Magnetism of (LaCoO$_3$)$_n$+(LaTiO$_3$)$_n$ superlattices with $n=1,2$

LaCoO$_3$ provides a poignant example of a transition metal oxide where the cobalt cations display multiple spin states and spin transitions and which continues to garner substantial attention. In this work, we describe first principles studies, based on DFT+$U$ theory, of superlattices containing LaCoO$_3$, specifically (LaCoO$_3$)$_n$+(LaTiO$_3$)$_n$ for $n=1,2$. The superlattices show strong electron transfer from Ti to Co resulting in Co$^{2+}$, significant structural distortions and a robust orbital polarization of Co$^{2+}$. We predict high-spin Co$^{2+}$ and a checkerboard or G-type antiferromagnetic (AFM) ground state. We provide a detailed analysis of the magnetic interactions and phases in the superlattices. We predict that ferromagnetic order on the Co${2+}$ can be stabilized by hole doping (e.g., replacing La by Sr) which is rather unusual for Co$^{2+}$ cations.