The field-induced magnetic ordering transition in TlCuCl$_3$

TL;DR

This paper investigates the magnetic ordering transition in TlCuCl$_3$ under magnetic field, using a bond-operator approach to model magnons as hard-core bosons, and discusses the effects of anisotropy and spin interactions.

Contribution

It provides a quantitative analysis of the magnon Bose-Einstein condensation scenario in TlCuCl$_3$ using an exact hard-core boson model and includes effects of anisotropy and spin interactions.

Findings

The model accurately reproduces experimental magnetization and specific heat data.

Predictions are made for the quasiparticle gap that can be tested experimentally.

The validity of the Hartree-Fock-Popov approximation is discussed.

Abstract

In the first part we investigate in detail if the Bose-Einstein condensation scenario for magnons can quantitatively explain the observed field-induced magnetic ordering in TlCuCl$_3$. We use a bond-operator approach to map the spin system onto hard-core bosons and exactly account for the hard-core constraint in the dilute limit. We solve the hard-core model within the Hartree-Fock-Popov approximation and discuss its validity and the consequences of this approximation for the critical properties. In the second part the effects of spin-phonon and spin-orbit coupling are discussed within this framework. We show that the experimental magnetization and specific heat data are well described if a certain type of anisotropy is included. We also present predictions for the quasiparticle gap which might be tested in the future.