Magnetic Susceptibility of the Kagome Antiferromagnet ZnCu_3(OH)_6Cl_2

We analyze the experimental data for the magnetic susceptibility of the material ZnCu_3(OH)_6Cl_2 in terms of the Kagome Lattice Heisenberg model (KLHM), discussing possible role of impurity spins, dilution, exchange anisotropy, and both out-of-plane and in-plane Dzyloshinski-Moriya (DM) anisotropies, with explicit theoretical calculations using the Numerical Linked Cluster (NLC) method and exact diagonalization (ED). The high-temperature experimental data are well described by the pure Heisenberg model with $J=170 K$. We show that the sudden upturn in the susceptibility around $T=75 K$ is due to DM interactions. We also observe that at intermediate temperatures, below $T=J$, our calculated magnetic susceptibility for KLHM fits remarkably well with a power law $T^{-0.25}$, and suggest possible origins of this behavior.