Magnonic Superfluidity Versus Bose Condensation
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Applied Magnetic Resonance
ORIGINAL PAPER
Magnonic Superfluidity Versus Bose Condensation Yury Bunkov1 Received: 28 April 2020 / Revised: 12 July 2020 © Springer-Verlag GmbH Austria, part of Springer Nature 2020
Abstract This article discusses two different coherent quantum phenomena of magnonic bosons: Bose–Einstein condensation (mBEC) and Superfluid State of Magnons (SSM). What is the difference between the two? Magnon BEC is a quantum phenomenon determined by local density of bosonic quasiparticles. The superfluid state of magnons is a long-range coherent quantum state characterized by the rigidity of the order parameter. This is similar to the states of mass superfluidity and superconductivity. In this state, the deflected magnetization can coherently precess even in a strongly inhomogeneous magnetic field. The magnons superflow restore the coherence of SSM after a perturbation. The critical Landau velocity of the coherent magnon flow is determined by an energy gap arising from the repulsion of magnons. This article describes in detail the mechanism of SSM formation.
1 Introduction Magnon is the quantum excitation of a magnetically ordered system. This corresponds to a quantum transition of single spin, the energy of which is distributed over an ensemble of magnetic moments at a distance characterized by the magnitude of the exchange interaction between them. Therefore, magnon is a quantum quasiparticle with integer spin and obeys Bose statistics. At a low concentration, a magnon gas produces spin waves—an object of classical physics described by the Landau–Lifshitz equations. The process of magnetic moment transfer due to the gradient of phase of magnetization precession in the limit of small excitation is also described in the framework of classical physics, analogous to the process of transfer of torsional moment in solids. Magnon quantum phenomena occur at a sufficiently high concentration of magnons and lead to the formation of a magnon Bose–Einstein condensation (mBEC). Strictly speaking, the properties of mBECs are beyond the scope of classical physics and are traditionally described by the Gross–Pitaevskii * Yury Bunkov [email protected] 1
Russian Quantum Center, Skolkovo 143025, Moscow, Russia
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formalism developed to describe the atomic Bose condensate [1]. The magnon density required for the formation of the Bose condensate is easy to calculate for various magnetically ordered substances, as shown in [2]. In particular, an increase in the number of magnons leads to a decrease in the magnetization of the sample. A change in magnetization is a direct result of a change in the density of magnons. Unlike atoms, the number of which is conserved, the density of quasiparticles can change due to their creation and annihilation from a vacuum (magnetically ordered state) according to the Holstein–Primakoff formalism [3]. Under conditions of a finite temperature, the concentration of thermally activated magnons is always lower than the concentration necessary for mBEC fo
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