Understanding the complex metallic element Mn.: II.: Geometric frustration in β-Mn, phase stability, and phase transitions -: art. no. 014408

In the preceding paper [D. Hobbs, J. Hafner, and D. Spisak, Phys. Rev. B 68, 014407 (2003)], we have started an ab initio spin-density-functional study of the complex structural and magnetic phase behaviors of Mn by a detailed investigation of alpha-Mn. It was shown that the complex crystalline and noncollinear antiferromagnetic structures are the results of the conflicting tendencies to maximize simultaneously bond strength and magnetic moment. The present work extends this study to the remaining four polymorphs of Mn. Frustration of antiferromagnetic exchange interaction (which is the driving force leading to noncollinearity in alpha-Mn) is found to be even stronger in beta-Mn. However, in contrast to the current assumption that the magnetic frustration is restricted to the sublattice of the Mn II atoms, with the Mn I atoms remaining nonmagnetic, we find that the antiferromagnetic Mn I-Mn II coupling is strongest, leading to the stabilization of a ferrimagnetic phase upon slight expansion. At equilibrium, a nonmagnetic and a weakly ferrimagnetic phase are energetically virtually degenerate. Antiferromagnetic ground states are found for gamma- and delta-Mn (face- and body-centered cubic, respectively), while hexagonal epsilon-Mn is only marginally magnetic at equilibrium. Magnetism strongly influences the mechanical properties of all polymorphs. Due to the stabilization of the antiferromagnetic state on expansion, the gamma- and delta-phase are exceptionally soft, whereas beta- and epsilon-Mn where magnetism is nearly completely suppressed are mechanically hard. alpha-Mn is found to be soft in the noncollinear antiferromagnetic state, but hard in the nonmagnetic phase. alpha-Mn is found to have the lowest energy at ambient pressure, under compression a structural phase transition to epsilon-Mn is predicted, in agreement with recent experiments. In summary, the structural and magnetic phase diagram of even the complex metallic element is well explained by the density-functional theory.