Magnetic interactions and spin orders in Cr${}_8$ and V${}_8$ ring-shaped molecular magnets from non-collinear ab initio calculations

Abstract

We investigate the magnetic interactions in the octanuclear molecular rings Cr${}_8$ and V${}_8$ using density functional theory within a non-collinear framework. By probing magnetic configurations with fully unconstrained three-dimensional spin orientations, we systematically explore the rotational degrees of freedom of neighboring spins and go beyond the conventional low-energy Heisenberg description. This approach distinguishes in-plane from out-of-plane exchange interactions, quantifies biquadratic spin couplings, and reveals significant antisymmetric exchange of the Dzyaloshinskii-Moriya type. The comparison with linear chains of equal composition reveals a clear dependence of the Dzyaloshinskii-Moriya interactions on the curvature of the annular structure. Exact diagonalization of the spin Hamiltonian constructed from the computed effective couplings demonstrates the role of these unconventional interactions and identifies an exotic ground state in V${}_8$, driven by the competition between nearest- and next-nearest-neighbor exchange couplings of opposite sign. The closest quantitative agreement with experiment, particularly for Cr${}_8$, is achieved using extended Hubbard functionals that explicitly incorporate intersite hybridization couplings.

arXiv comment20 pages, 17 figures