Title: Effects of anisotropy in spin molecular-orbital coupling on effective spin models of trinuclear organometallic complexes,
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$^\circ$ honeycomb quantum compass model. The intrinsic non-spherical
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 a XXZ model with anisotropic biquadratic terms. As the correlation
strength increases the systems 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.