  The Ohmic spin diode (OSD) is a recent concept in spintronics, which is based
on half-metallic magnets (HMMs) and spin-gapless semiconductors (SGSs).
Quaternary Heusler compounds offer a unique platform to realize the OSD for
room temperature applications as these materials possess very high Curie
temperatures as well as half-metallic and spin-gapless semiconducting behavior
within the same family. Using state-of-the-art first-principles calculations
combined with the non-equilibrium Green's function method we design four
different OSDs based on half-metallic and spin-gapless semiconducting
quaternary Heusler compounds. All four OSDs exhibit linear current-voltage
($I-V$) characteristics with zero threshold voltage $V_T$. We show that these
OSDs possess a small leakage current, which stems from the overlap of the
conduction and valence band edges of opposite spin channels around the Fermi
level in the SGS electrodes. The obtained on/off current ratios vary between
$30$ and $10^5$. Our results can pave the way for the experimental fabrication
of the OSDs within the family of ordered quaternary Heusler compounds.
