{'fraction_non_alphanumeric': 0.016052880075542966, 'fraction_numerical': 0.004721435316336166, 'mean_word_length': 5.127167630057803, 'pattern_counts': {'":': 0, '<': 0, '<?xml version=': 0, '>': 0, 'https://': 0, 'lorem ipsum': 0, 'www.': 0, 'xml': 0}, 'pii_count': 0, 'substrings_counts': 0, 'word_list_counts': {'cursed_substrings.json': 0, 'profanity_word_list.json': 0, 'sexual_word_list.json': 0, 'zh_pornsignals.json': 0}}
Ab initio density functional study of phase stability and noncollinear magnetism in Mn

The crystalline and magnetic structures of all known polymorphs of Mn have been investigated using generalized spin-density functional theory based on an unconstrained vector-field description of the magnetization density. We find that at atomic volumes smaller than 12 Å3, the magnetic ground state of α-Mn is collinear with magnetic moments ranging between 0 and 3 µB depending on the local symmetry of the atomic positions. At larger atomic volumes, a metastable collinear configuration coexists with a stable noncollinear state. The noncollinearity of the magnetic structure is driven by the appearance of magnetic moments on sites IV, leading to a frustration of exchange interactions in local triangular configurations. A similar situation is found in β-Mn, with a collinear structure with coexisting magnetic and nonmagnetic sites. The α-phase is found to be stable over a wide range of volumes; under compression a phase transition to hexagonal ϵ-Mn is predicted.