Bose-Einstein condensation of magnons in quantum magnets with spin-orbit coupling in a Zeeman field

Abstract

We study the response of a quantum magnet with spin-orbit coupling (SOC) to a Zeeman field by constructing effective actions and performing renormalization group (RG) analysis. There are several novel classes of quantum phase transitions at a low ${h}_{c1}$ and an upper critical field ${h}_{c2}$ driven by magnon condensations at commensurate (C) or incommensurate (IC) momenta $0<{k}_{0}<\ensuremath{\pi}$. The intermediate IC-skyrmion crystal (IC-SkX) phase is controlled by a line of fixed points in the RG flows labeled by ${k}_{0}$. We derive the relations between the quantum spin and the order parameters of the effective actions which determine the spin-orbital structures of the IC-SkX phase. We also analyze the operator contents near ${h}_{c1}$ and ${h}_{c2}$ which determine the exotic excitation spectra inside the IC-SkX. The intrinsic differences between the magnon condensations at the C and IC momenta are explored. The two critical fields ${h}_{c1}<{h}_{c2}$ and the intermediate IC-SkX phase could be a generic feature to any quantum magnets with SOC in a Zeeman field. Experimental implications to some materials or cold atom systems with SOC in a Zeeman field are presented.