Phonon-Mode Calculation, Far- and Mid-Infrared, and Raman Spectra of an ε-Ga_0.5Fe_1.5O₃ Magnet

Abstract

Gallium-substituted epsilon iron oxide (ε-Ga 0.5 Fe 1.5 O 3 ) has drawn attention because its millimeter wave absorption frequency meets the millimeter wave radar frequency for automobiles. We report the phonon modes of ε-Ga 0.5 Fe 1.5 O 3, which has an orthorhombic structure in the Pna 2 1 space group. First-principles phonon-mode calculations show that ε-Ga 0.5 Fe 1.5 O 3 has 117 optical phonon modes (fundamental vibrations) with symmetries of A 1, A 2, B 1, and B 2 as well as three acoustic phonon modes. The phonon density of states demonstrates that the movements of Fe and Ga contribute to the phonon modes in the lower energy region of 20–370 cm –1, while the movements of O contribute to the phonon modes in the higher energy region of 370–720 cm –1 . We directly measure the optical phonon modes of ε-Ga 0.48 Fe 1.52 O 3 nanoparticles using far- and mid-infrared (IR) and Raman spectroscopies, which agree well with those obtained by first-principles phonon-mode calculations. Additionally, the thermodynamic parameters of the internal energy ( U ), the vibrational entropy ( S vib ), and the Helmholtz energy ( A ) are calculated and understood through the investigation of the phonon modes. Heat capacity measurements confirm that the observed thermodynamic parameters are consistent with the predicted values.