Hard-core boson approach to the spin-1/2 triangular-lattice antiferromagnet Cs$_2$CuCl$_4$ at finite temperatures in magnetic fields higher than the saturation field

摘要

We study the high magnetic field regime of the antiferromagnetic insulatorCs$_2$CuCl$_4$ by expressing the spin-1/2 operators in the relevant Heisenbergmodel in terms of hard-core bosons and implementing the hard-core constraintvia an infinite on-site interaction. We focus on the case where the externalmagnetic field exceeds the saturation field $B_{c}\approx8.5\;\mathrm{T}$ andis oriented along the crystallographic $a$ axis perpendicular to the latticeplane. Because in this case the excited states are separated by an energy gapfrom the ground state, we may use the self-consistent ladder approximation totake the strong correlations due to the hard-core constraint into account. InCs$_2$CuCl$_4$ there are additional interactions besides the hard-coreinteraction which we treat in self-consistent Hartree-Fock approximation. Wecalculate the spectral function of the hard-core bosons from which we obtainthe in-plane components of the dynamic structure factor, the magneticsusceptibility, and the specific heat. Our results for the specific heat are ingood agreement with the available experimental data. We conclude that theself-consistent ladder approximation in combination with a self-consistentHartree-Fock decoupling of the non-hard-core interactions gives an accuratedescription of the physical properties of gapped hard-core bosons in twodimensions at finite temperatures.