  We investigate the electronic and magnetic structures and the character and
direction of spin and orbital moments of the recently synthesized quadruple
perovskite cobaltovanadate CaCo3V4O12 using a selection of methods from density
functional theory. Implementing the generalized gradient approximation and the
Hubbard U correction (GGA+U), ferromagnetic spin alignment leads to
half-metallicity rather than the observed narrow gap insulating behavior.
Including spin-orbit coupling (SOC) leaves a half-semimetallic spectrum which
is essentially Mott insulating. SOC is crucial for the Mott insulating
character of the V d^1 ion, breaking the d_{m=\pm 1} degeneracy and also giving
a substantial orbital moment. Evidence is obtained of the large orbital moments
on Co that have been inferred from the measured susceptibility. Switching to
the orbital polarization (OP) functional, GGA+OP+SOC also displays clear
tendencies toward very large orbital moments but in its own distinctive manner.
In both approaches, application of SOC, which requires specification of the
direction of the spin, introduces large differences in the orbital moments of
the three Co ions in the primitive cell. We study a fictitious but simpler
cousin compound Ca3CoV4O12 (Ca replacing two of the Co atoms) to probe in more
transparent fashion the interplay of spin and orbital degrees of freedom with
the local environment of the planar CoO4 units. The observation that the
underlying mechanisms seems to be local to a CoO4 plaquette, and that there is
very strong coupling of the size of the orbital moment to the spin direction,
strongly suggest non-collinear spins, not only on Co but on the V sublattice as
well.
