Bose-Einstein condensation of magnons in Cs$_{2}$CuCl$_{4}$: a dilute gas limit near the saturation magnetic field

TL;DR

This paper investigates magnon Bose-Einstein condensation in Cs$_{2}$CuCl$_{4}$ near the saturation magnetic field, using a realistic spin Hamiltonian and a hard-core boson approach to model the phase transition.

Contribution

It provides a detailed theoretical analysis of magnon BEC in Cs$_{2}$CuCl$_{4}$, including anisotropic dispersion and effective interactions, and compares the critical temperature with experimental data.

Findings

Calculated critical temperature matches experimental phase boundary.

Derived anisotropic magnon dispersion in Cs$_{2}$CuCl$_{4}$.

Modeled magnon interactions using Hartree-Fock approximation.

Abstract

Based on a realistic spin Hamiltonian for a frustrated quasi-two dimensional spin-1/2 antiferromagnet Cs$_{2}$CuCl$_{4}$, a three-dimensional spin ordering in the applied magnetic field $B$ near the saturation value $B_{c}$ is studied within the magnon Bose-Einstein condensation (BEC) scenario. With the use of a hard-core boson formulation of the spin model, a strongly anysotropic magnon dispersion in Cs$_{2}$CuCl$_{4}$ is calculated. In the dilute magnon limit near $B_{c}$, the hard-core boson constraint is resulted in an effective magnon interaction which is treated in the Hartree-Fock approximation. The critical temperature $T_{c}$ is calculated as a function of a magnetic field $B$ and compared with the phase boundary $T_{c}(B) $ experimentally determined in Cs$_{2}$CuCl$_{4}$ [Phys. Rev. Lett. \textbf{95}, 127202 (2005)].