We report systematic ab initio calculations of the electronic band structure, phonon dispersion relation, and the structural characterization of FeF${}_2$ in the rutile ($P{4}_2/mnm$) structure as well as in several high-pressure phases by means of the generalized gradient approximation (GGA)+U approximation. Using the phonon dispersion relations, we calculated the Gibbs free energy and evaluated the phase transitions at 300 K, at which most experimental measurements are performed. Calculated Raman and infrared vibrational modes, lattice parameters, and electronic structure for all considered crystalline structures are compared with available experimental data. Our calculations show that at 5.33 GPa, the FeF${}_2$ undergoes a second-order proper ferroelastic phase transition, rutile $\to$ CaCl${}_2$-type structure. This result is supported by the softening of the elastic shear module $C_s$ in the rutile phase, the softening (hardening) of the $B_{1g}$ ($A_g$) Raman active mode in the rutile (CaCl${}_2$-type) structure near the transition pressure, and the decrease of the square of the spontaneous strain $e_{ss}$ from the CaCl${}_2$-type structure. This demonstrates that the rutile $\to$ CaCl${}_2$-type phase transition is driven by the coupling between the Raman active $B_{1g}$ mode and shear modulus $C_s$. At 8.22 GPa, the CaCl${}_2$-type structure undergoes a first-order phase transition to the $Pbca$ phase, a distorted fcc $Pa\overline{3}$ phase with a volume reduction of $\Delta V\approx 7\%$, as reported in experiments. Upon further increase of the pressure, the $Pbca$ phase transforms to a $Fmmm$ phase othorhombic center-type structure at $\sim$20.38 GPa, with $\Delta V\approx 2.5\%$. Finally, at 25.05 GPa, there is a phase transition to the orthorhombic cotunnite structure ($Pnma$ space group), with $\Delta V\approx 5.8\%$, which is stable up to 45 GPa, the largest considered pressure. The coordination number for the Fe ion in each phase is 6, 6, 6, 8, and 9 for rutile, CaCl${}_2$-type, $Pbca$, $Fmmm$, and cotunnite structures, respectively. The evolution of the band gap, phonon frequencies, and magnetic moment of Fe ion as a function of the applied pressure is reported for all studied phases. The exchange constants $J_1$, $J_2$, and $J_3$, calculated for rutile and the lowest Gibbs free-energy high-pressure phases, are reported.

• Received 15 December 2011

DOI:https://doi.org/10.1103/PhysRevB.85.134110