The resolution of the weak-exchange limit made rigorous, simple and general in binuclear complexes

Abstract

The correct interpretation of magnetic properties in the weak-exchange regime has remained a challenging task for several decades. In this regime, the effective exchange interaction between local spins is quite weak, of the same order of magnitude or smaller than the various anisotropic terms, which \textit{in fine} generates a complex set of levels characterized by spin intercalation if not significant spin mixing. Although the model multispin Hamiltonian, \hms{} = \js{} + \da{} +\db{} + \dab{}, is considered good enough to map the experimental energies at zero field and in the strong-exchange limit, theoretical works pointed out limitations of this simple model. This work revives the use of \hms{} from a new theoretical perspective, detailing point-by-point a strategy to correctly map the computational energies and wave functions onto \hms{}, thus validating it regardless of the exchange regime. We will distinguish two cases, based on experimentally characterized dicobalt(II) complexes from the literature. If centrosymmetry imposes alignment of the various rank-2 tensors constitutive of \hms{} in the first case, the absence of any symmetry element prevents such alignment in the second case. In such a context, the strategy provided herein becomes a powerful tool to rationalize the experimental magnetic data, since it is capable of fully and rigorously extracting the multispin model without any assumption on the orientation of its constitutive tensors. Finally, previous theoretical data related to a known dinickel(II) complex is reinterpreted, clarifying initial wanderings regarding the weak-exchange limit