Based on the realistic spin Hamiltonian for the frustrated quasi-two-dimensional spin-$1∕2$ antiferromagnet ${\mathrm{Cs}}_2{\mathrm{CuCl}}_4$, 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 scenario. Using a hard-core boson formulation of the spin model, a strongly anisotropic magnon dispersion in ${\mathrm{Cs}}_2{\mathrm{CuCl}}_4$ is calculated. In the dilute magnon limit near $B_c$, the hard-core boson constraint results in an effective magnon interaction which is treated in the Hartree-Fock approximation. The critical temperature $T_c$ is calculated as a function of the magnetic field $B$ and compared with the phase boundary $T_c\left(B\right)$ experimentally determined in ${\mathrm{Cs}}_2{\mathrm{CuCl}}_4$ [Phys. Rev. Lett. 95, 127202 (2005)].

• Received 20 September 2005

DOI:https://doi.org/10.1103/PhysRevB.74.134417