Magnetic analytic bond-order potential for modeling the different phases of Mn at zero Kelvin

Abstract

It is known that while group VII 4$d$ Tc and 5$d$ Re have hexagonally close-packed (hcp) ground states, 3$d$ Mn adopts a complex $\ensuremath{\chi}$-phase ground state, exhibiting complex noncollinear magnetic ordering. Density functional theory (DFT) calculations have shown that without magnetism, the $\ensuremath{\chi}$ phase is still the ground state of Mn implying that magnetism and the resultant atomic-size difference between large- and small-moment atoms are not the critical factors, as is commonly believed, in driving the anomalous stability of the $\ensuremath{\chi}$ phase over hcp. Using a canonical tight-binding (TB) model, it is found that for a more than half-filled $d$ band, while harder potentials stabilize close-packed hcp, a softer potential stabilizes the more open $\ensuremath{\chi}$ phase. By analogy with the structural trend from open to close-packed phases down the group IV elements, the anomalous stability of the $\ensuremath{\chi}$ phase in Mn is shown to be due to 3$d$ valent Mn lacking $d$ states in the core which leads to an effectively softer atomic repulsion between the atoms than in 4$d$ Tc and 5$d$ Re. Subsequently, an analytic bond-order potential (BOP) is developed to investigate the structural and magnetic properties of elemental Mn at 0 K. It is derived within BOP theory directly from a new short-ranged orthogonal $d$-valent TB model of Mn, the parameters of which are fitted to reproduce the DFT binding energy curves of the four experimentally observed phases of Mn, namely, $\ensuremath{\alpha}$, $\ensuremath{\beta}$, $\ensuremath{\gamma}$, $\ensuremath{\delta}$, and $\ensuremath{\epsilon}$-Mn. Not only does the BOP reproduce qualitatively the DFT binding energy curves of the five different structure types, it also predicts the complex collinear antiferromagnetic (AFM) ordering in $\ensuremath{\alpha}$-Mn, the ferrimagnetic ordering in $\ensuremath{\beta}$-Mn, and the AFM ordering in $\ensuremath{\gamma}$-, $\ensuremath{\delta}$-, and $\ensuremath{\epsilon}$-Mn that are found by DFT. A BOP expansion including 14 moments is sufficiently converged to reproduce most of the properties of the TB model with the exception of the elastic shear constants, which require further moments. The current TB model, however, predicts values of the shear moduli and the vacancy formation energies that are approximately a factor of 2 too small, so that a future more realistic model for MD simulations will require these properties to be included from the outset in the fitting database.