Determination of the effective spin Hamiltonian of Mn6R6 referring to the spin density functional theory

An ab-initio calculation determines the effective spin model of Mn6R6. The model including the three-spin interactions (TSI model) shows inconsistency in the spatial configuration of the spin density (Fig. a). The best fit of the spin-density configuration is achieved by the frustrated spin interaction model (FSI model) (Fig. b).