  First-principles density functional theory (DFT) is used to investigate the
electronic and magnetic properties of Sr$_4$Rh$_3$O$_{10}$, a member of the
Ruddlesden-Popper series. Based on the DFT calculations taking into account the
co-operative effect of Coulomb interaction ($U$) and spin-orbit couplings
(SOC), Sr$_4$Rh$_3$O$_{10}$ is found to be a half metallic ferromagnet (HMF)
with total angular moment $\mu_{\rm {tot}}$=12$\mu_B$ per unit cell. The
material has almost 100$\%$ spin-polarization at the Fermi level despite of
sizable SOC. Replacement of Rh atom by the isovalent Co atom is considered.
Upon full-replacement of Co, a low-spin to intermediate spin transition happens
resulting in a HMF state with the total angular moment three-time larger (i.e.
$\mu_{\rm {tot}}$=36$\mu_B$ per unit cell), compared to Sr$_4$Rh$_3$O$_{10}$.
We propose Sr$_4$Rh$_3$O$_{10}$ and Sr$_4$Co$_3$O$_{10}$ as candidates of half
metals.

Materials Science;Mesoscale and Nanoscale Physics