Characterizing and Overcoming Surface Paramagnetism in Magnetoelectric Antiferromagnets

We use a combination of density functional theory and Monte Carlo calculations to calculate the surface magnetization in magnetoelectric $\mathrm{C}{\mathrm{r}}_2{\mathrm{O}}_3$ at finite temperatures. Such antiferromagnets, lacking both inversion and time-reversal symmetries, are required by symmetry to posses an uncompensated magnetization density on particular surface terminations. Here, we first show that the uppermost layer of magnetic moments on the $(001)$ surface remain paramagnetic at the bulk Néel temperature, bringing the theoretical estimate of surface magnetization density in line with experiment. We demonstrate that the lower surface ordering temperature compared to bulk is a generic feature of surface magnetization when the termination reduces the effective Heisenberg coupling. We then propose two methods by which the surface magnetization in $\mathrm{C}{\mathrm{r}}_2{\mathrm{O}}_3$ could be stabilised at higher temperatures. Specifically, we show that the effective coupling of surface magnetic ions can be drastically increased either by a different choice of surface Miller plane, or by $\mathrm{F}\mathrm{e}$ doping. Our findings provide an improved understanding of surface magnetization properties in AFMs.