Consequences of spin-orbit coupling for the Bose-Einstein condensation of magnons

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Abstract
In the first part we discuss how the BEC picture for magnons is modified by anisotropies induced by spin-orbit coupling. In particular, we focus on the effects of antisymmetric spin interactions and/or a staggered component of the g (gyromagnetic) tensor. Such terms lead to a gapped quasiparticle spectrum and a non-zero condensate density for all temperatures so that no phase transition occurs. We contrast this to the effect of crystal field anisotropies which are also induced by spin-orbit coupling. In the second part, we study the field-induced magnetic ordering in TlCuCl3 on a quantitative level. We show that the usual BEC picture does not allow for a good description of the experimental magnetisation data and argue that antisymmetric spin interactions and/or a staggered g tensor component are still crucial, although both are expected to be tiny in this compound due to crystal symmetries. Including this type of interaction, we obtain excellent agreement with experimental data.