Density Functional Theory Approach to the Vibrational Properties and Magnetic Specific Heat of the Covalent Chain Antiferromagnet KFeS2

Abstract

Ternary potassium-iron sulfide, KFeS2, belongs to the family of highly anisotropic quasi-one-dimensional antiferromagnets with unusual “anti-Curie–Weiss” susceptibility, quasi-linearly growing with a rising temperature up to 700 K, an almost vanishing magnetic contribution to the specific heat, drastically reduced magnetic moment, etc. While some of the measurements can be satisfactorily described, the deficiency of the entropy changes upon the magnetic transition and the spin state of the iron ion remains a challenge for the further understanding of magnetism. In this work, high-quality single-crystalline samples of KFeS2 were grown by the Bridgman method, and their stoichiometry, crystal structure, and absence of alien magnetic phases were checked, utilizing wave-length dispersive X-ray electron-probe microanalysis, powder X-ray diffraction, and 57Fe Mössbauer spectroscopy, respectively. An ab initio approach was developed to calculate the thermodynamic properties of KFeS2. The element-specific phonon modes and their density of states (PDOS) were calculated applying the density functional theory in the DFT + U version, which explicitly takes into account the on-site Coulomb repulsion U of electrons and their exchange interaction J. The necessary calibration of the frequency scale was carried out by comparison with the experimental iron PDOS derived from the inelastic nuclear scattering experiment. The infrared absorption measurements confirmed the presence of two high-frequency peaks consistent with the calculated PDOS. The calibrated PDOS allowed the calculation of the lattice contribution to the specific heat of KFeS2 by direct summation over the phonon modes without approximations and adjustable parameters. The temperature-dependent magnetic specific heat evaluated by subtraction of the calculated phonon contribution from the experimental specific heat provides a lower boundary for estimating the reduced spin state of the iron ion.

In situ thermo‐Raman spectroscopy and ab initio vibrational assignment calculations of cubanite CuFe2S3

“…The calculations of phonon modes for the compounds belonging to the ternary Cu‐Fe‐S system have not been found in the literature. A detailed description of theoretical modeling of Raman spectra has been previously given for iron‐containing sulfides such as KFeS 2 using VASP 24 and mackinawite (FeS) using the VASP 25 and QUANTUM ESPRESSO 26 packages. Publications devoted to the phonon mode calculations for copper‐containing sulfides are found, in particular, for the family of compounds with the general formula Cu 2 Zn(Sn 1−x Ge x )S 4 using the Perdew–Burke–Ernzerhof local functional and norm‐conserving pseudopotentials as implemented in the CASTEP code 27 or similar systems 28 …”

Classical Density Functional Theory Approach to the Vibrational Properties and Lattice Specific Heat of a Quasi-One-Dimensional Antiferromagnet KFeSe2

“…Strongly non-localized states of Fe 3d -electrons cannot be satisfactorily described by the Generalized Gradient Approximation (GGA), and it is necessary to introduce a Hubbard-like correction to take these electrons into account explicitly. In [10] for KFeS 2 we used the rotationally invariant LSDA + U approach [11] with parameters U = 1.5 eV and J = 2 eV, where U is the on site Coulomb repulsion and J is the exchange interaction. The parameter values had been approbated on the electronic structure, magnetic subsystem, and phonon spectrum of the KFeS 2 crystal.…”