Electronic structure and magnetic anisotropies of antiferromagnetic transition-metal difluorides

We compare GGA+U calculations with available experimental data and analyze the origin of magnetic anisotropies in MnF$_2$, FeF$_2$, CoF$_2$, and NiF$_2$. We confirm that the magnetic anisotropy of MnF$_2$ stems almost completely from the dipolar interaction, while magnetocrystalline anisotropy energy plays a dominant role in the other three compounds, and discuss how it depends on the details of band structure. The latter is critically compared to available optical measurements. The case of CoF$_2$, where magnetocrystalline anisotropy energy strongly depends on $U$, is put into contrast with FeF$_2$ where theoretical predictions of magnetic anisotropies are nearly quantitative.