### Abstract:

Total energy calculations based on density functional theory are generally a good
approach to obtain the properties of solids. The local density approximation (LDA) is
widely used for calculating the ground state properties of electronic systems; for excited
states the errors are in general unknown. The important aspects of LDA pertain to the
modeling of the exchange-correlation interaction. If the exchange-correlation potential is
approximately the same for the ground and excited states, one expects good results from
the LDA calculations for excited states. In this thesis, we utilize the total energy technique
for numerical computations of the electronic structure of iron in several magnetic phases
and crystalline structures.
1. Body-centered-cubic iron in the ferromagnetic and several antiferromagnetic
configurations. We use the total energy results to obtain the parameters in a model
Heisenberg Hamiltonian. These include the interaction parameters up to 6-th nearest
neighbors. Based on this model Hamiltonian we calculate properties such as the critical
(Curie) temperature and spin stiffness constant. We assume that the total exchangecorrelation
energy functional is the same in the ferromagnetic ground state and the
antiferromagnetic excited states. Our model parameters are based directly on ab initio
calculations of the electronic structure. Our calculation yields good results compared with
experimental values and earlier work. Some other physical quantities, related to the phase
transition, and spin waves are also discussed.
2. Face-centered-tetragonal iron. If iron is grown on a proper substrate ( e.g.,
Cu(100) ), the crystal structure of the thin film displays a face-centered-tetragonal distortion
due to the lattice constant misfit between the film and substrate. Therefore, we performed
calculations for fct iron in its ferromagnetic, antiferromagnetic, and nonmagnetic phases for
a wide range of values of the lattice parameters. In the ferromagnetic calculations, we found
two minima in the total energy: one is close to.the bcc structure and the other ( with a lower
energy ) is close to fcc. In the antiferromagnetic and nonmagnetic calculations, we found in
each case that there is only one minimum near the fcc structure, providing us clear evidence
that the antiferromagnetic and nonmagnetic states are (meta)stable near the fcc region and
unstable in bcc region. The antiferromagnetic and nonmagnetic states are almost degenerate
near the fcc minimum, but the antiferromagnetic phase has the lowest total energy in the
whole fct region. Magnetic moments are also calculated for a variety of fct structures. Near
the fcc minimum we found that two ferromagnetic phases co-exist, one with a low spin and
one with a high spin. These results are consistent with experimental facts and other earlier
calculations. Some structural properties, such as the elastic constants and the bulk
modulus, are also studied and compared with experimental data and some earlier
calculations.