Interplay of spin and mass superfluidity in antiferromagnetic spin-1 Bose-Einstein condensates and bicirculation vortices

E. B. Sonin

doi:10.1103/physrevresearch.1.033103

Abstract

The paper investigates the coexistence and interplay of spin and mass superfluidity in the antiferromagnetic spin-1 BEC. The hydrodynamical theory describes the spin degree of freedom by the equations similar to the Landau--Lifshitz--Gilbert theory for bipartite antiferromagnetic insulator. The variables in the spin space are two subspins with absolute value $\hbar/2$, which play the role of two sublattice spins in the antiferromagnetic insulators. As well as in bipartite antiferromagnetic insulators, in the antiferromagnetic spin-1 BEC there are two spin-wave modes, one is a gapless Goldstone mode, another is gapped. The Landau criterion shows that in limit of small total spin (two subspins are nearly antiparallel) instability of supercurrents starts from the gapped mode. In the opposite limit of large total spin (two subspins are nearly parallel) the gapless modes become unstable earlier than the gapped one. Mass and spin supercurrents decay via phase slips, when vortices cross streamlines of supercurrent. The vortices participating in phase slips are nonsingular bicirculation vortices. They are characterized by two topological charges, which are winding numbers describing circulations of two angles around the vortex axis. The winding numbers can be half-integer. A particular example of a half-integer vortex is a half-quantum vortex with the superfluid velocity circulation $h/2m$. But the superfluid velocity circulation is not a topological charge, and in general the quantum of this circulation can be continuously tuned from 0 to $h/2m$.

Highlights

Spin superfluidity in magnetically ordered systems has been discussed for several decades [1,2,3,4,5,6,7,8,9,10,11,12]
In the present paper we demonstrate that the hydrodynamics of the antiferromagnetic spin-1 Bose-Einstein condensates (BEC) is similar to the LLG theory for a bipartite antiferromagnet with two sublattices, each of which is characterized by a vector of magnetization
The core radius of this vortex is of the order of the coherence length ξ0, and the condition of stability with respect to phase slips is similar to that obtained from the Landau criterion

Summary

INTRODUCTION

Spin superfluidity in magnetically ordered systems has been discussed for several decades [1,2,3,4,5,6,7,8,9,10,11,12]. It was already known that the hydrodynamics of ferromagnetic spin-1 BEC is described by equations of spin motion similar to those in the LLG theory in magnetism but taking into account the possibility of superfluid motion as a whole [17,18,19] This allowed us to use some results known from investigations of spin superfluidity in magnetically ordered solids. In the spin-1 BEC the singularity 1/r can be compensated without suppression of the superfluid density in the vortex core by a proper choice of the ratio between two topological charges (winding numbers) Such vortices are called nonsingular or continuous [21]. Magnetic field or by the intensity of spin pumping, which supports the nonequilibrium coherent precession state with a fixed z component of spin

HYDRODYNAMICS FROM THE GROSS-PITAEVSKII THEORY OF SPIN-1 BEC

COLLECTIVE MODES AND THE LANDAU CRITERION

NONSINGULAR VORTICES IN ANTIFERROMAGNETIC SPIN-1 BEC

BICIRCULATION VORTICES AND PHASE SLIPS

CONCLUSION