Bose-Einstein condensation of magnons in magnets with predominant ferromagnetic interactions

Abstract

We discuss Bose-Einstein condensation (BEC) of magnons in magnets with predominant ferromagnetic (FM) interaction in a magnetic field $H$ near saturation $({H}_{c})$. Because ${H}_{c}$ is independent of FM couplings, magnetic materials of this type can have small ${H}_{c}$ which makes them promising candidates for experimental investigation of BECs. Ferromagnets with easy-plane anisotropy and antiferromagnets (AFs) containing weakly coupled FM planes or chains are discussed in detail. We observe a small effective interaction between magnons near the quantum critical point in such magnets, in contrast to the AFs with strong AF coupling previously discussed. In particular, this smallness allows us to find crossovers in the critical temperature ${T}_{c}(H)\ensuremath{\propto}{({H}_{c}\ensuremath{-}H)}^{1∕\ensuremath{\phi}}$ from $\ensuremath{\phi}=3∕2$ to $\ensuremath{\phi}=1$ in quasi-one-dimensional magnets, and from $\ensuremath{\phi}=3∕2$ to $\ensuremath{\phi}\ensuremath{\approx}1$ $({T}_{c}\phantom{\rule{0.2em}{0ex}}\mathrm{ln}\phantom{\rule{0.2em}{0ex}}{T}_{c}\ensuremath{\propto}{H}_{c}\ensuremath{-}H)$ in quasi-two-dimensional ones.