Magnetic structure of a multiferroic compound: Cu$_2$OCl$_2$
Résumé
The Cu$_2$OCl$_2$ compound has been shown to be a high-temperature spin-driven
multiferroic system, with a linear magneto-electric coupling. In this paper
we propose a complete study of its magnetic structure. We derive the low
energy magnetic Hamiltonian using ab-initio multi-reference configuration
interaction and the spin structure using Monte-Carlo simulations. Among
the three magnetic structures proposed in the literature from different
experimental results, our calculations support the incommensurate cycloid
magnetic structure with a $\vec q=(q_a,0,0)$ propagation vector. Using
symmetry analysis, we show that all experimental results (polarization,
magnetic order, magneto-electric coupling) can be accounted for in the
$Fd'd'2$ magnetic space group (2-fold axis along $\vec c$).