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

TL;DR

This paper examines how spin-orbit coupling-induced anisotropies modify magnon Bose-Einstein condensation, revealing that antisymmetric interactions lead to a gapped spectrum and continuous condensate presence, challenging traditional phase transition models.

Contribution

It introduces the impact of spin-orbit coupling-induced anisotropies on magnon BEC and demonstrates their importance in accurately describing experimental magnetization data in TlCuCl3.

Findings

Antisymmetric spin interactions create a gapped quasiparticle spectrum.

Continuous condensate density exists without a phase transition.

Including tiny antisymmetric interactions aligns theory with experimental data.

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 nonzero 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 TlCuCl$_3$ 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.