Bose-Einstein condensation of magnons in Cs${}_2$CuCl${}_4$: a dilute gas limit near the saturation magnetic field

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)].