Is Herbertsmithite far from an ideal antiferromagnet? Ab-initio answer including in-plane Dzyaloshinskii-Moriya interactions and coupling with extra-plane impurities
Herbertsmithite is known as the archetype of a S=1/2 nearest-neighbor Heisenberg antiferromagnet on the Kagomé lattice, theoretically presumed to be a quantum gapless spin liquid. However, more and more experiments reveal that the model suffers from deviations from the ideal one, evidenced at very low temperatures. This detailed ab initio study focuses on two such deviations that have never been quantitatively calculated: the anisotropic exchange interactions and the Heisenberg exchange with extra-plane magnetic impurities. The Dzyaloshinskii-Moriya interaction is found to have an in-plane component almost three times larger than the out-of-plane component, but typically obviated in theoretical studies. Moreover, it is shown that the extra-plane magnetic impurities have a strong ferromagnetic interaction (minus half the main exchange $J_1$ ) with the Kagomé magnetic sites. Combined with an estimated occurrence of these magnetic impurities of $\sim15\%$, the present results indicate that two-dimensional magnetic models only describe part of the physics.