Dzyaloshinskii-Moriya anisotropy and nonmagnetic impurities in the s=12 kagome system ZnCu3(OH)6Cl2

Abstract

Motivated by recent nuclear magnetic resonance experiments on ${\text{ZnCu}}_3{\left(\text{OH}\right)}_6{\text{Cl}}_2$, we present an exact-diagonalization study of the combined effects of nonmagnetic impurities and Dzyaloshinskii-Moriya (DM) interactions in the $s=1/2$ kagome antiferromagnet. The local response to an applied field and correlation-matrix data reveal that the dimer freezing which occurs around each impurity for $D=0$ persists at least up to $D/J\simeq 0.06$, where $J$ and $D$ denote, respectively, the exchange and DM interaction energies. The phase transition to the $\left(Q=0\right)$ semiclassical $120°$ state favored at large $D$ takes place at $D/J\simeq 0.1$. However, the dimers next to the impurity sites remain strong up to values $D\sim J$, far above this critical point, and thus do not participate fully in the ordered state. We discuss the implications of our results for experiments on ${\text{ZnCu}}_3{\left(\text{OH}\right)}_6{\text{Cl}}_2$.