Analysis of the physical contributions to magnetic couplings in broken symmetry density functional theory approach

We present a new and simple scheme that aims to decompose into its main physical contributions the magnetic exchange interaction between two unpaired electrons. It is based on the popular broken-symmetry density functional theory (DFT) approach and relies on the frozen orbital capabilities of the local self-consistent field method. Accordingly, the magnetic exchange interaction energy can be separated into three main contributions: the direct exchange between magnetic orbitals, the spin polarization of the core orbitals, and the relaxation of the magnetic orbitals (kinetic exchange). This decomposition scheme is applied to a series of binuclear inorganic magnetic compounds both ferromagnetic and antiferromagnetic. The direct exchange is determined from the restricted DFT description. On the one hand, starting from the restricted orbital set and relaxing only the magnetic orbitals provides the kinetic exchange contribution and an estimate of the t and U parameters of the generalized Anderson mechanism. On the other hand, relaxing the core orbitals only introduces the spin polarization contribution. The decomposition leads to almost additive contributions. The effect of the amount of Hartree-Fock exchange on the different contributions is analyzed.