Robust half-metallic antiferromagnets $\mathrm{La}A\mathrm{V}\mathrm{Os}{\mathrm{O}}_6$ and $\mathrm{La}A\mathrm{Mo}Y{\mathrm{O}}_6$ ($A=\mathrm{Ca}$,Sr,Ba; $Y=\mathrm{Re}$,Tc) from first-principles calculations

We have theoretically designed three families of the half-metallic (HM) antiferromagnets (AFM), namely, $\mathrm{La}A\mathrm{V}\mathrm{Os}{\mathrm{O}}_6$, $\mathrm{La}A\mathrm{Mo}\mathrm{Tc}{\mathrm{O}}_6$, and $\mathrm{La}A\mathrm{Mo}\mathrm{Re}{\mathrm{O}}_6$ ($A=\mathrm{Ca}$,Sr,Ba), based on a systematic ab initio study of the ordered double perovskites $\mathrm{La}AB{B}^{\prime }{\mathrm{O}}_6$ with the possible $B$ and $B^{\prime }$ pairs from all the $3d$, $4d$, and $5d$ transition metal elements being considered. Electronic structure calculations based on first-principles density-functional theory with generalized gradient approximation for more than 60 double perovskites $\mathrm{La}\mathrm{Ca}B{B}^{\prime }{\mathrm{O}}_6$ have been performed using the all-electron full-potential linearized augmented-plane-wave method. The found HM-AFM state in these materials survives the full ab initio lattice constant and atomic position optimizations which were carried out using the frozen-core full potential projector augmented wave method. It is found that the HM-AFM properties predicted previously in some of the double perovskites would disappear after the full structural optimizations. The AFM is attributed to both the superexchange mechanism and the generalized double exchange mechanism via the $B\left(t_{2g}\right)\text{−}\mathrm{O}\left(2p_{\pi }\right)\text{−}{B}^{\prime }\left(t_{2g}\right)$ coupling and the latter is also believed to be the origin of the HM. Finally, in our search for the HM-AFMs, we find $\mathrm{La}A\mathrm{Cr}\mathrm{Tc}{\mathrm{O}}_6$ and $\mathrm{La}A\mathrm{Cr}\mathrm{Re}{\mathrm{O}}_6$ to be AFM insulators of an unconventional type in the sense that the two antiferromagnetic coupled ions consist of two different elements and that the two spin-resolved densities of states are no longer the same. It is hoped that our interesting predictions would stimulate further experimental searches for the HM-AFMs which have so far been unsuccessful.