Magnetic Susceptibility of the Kagome Antiferromagnet ${\mathrm{ZnCu}}_3(\mathrm{OH}{)}_6{\mathrm{Cl}}_2$

We analyze the experimental data for the magnetic susceptibility of the material ${\mathrm{ZnCu}}_3(\mathrm{OH}{)}_6{\mathrm{Cl}}_2$ 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 method and exact diagonalization. The high-temperature experimental data are well described by the pure Heisenberg model with $J=170\mathrm{K}$. We show that the sudden upturn in the susceptibility around $T=75\mathrm{K}$ is due to DM interactions. We also observe that at intermediate temperatures, below $T=J$, our calculated susceptibility for KLHM fits well with a power law $T^{-0.25}$.

Figure 1

Temperature dependent effective Curie-Weiss temperature $T_{\mathrm{CW}}^{\mathrm{eff}}$ for the KLHM. The inset shows fits to the experimental data of Refs. 5, 6. For both experimental cases we have taken $J=170\mathrm{K}$. The $g$ factors needed for the fit are 2.19 for the data from Ref. 5 and 2.33 for the data from Ref. 6. On the theoretical side, the two highest order NLC results are shown.

Figure 2

Comparison of KLHM susceptibility with experimental susceptibility after subtracting Curie contributions from 3% and 6% impurities.

Figure 3

NLC results for the magnetic susceptibility of the KLHM with hole concentration $c$ ranging from 0% to 10%.

Figure 4

(a) 15 sites ED calculation of the powder susceptibility with a DM term $D_p=0.3J$ and different values of $D_z$, compared with experiments and pure KLHM. (b) Anisotropy vs temperature for $D_p=0.3J$ and different values of $D_z$.

Figure 5

Log-log plot of the susceptibility of the KLHM. In the inset we show log-log plots of the entropy of the pure KLHM and in the presence of DM terms. Straight lines following the data are $\chi \sim T^{-0.25}$ (low $T$), $\chi =1/(4T)$ (high $T$), and $S\sim T^{0.4}$ (inset).