First-principles study on the electronic and magnetic properties of Ba2FeSi2O7 and Ba2CoGe2O7

Melilite structural materials have been widely studied in the past two decades due to their interesting physical properties, such as noncollinear magnetism and multiferroicity. Here, we present a theoretical investigation on the electronic and magnetic properties of melilite structural materials Ba₂FeSi₂O₇ and Ba₂CoGe₂O₇. First-principles calculations confirm that Ba₂FeSi₂O₇ and Ba₂CoGe₂O₇ are both antiferromagnetic semiconductors with the magnetic easy axis being along the [110] direction. Two flat bands with a bandwidth of less than 20 meV, which come from the $d_{3z^2-r^2}$ orbitals of Fe²⁺ or Co²⁺ ions, are found in both materials. More interestingly, we find that the magnetocrystalline anisotropy energy of the Ba₂FeSi₂O₇ is about 5.19 meV per unit cell, which is more than eight times larger than that of Ba₂CoGe₂O₇. Further calculations show that their MAEs are mainly contributed by the single-ion anisotropy. The perturbation calculations indicate that the different electron numbers in the d orbitals and their different orbital occupations in the two materials lead to the large difference in their single-ion anisotropy. Our work could be helpful to understand the magnetic behaviors in similar melilite structural materials.