  In order to explore the effects of structural geometry on properties of
correlated metals we investigate the magnetic properties of cubic (3C) and
hexagonal (4H) BaRuO$_3$. While the 3C variant of BaRuO$_3$ is ferromagnetic
below 60K, the 4H phase does not show any long-range magnetic order, however,
there is experimental evidence of short-range antiferromagnetic correlations.
Employing a combination of computational tools, namely density-functional
theory and dynamical mean-field theory calculations, we probe the origin of
contrasting magnetic properties of BaRuO$_3$ in the 3C and 4H structures. Our
study reveals that the difference in connectivity of RuO$_6$ octahedra in the
two phases results in different Ru-O covalency, which in turn influences
substantially the strengths of screened interaction values for Hubbard $U$ and
Hund's rule $J$. With estimated $U$ and $J$ values, the 3C phase turns out to
be a ferromagnetic metal, while the 4H phase shows paramagnetic behavior with
vanishing ordered moments. However, this paramagnetic phase bears signatures of
antiferromagnetic correlations, as confirmed by a calculation of the magnetic
susceptibility. We find that the 4H phase is found to be at the verge of
antiferromagnetic long-range order, which can be stabilized upon slight changes
of screened Coulomb parameters $U$ and $J$, opening up the possibility of
achieving a rare example of an antiferromagnetic metal.
