Magnetism of Cu${X}_{2}$ frustrated chains ($X$ = F, Cl, Br): Role of covalency

Magnetism of Cu $X_{2}$ frustrated chains ( $X$ = F, Cl, Br): Role of covalency

S. Lebernegg, M. Schmitt, A. A. Tsirlin, O. Janson, and H. Rosner

Phys. Rev. B 87, 155111 – Published 3 April 2013

Abstract

Periodic and cluster density functional theory (DFT) calculations, including DFT+ $U$ and hybrid functionals, are applied to study magnetostructural correlations in spin- $\frac{1}{2}$ frustrated chain compounds Cu $X$ $_{2}$ : CuCl $_{2}$ , CuBr $_{2}$ , and a fictitious chain structure of CuF $_{2}$ . The nearest-neighbor and second-neighbor exchange integrals $J_{1}$ and $J_{2}$ are evaluated as a function of the Cu– $X$ –Cu bridging angle $θ$ in the physically relevant range 80 $^{\circ}$ –110 $^{\circ}$ . In the ionic CuF $_{2}$ , $J_{1}$ is ferromagnetic for $θ \leq 100^{\circ}$ . For larger angles, the antiferromagnetic superexchange contribution becomes dominant, in accord with the Goodenough-Kanamori-Anderson rules. However, both CuCl $_{2}$ and CuBr $_{2}$ feature ferromagnetic $J_{1}$ in the whole angular range studied. This surprising behavior is ascribed to the increased covalency in the Cl and Br compounds, which amplifies the contribution from Hund's exchange on the ligand atoms and renders $J_{1}$ ferromagnetic. At the same time, the larger spatial extent of $X$ orbitals enhances the antiferromagnetic $J_{2}$ , which is realized via the long-range Cu– $X$ – $X$ –Cu paths. Both periodic and cluster approaches supply a consistent description of the magnetic behavior which is in good agreement with the experimental data for CuCl $_{2}$ and CuBr $_{2}$ . Thus, owing to their simplicity, cluster calculations have excellent potential to study magnetic correlations in more involved spin lattices, and facilitate application of quantum-chemical methods.