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arXiv:1703.08343 · Physical review. B./Physical review. B

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

Jaime Merino, A. C. Jacko, Amie L. Khosla, Benjamin James Powell

Published Nov 10, 2017• 9 citations
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Abstract

We consider layered decorated honeycomb lattices at two-thirds filling, as realized in some trinuclear organometallic complexes. Localized $S=1$ moments with a single-spin anisotropy emerge from the interplay of Coulomb repulsion and spin molecular-orbit coupling (SMOC). Magnetic anisotropies with bond-dependent exchange couplings occur in the honeycomb layers when the direct intracluster exchange and the spin molecular-orbital coupling are both present. We find that the effective spin exchange model within the layers is an XXZ + ${120}^{\ensuremath{\circ}}$ honeycomb quantum compass model. The intrinsic nonspherical symmetry of the multinuclear complexes leads to very different transverse and longitudinal spin molecular-orbital couplings, which greatly enhances the single-spin and exchange coupling anisotropies. The interlayer coupling is described by an XXZ model with anisotropic biquadratic terms. As the correlation strength increases the system becomes increasingly one-dimensional. Thus, if the ratio of SMOC to the interlayer hopping is small this stabilizes the Haldane phase. However, as the ratio increases there is a quantum phase transition to the topologically trivial ``$D$ phase.'' We also predict a quantum phase transition from a Haldane phase to a magnetically ordered phase at sufficiently strong external magnetic fields.

DOI
10.1103/physrevb.96.205118

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The single-orbital Hubbard model is often a good description of the low energy dynamics of strongly correlated electron systems. Importantly, the single-orbital Hubbard model at half-filling is able to capture the Mott metal-insulator transition that occurs in many materials. However, there are insulating phases (as well as other exotic phases) that occur due to strong electronic correlations in materials that are away from half-filling. In many cases, these additional phases occur because the constituent electrons of the material come from multi-orbital atomic environments that require more complicated descriptions such as the multi-orbital Hubbard model. In other cases, as we show in this thesis, the rich phase diagram arises from the underlying lattice because of special geometric features.For example, decorated lattices, which often occur in organometallics (e.g., metal-organic frameworks (MOFs)), have geometrical complexity due to the molecular structures that decorate the lattice. We argue that the effective description for many of these materials is the single-orbital Hubbard model. Yet, these materials still have rich phase diagrams because the molecular structures of the material cause effective multi-orbital interactions generated from the local Coulomb interaction.We investigate the single-orbital Hubbard model on the decorated honeycomb lattice at zero temperature using rotationally invariant slave-boson (RISB) theory in the mean-field approximation, at a range of fillings. Numerous metal-insulator transitions occur - the insulating phases include a real-space Mott insulator, a dimer Mott insulator, a trimer Mott insulator, flat-band ferromagnets, and a spin-1 Mott insulator, dominated by spin-triplet fluctuations. This menagerie of phases is caused by effective multi-orbital interactions arising from the interplay of electronic correlations, lattice structure, and band filling effects. For example, with only on-site Coulomb interactions, the spin-1 Mott insulator is driven by an effective Hund's coupling on a three-site ring that favors the formation of triplets when the three-site ring has four electrons. We argue that this exotic phase may be realized in layers of the organometallic molecular crystal Mo3S7(dmit)3.
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