Dzyaloshinskii-Moriya anisotropy and non-magnetic impurities in the $s = 1/2$ kagome system ZnCu_3(OH)_6Cl_2

TL;DR

This study uses exact diagonalization to explore how non-magnetic impurities and Dzyaloshinskii-Moriya interactions influence the magnetic properties of the $s=1/2$ kagome antiferromagnet, relevant for understanding experimental observations in ZnCu$_3$(OH)$_6$Cl$_2$.

Contribution

It provides the first detailed analysis of impurity effects combined with DM interactions in the kagome system using exact diagonalization, revealing persistence of dimer freezing and phase transition points.

Findings

Dimer freezing persists up to D/J ≈ 0.06.

Phase transition to semiclassical order occurs at D/J ≈ 0.1.

Impurity-adjacent dimers remain strong even at high D values.

Abstract

Motivated by recent nuclear magnetic resonance experiments on ZnCu$_3$(OH)$_6$Cl$_2$, we present an exact-diagonalization study of the combined effects of non-magnetic 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 ($Q = 0$) semiclassical, 120$^\circ$ 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 ZnCu$_3$(OH)$_6$Cl$_2$.