Spin transport in an electrically-driven magnon gas near Bose-Einstein condensation: Hartree-Fock-Keldysh theory

Abstract

An easy-plane ferromagnetic insulator in a uniform external magnetic field and in contact with a phonon bath and a normal metal bath is studied theoretically in the presence of dc spin current injection via the spin Hall effect in the metal. The Keldysh path integral formalism is used to model the magnon gas driven into a nonequilibrium steady state by mismatched bath temperatures and/or electrical injection, and we analyze the magnon system in the normal (uncondensed) state, but close to the instability to Bose-Einstein condensation (BEC), within the self-consistent Hartree-Fock approximation. We find that the steady state magnon distribution function generally has a non-thermal form that cannot be described by a single effective chemical potential and effective temperature. We also show that the BEC instability in the electrically-driven magnon system is signaled by a sign change in the imaginary part of the poles for long-wavelength magnon modes and by the divergence of the nonequilibrium magnon distribution function. In the presence of two bath temperatures, we find that the correlation length of the superfluid order parameter fluctuations exhibits nontrivial finite temperature crossover behaviors that are richer than the standard crossover behaviors obtained for the vacuum-superfluid transition in an equilibrium dilute Bose gas. We study the consequences of these thermal crossovers on the magnon spin conductivity and obtain an inverse square-root divergence in the spin conductivity in the vicinity of the electrically-induced BEC instability. A spintronics device capable of testing our spin transport predictions is discussed.

14 pages, 8 figures, appendices

References in corpus (6)

• Bose-Einstein condensation of photons in an optical microcavity
• Non-equilibrium quantum condensation in an incoherently pumped dissipative system
• Dynamic phase diagram of dc-pumped magnon condensates
• Chemical potential of quasi-equilibrium magnon gas driven by pure spin current
• Green's function formalism for spin transport in metal-insulator-metal heterostructures
• Many-body theory of spin-current driven instabilities in magnetic insulators

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• Quantum Theory of Spin-Transfer and Spin-Pumping in Collinear Antiferromagnets and Ferrimagnets
• Ferroelectricity in a magnon Bose-Einstein condensate: Nonreciprocal superfluidity, exceptional points, and Majorana bosons
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