1 8 O ct 2 00 7 Spin Vortex inMagnonBEC of Superfluid 3 He - B

The phenomenon of the spontaneous phase-coherent precession of magnetization in superfluid 3 He and the related effects of spin superfluidity are based on the true Bose-Einstein condensation of magnons. Several different magnon BEC states have been observed: homogeneously precessing domain (HPD); BEC condensation in the spin-orbit potential trap (Q-balls); coherent precession with fractional magnetization; and two modes of the coherent precession in squeezed aerogel. The spin superfluidity effects, like spin Josephson phenomena, spin current vortices, spin phase slippage, long distance magnetization transport by spin supercurrents have been observed. Bose-Einstein condensation (BEC) is a phenomenon of formation of collective quantum state, in which the macroscopic number of particles is governed by a single wave function. The phenomenon of Bose-Einstein condensate was predicted by Ein-stein in 1925. For a review see, for example Ref. [1]. The almost perfect BEC state was observed in ul-tra could atomic gases. In Bose liquids, the BEC is strongly modified by interactions, but still remains the key mechanism for the formation of a coherent quantum state in Bose systems, which exhibits the phenomenon of superfluidity characterized by non-dissipative superfluid mass currents discovered first in 4 He by P.L. Kapitza [2]. Superfluidity proved to be a more general phenomenon: superfluid mass current has been found in Fermi liquid 3 He; su-perfluidity of electric charge – superconductivity – is known in metals; superfluidity of chiral charge is discussed in quantum chromodynamics; color superfluidity – in quark matter and baryonic su-perfluidity – in neutron stars; etc. Here we discuss magnon BEC with spin current superfluidity. Strictly speaking, the theory of superfluidity and Bose-Einstein condensation is applicable to systems with conserved U (1) charge or particle number. However, it can be extended to systems with a weakly violated conservation: it can be applicable to a system of sufficiently long-lived quasiparticles – discrete quanta of energy that can be treated as condensed matter counterpart of elementary particles. In magnetically ordered materials, the corresponding propagating excitations are magnons – quanta of spin waves. Under stationary conditions the density of thermal magnons is small, but they can be pumped by resonance radio-frequency (RF) field (magnetic resonance). One may expect that at very low temperatures, the non-equilibrium gas of magnons could live a relatively long time, sufficient for formation of coherent magnon condensate. Recently there appeared a number of articles, where authors claimed the observation of BEC of quasiparticles: excitons [3] and magnons [4]. To