# Epitaxial Bain path of tetragonal Fe

## Abstract

The epitaxial Bain paths (EBP’s) of tetragonal Fe are found by minimizing the total energy with respect to c at each a using first-principles total-energy calculations with the local-spin-density approximation plus a generalized gradient approximation and relativistic corrections. The energy minima along the EBP’s give the equilibrium states of the ferromagnetic, nonmagnetic and two antiferromagnetic phases—the type-I phase, called here AF1, and a phase in which pairs of ferromagnetically coupled (001) layers alternate in moment, called here AF2. The AF2 phase is found to be lower in energy than AF1 when each is in equilibrium and also when the (001) plane lattice constant is strained to the Cu(001) lattice constant. Calculations of the six elastic constants of AF2 at equilibrium inserted in the four tetragonal stability conditions show that it is unstable for [100] and [010] shears in the (001) plane, but is stabilized by epitaxy on Cu(001). The AF2 phase is indicated to be the phase of the bulk of epitaxial Fe films on Cu(001). The bulk structure of Fe films on Cu(001) found by quantitative low-energy electron diffraction analysis is shown to be close to the EBP’s of the AF1 phase, but farther from the AF2 phase. On substrates with slightly larger lattice constants than Cu(001), the ferromagnetic phase is found to be more stable than AF2. © 2001 The American Physical Society.