Structural distortion and band gap opening of hard MnB₄ in comparison with CrB₄ and FeB₄

MnB₄ was newly synthesized to crystallize in a monoclinic P2₁/c structure, different from previous experimental and theoretical reports. Here, based on first-principles calculations, we perform a comparative study of geometric and energetic features, mechanical behaviors, electronic property and chemical bonding of the experimentally identified monoclinic MnB₄, as well as orthorhombic CrB₄ and FeB₄. The results demonstrate that the presence of distorted rhomboidal-B₄ units and one-dimensional Mn chains in the monoclinic MnB₄ breaks the structural symmetry and lowers the total energy in comparison to the orthorhombic phase. The opening of band gap in MnB₄ is induced by Peierls-paired Mn atoms, differing from the metallic behaviors of recently studied tetraborides. Specifically, the preservations of covalent bonding in distorted boron-rhomboids in MnB₄ explain the relatively higher incompressibility and hardness.