Phonon spectrum attributes for the negative thermal expansion of MZrF6 (M = Ca, Mn–Ni, Zn)

Abstract

In this paper, we systematically studied the thermal expansion of the metal fluorides MZrF₆ (M = Ca, Mn–Ni, Zn) in the framework of the first-principles calculations based on the density functional theory (DFT)/density functional perturbation theory (DFPT) within quasi-harmonic approximation (QHA). It has been found that the dominant phonon mode responsible for the negative thermal expansion (NTE) of CaZrF₆ is the optic transverse fluorine vibration mode, while the dominant NTE mode for MnZrF₆ and FeZrF₆ is the acoustic phonon mode at a high symmetric X point. Moreover, we have addressed that the thermal expansion of MZrF₆ (M = Ca, Mn–Ni, Zn) should be an overall effect of abundant phonon modes in the whole frequency (ω) and wavevector (k) space, and in detail, similar to the case of MZrF₆ (M = Ca, Mg, Sr) [M. K. Gupta, B. Singh, R. Mittal, and S. L. Chaplot, Phys. Rev. B, 2018, 98, 014301], thermal expansion is positively correlated with the ratio of the anisotropic mean square displacement (u_⊥²/u_‖²) of the F atom, composed of all phonon modes involving the vibration of the F atom in the entire phonon spectrum. On the other hand, the magnetic order is also predicted to be critical for the thermal expansion of FeZrF₆ and CoZrF₆, and the AFM state is expected for FeZrF₆ and CoZrF₆ in the experiment.