Magnon Bose–Einstein condensation and spin superfluidity

Abstract

Bose–Einstein condensation (BEC) is a quantum phenomenon of formation of a collectivequantum state in which a macroscopic number of particles occupy the lowest energy stateand thus is governed by a single wavefunction. Here we highlight the BEC in a magneticsubsystem—the BEC of magnons, elementary magnetic excitations. The magnon BEC ismanifested as the spontaneously emerging state of the precessing spins, in whichall spins precess with the same frequency and phase even in an inhomogeneousmagnetic field. The coherent spin precession was observed first in superfluid 3He-B and this domain was called the homogeneously precessing domain (HPD).The main feature of the HPD is the induction decay signal, which ranges overmany orders of magnitude longer than is prescribed by the inhomogeneity ofmagnetic field. This means that spins precess not with a local Larmor frequency, butcoherently with a common frequency and phase. This BEC can also be created andstabilized by continuous NMR pumping. In this case the NMR frequency playsthe role of a magnon chemical potential, which determines the density of themagnon condensate. The interference between two condensates has also beendemonstrated. It was shown that HPD exhibits all the properties of spin superfluidity. Themain property is the existence of a spin supercurrent. This spin supercurrentflows separately from the mass current. Transfer of magnetization by the spinsupercurrent by a distance of more than 1 cm has been observed. Also related phenomenahave been observed: the spin current Josephson effect; the phase-slip processes atthe critical current; and the spin current vortex—a topological defect which isthe analog of a quantized vortex in superfluids and of an Abrikosov vortex insuperconductors; and so on. It is important to mention that the spin supercurrent is amagnetic phenomenon, which is not directly related to the mass superfluidity of 3He: it is the consequence of a specific antiferromagnetic ordering in superfluid 3He. Several different states of coherent precession have been observed in 3He-B: the homogeneously precessing domain (HPD); a persistent signal formed byQ-balls at very low temperatures; coherent precession with fractionalmagnetization; and two new modes of coherent precession in compressedaerogel. In compressed aerogel the coherent precession has been also found in 3He-A. We demonstrate that the coherent precession of magnetization is a true BEC ofmagnons, with the magnon interaction term in the Gross–Pitaevskii equation beingprovided by spin–orbit coupling which is different for different states of the magnonBEC.