Linear magnetoelectricity in the Zintl phase pnictides (Ba, Ca, Sr)${\mathrm{Mn}}_2$(P, As, Sb)${}_2$ from first-principles calculations

We report a comprehensive set of density functional theory calculations on the family of layered antiferromagnetic manganese pnictides $(\mathrm{Ba},\mathrm{Ca},\mathrm{Sr}){\mathrm{Mn}}_2{(P,\mathrm{As},\mathrm{Sb})}_2$. We characterize all components to the linear magnetoelectric (ME) tensor $\alpha$, which are parsed into their contributions from spin and orbital moments for both lattice-mediated and their clamped-ion electronic analogs. Our main results show that the orbital magnetization components cannot be neglected in these systems. The ME response is dominated by electronic effects with total $\alpha$ values exceeding those of the prototypical ${\mathrm{Cr}}_2{O}_3$ (i.e., $\alpha \simeq 6.79$ ps/m in ${\mathrm{BaMn}}_2{\mathrm{As}}_2$). We also identify a strong correlation with the computed ME susceptibility on pnictogen substitution in the trigonal subfamily albeit with weaker amplitudes ($\alpha \approx 0.2$–1.7 ps/m). Additionally, we provide the dependence of these predictions on the Hubbard $+U$ correction, at the level of the local density approximation, which shows large variations on the calculated ME coefficients in the tetragonal compounds highlighting the role of strong correlation in these compounds.