number of magnons are conserved globally but not locally, since they transfer spin momentum to the lattice. These peculiarities of the stationary superfluid flow are caused by dipolar forces.