Full potential calculations of the spiral spin density wave ground state of ?-Fe

Abstract

All previous ab initio calculations of spiral spin density waves (SSDW) have used the atomic sphere approximation (ASA) in which not only is the charge density approximated by its spherical average, but the magnetization direction is also held fixed within each Wigner–Seitz sphere. Using the Vanderbilt ultrasoft pseudopotential method, we have performed the first full potential calculations of a system with a SSDW ground state, γ-Fe. We report calculations made using the local spin density approximation (LSDA) as well as two forms of the generalized gradient approximation (GGA) for the exchange–correlation (xc) energy density functionals. These calculations were performed for SSDW wave vectors q=(2π/a)(α,0,0) and q=(2π/a)(1,γ,0) with the ground state q found close to (2π/a)(0.55,0,0) for both xc functionals. These as well as the ASA calculations failed to obtain the experimental value, q=(2π/a)(1,0.13,0). Interesting results were obtained for the angle of the magnetization vector (in the xy plane), \documentclass{article}\usepackage{amsbsy}\pagestyle{empty}\begin{document}$\varphi(\mathbf{r})=\mathbf{q}\,\boldsymbol{\cdot}\,\mathbf{r}+\hat{\varphi}(\mathbf{r})$\end{document}, where \documentclass{article}\pagestyle{empty}\begin{document}$e^{i\hat{\varphi}(\mathbf{r})}$\end{document} is a periodic function of r that is calculated self-consistently. We attribute the failure to obtain the experimental ground state q to the fact that the LSDA and GGA depend upon the local magnetization and are oblivious to the variation of its direction. A term proportional to ∣∇φ(r)∣2 is derived that, when added to the LSDA, improves agreement with experiment. © 2000 John Wiley & Sons, Inc. Int J Quant Chem 77: 940–950, 2000