Temperature dependence of the magnetic susceptibility for triangular-lattice antiferromagnets with spatially anisotropic exchange constants

Abstract

We present the temperature dependence of the uniform susceptibility of spin-half quantum antiferromagnets on spatially anisotropic triangular lattices, using high-temperature series expansions. We consider a model with two exchange constants ${J}_{1}$ and ${J}_{2}$ on a lattice that interpolates between the limits of a square lattice $({J}_{1}=0)$, a triangular lattice $({J}_{2}={J}_{1})$, and decoupled linear chains $({J}_{2}=0)$. In all cases, the susceptibility, which has a Curie-Weiss behavior at high temperatures, rolls over and begins to decrease below a peak temperature ${T}_{p}$. Scaling the exchange constants to get the same peak temperature shows that the susceptibilities for the square lattice and linear chain limits have similar magnitudes near the peak. Maximum deviation arises near the triangular-lattice limit, where frustration leads to much smaller susceptibility and with a flatter temperature dependence. We compare our results to the inorganic materials ${\mathrm{Cs}}_{2}{\mathrm{CuCl}}_{4}$ and ${\mathrm{Cs}}_{2}{\mathrm{CuBr}}_{4}$ and to a number of organic molecular crystals. We find that the former (${\mathrm{Cs}}_{2}{\mathrm{CuCl}}_{4}$ and ${\mathrm{Cs}}_{2}{\mathrm{CuBr}}_{4}$) are weakly frustrated and their exchange parameters determined through the temperature dependence of the susceptibility are in agreement with neutron-scattering measurements. In contrast, the organic materials considered are strongly frustrated with exchange parameters near the isotropic triangular-lattice limit.