The structure, magnetic properties, and lattice dynamics of ordered Fe-Pt alloys with three stoichiometric compositions, Fe$_3$Pt, FePt and FePt$_3$, have been investigated using the density functional theory. Additionally, the existing experimental
data have been complemented by new measurements of the Fe projected phonon density of states performed for the Fe$_3$Pt and FePt$_3$ thin films using the nuclear inelastic scattering technique. The calculated phonon dispersion relations and phonon density of states have been compared with the experimental data. The dispersion curves are very well reproduced by the calculations, although, the softening of the transversal acoustic mode TA$_1$ leads to some discrepancy between the theory and experiment in Fe$_3$Pt. A very goood agreement between the measured spectra and calculations performed for the tetragonal structure derived from the soft mode may signal that the tetragonal phase with the space group $P4/mbm$ plays an important role in the martensitic transformation observed in Fe$_3$Pt. For FePt$_3$, the antiferromagnetic order appearing with decreasing temperature has been also investigated. The studies showed that the phonon density of states of FePt$_3$ very weakly depends on the magnetic configuration.
We present the results of inelastic x-ray scattering for magnetite and analyze the energies and spectral widths of the phonon modes with different symmetries in a broad range of temperature 125<T<293 K. The phonon modes with X_4 and Delta_5 symmetrie
s broaden in a nonlinear way with decreasing temperature when the Verwey transition is approached. It is found that the maxima of phonon widths occur away from high-symmetry points which indicates the incommensurate character of critical fluctuations. Strong phonon anharmonicity induced by electron-phonon coupling is discovered within ab initio calculations which take into account local Coulomb interactions at Fe ions. It (i) explains observed anomalous phonon broadening, and (ii) demonstrates that the Verwey transition is a cooperative phenomenon which involves a wide spectrum of phonons coupled to charge fluctuations condensing in the low-symmetry phase.
The electronic properties of two spinels Fe$_3$O$_4$ and Fe$_2$SiO$_4$ are studied by the density functional theory. The local Coulomb repulsion $U$ and the Hunds exchange $J$ between the $3d$ electrons on iron are included. For $U=0$, both spinels a
re half-metals, with the minority $t_{2g}$ states at the Fermi level. Magnetite remains a metal in a cubic phase even at large values of $U$. The metal-insulator transition is induced by the $X_3$ phonon, which lowers the total energy and stabilizes the charge-orbital ordering. Fe$_2$SiO$_4$ transforms to a Mott insulating state for $U>2$ eV with a gap $Delta_gsim U$. The antiferromagnetic interactions induce the tetragonal distortion, which releases the geometrical frustration and stabilizes the long-range order. The differences of electronic structures in the high-symmetry cubic phases and the distorted low-symmetry phases of both spinels are discussed.
The Verwey phase transition in magnetite is analyzed on the basis of the Landau theory. The free energy functional is expanded in a series of components belonging to the primary and secondary order parameters. A low-temperature phase with the monocli
nic P2/c symmetry is a result of condensation of two order parameters X_3 and Delta_5 . The temperature dependence of the shear elastic constant C_44 is derived and the mechanism of its softening is discussed.
