  Recently, in the seemingly narrow gap insulating NiCrO$_3$ with the
trigonally distorted (R-3c) perovskite-like structure, a compensated half-metal
(CHM) is predicted, as applying a modest pressure. Using ab initio calculations
including both Coulomb correlations and spin-orbit coupling (SOC), we
investigate the as-yet-unsynthesized PdCrO$_3$, isostructural and isovalent to
NiCrO$_3$. Upon applying the on-site Coulomb repulsion $U$ to both Pd and Cr
ions, the Cr spin moment is precisely compensated with the antialigned spin
moments of Pd and oxygens. Coincidentally only one spin channel remains
metallic due to the twice larger width of the Pd 4d bands than the Ni 3d bands
in NiCrO$_3$, indicating CHM in ambient pressure. Inclusion of SOC as well as
correlation effects (LDA+U+SOC) produces a SOC constant enhanced twice over the
value of LDA+SOC, leading to unusually large orbital moment of --0.25 $\mu_B$
on Pd. However, the half-metallicity still survives, so that a transition of
CHM to a half-metallic ferrimagnet occurs due to Coulomb enhanced SOC. On the
other hand, an isovalent, but presumed cubic double perovskite La$_2$PdCrO$_6$
is expected to be a half-metal ferromagnet with tiny orbital moments.
