Erratum: Heisenberg and Dzyaloshinskii-Moriya interactions controlled by molecular packing in trinuclear organometallic clusters [Phys. Rev. B 95 , 094432 (2017)]

Effects of anisotropy in spin molecular-orbital coupling on effective spin models of trinuclear organometallic complexes

“…SMOC is an emergent coupling between electron currents circulating around the cyclic molecules and the electron spin. Also by tuning the relative orientation between molecules in the crystal a Dzyaloshinskii-Moriya interaction can be generated [15]. All the above suggests that these materials are ideal playgrounds for the realization of quantum compass models [3].…”

“…This suggests that anisotropic spin exchange interactions may be easily generated in organometallic complexes due to their intrinsic structure. These anisotropies may be further enhanced by the anisotropic SMOC typically found in these systems [13,15]. SMOC is an emergent coupling between electron currents circulating around the cyclic molecules and the electron spin.…”

“…The onsite Coulomb repulsion U leads to S = 1 moments localized at each triangular cluster from which SMOC, λ, induces a single-spin anisotropy D. The S = 1 moments behave as weakly coupled chains due to the decorated lattice structure of trinuclear organometallic complexes [14,15]. The lattice structure is such that three hopping amplitudes connect two nearest-neighbor molecules along the c direction while only one hopping amplitude connects nearest-neighbor molecules in the a-b planes; cf.…”

“…Recently [14,15] we derived an effective superexchange Hamiltonian that captures the magnetic properties of trinuclear coordinated complexes at strong coupling. The onsite Coulomb repulsion U leads to S = 1 moments localized at each triangular cluster from which SMOC, λ, induces a single-spin anisotropy D. The S = 1 moments behave as weakly coupled chains due to the decorated lattice structure of trinuclear organometallic complexes [14,15].…”

“…There are several strongly correlated molecular materials in which spin-orbit coupling is relevant including, metalorganic frameworks [8], layered organic salts [9,10], and multinuclear coordinated organometallic complexes [11][12][13][14][15]. The elementary building blocks of multinuclear complexes are molecular clusters containing transition metal ions whose d orbitals are hybridized with molecular orbitals where each of the hybrids is typically described by a single Wannier orbital [16].…”