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We present an in-depth study of the structural, electronic, magnetic, and lattice dynamical properties of the Fe$_4$(P$_2$O$_7$)$_3$ compound, employing first-principles calculations based on Density Functional Theory (DFT) within the DFT+U formalism. The monoclinic structure of Fe$_4$(P$_2$O$_7$)$_3$ belongs to the P2$_1$/n space group [1], with optimized lattice parameters a = 7.406 Å, b= 21.425 Å, and c = 9.529 Å [2]. These parameters exhibit a very good agreement with experimental measurements, attributed to the inclusion of local Coulomb interactions and van der Waals (vdW) forces. Our study systematically explores various magnetic configurations, with the antiferromagnetic (AFM) arrangement yielding the lowest total energy and a magnetic moment of ~4.6 $\mu_{\text{B}}$ per Fe atom, in close agreement with neutron diffraction data.
The electronic structure analysis reveals that Fe$_4$(P$_2$O$_7$)$_3$ is a Mott insulator, with an energy gap $E_g$ of 2.87 eV. Phonon dispersion relations and the phonon density of states (PDOS) were computed using the temperature-dependent effective potential (TDEP) method [3], revealing soft modes that suggest dynamic instability and a potential structural phase transition at low temperatures. These phonon soft modes, particularly at the Y point of the Brillouin zone, highlight the presence of structural instability, which may drive the phase transition to an alternative low-temperature configuration.
Iron pyrophosphate compounds, such as Fe$_4$(P$_2$O$_7$)$_3$, have attracted significant scientific and technological interest due to their diverse physical properties and applications, ranging from sorbents for radionuclide removal to photocatalysis and electrochemical energy storage. Despite their broad potential, limited research exists on the ab initio analysis of their crystal structure, electronic, and lattice dynamical properties. Our findings contribute to this gap by offering theoretical insights into the influence of local Coulomb interactions on electronic structure and magnetism, as well as by investigating lattice dynamics.
The comprehensive investigation of Fe$_4$(P$_2$O$_7$)$_3$ presented here provides critical insights into its magnetic ground state, electronic band structure, and lattice dynamics, making it a promising candidate for future studies in electronic and magnetic applications. Furthermore, the identification of soft phonon modes opens avenues for exploring temperature-dependent structural phase transitions, enhancing the potential utility of this compound in low-temperature applications.
[1] A. K. Padhi, K. S. Nanjundaswamy, C. Masquelier, S. Okada, and J. B. Goodenough. Effect of structure on the Fe3+/Fe2+ redox couple in iron phosphates. Journal of the Electrochemical Society, 144(5):1609, 1997.
[2] L. K. Elbouaanani, B. Malaman, R. Gérardin, and M. Ijjaali. Crystal structure refinement and magnetic properties of Fe$_4$(P$_2$O$_7$)$_3$ studied by neutron diffraction and mössbauer techniques. Journal of Solid State Chemistry, 163(2):412–420, 2002.
[3] O. Hellman, I. A. Abrikosov, and S. I. Simak. Lattice dynamics of anharmonic solids from first principles. Phys. Rev. B, 84:180301, Nov 2011. doi: 10.1103/PhysRevB.84.180301.
