Low-temperature structural investigations of the frustrated quantum antiferromagnetsCs2Cu(Cl4−xBrx)

Abstract

Powder x-ray diffraction (PXRD) and single-crystal neutron scattering were used to study in detail the structural properties of the ${\mathrm{Cs}}_{2}\mathrm{Cu}({\mathrm{Cl}}_{4\ensuremath{-}x}{\mathrm{Br}}_{x})$ series, good realizations of layered triangular antiferromagnets. Detailed temperature-dependent PXRD reveal a pronounced anisotropy of the thermal expansion for the three different crystal directions of the orthorhombic structure without any structural phase transition down to 20 K. Remarkably, the anisotropy of the thermal expansion varies for different $x$, leading to distinct changes of the geometry of the local Cu environment as a function of temperature and composition. The refinement of the atomic positions confirms that for $x=1$ and 2, the Br atoms occupy distinct halogen sites in the $[{\text{Cu}X}_{4}]$ tetrahedra ($X$ = Cl, Br). The precise structure data are used to calculate the magnetic exchange couplings using density functional methods for $x=0$. We observe a pronounced temperature dependence of the calculated magnetic exchange couplings, reflected in the strong sensitivity of the magnetic exchange couplings on structural details. These calculations are in good agreement with the experimentally established values for ${\mathrm{Cs}}_{2}{\mathrm{CuCl}}_{4}$ if one takes the low-temperature structure data as a starting point.