Ab initio calculation on Herbertsmithite: exchange interactions including extra-plane magnetic impurities, Dzyaloshinskii-Moriya and anisotropic coupling

Abstract: A detailed ab initio evaluation of the isotropic and anisotropic exchange interactions of Herbertsmithite is presented. This compound crystallizes in a so-called Kagome lattice and the S=1/2 spin structure is not fully resolved despite numerous experimental and theoretical studies. The present study not only focusses on the leading in-plane nearest neighbor isotropic interactions, but also other less well studied interactions such as the anisotropic exchange and the Dzyaloshinskii-Moriya (DM) interactions. The anisotropic exchange is very weak, but the DM interactions are sizeable with a strong in-plane component, typically obviated in model studies. Moreover, it is shown that the extra-plane magnetic impurities have a non-negligible interaction with the regular in-plane magnetic sites. Combined with an estimated occurrence of these magnetic impurities of ~15%, the present results indicate that two-dimensional magnetic models only describe part of the physics.