Achieving Colossal Negative Thermal Expansion in Cubic Double ReO₃ Type Fluorides though Resonance-like Coupling of Phonon Vibration Modes

The design of materials with colossal negative thermal expansion (NTE) is of significant fundamental and technological importance in the field of thermal engineering. Using the first-principles calculations and the quasi-harmonic approximation (QHA), the NTE properties of cubic double ReO₃-type M^IIX^IVF₆ (M=Mg, Ca, Sr, and X=Zr, Hf) are systematically investigated. We find that these fluorides exhibit relatively large NTE over a wide coefficient range, especially for CaHfF₆ and SrHfF₆ which the coefficients of NTE (CNTEs) can reach up to -70~75× 10^-6 K^-1, being about two times more than that of ScF₃ with similar structure. By analyzing the changes of vibration frequency and negative Grüneisen parameters(NGP), we reveal that the underlying physics of such colossal NTE is attributed to the so-called resonance-like effect of two unique transverse vibration modes with nearly the same frequencies at both the Γ and X points in the Brillouin zone(BZ), which in turn greatly enhance the lattice distortion through flexible rotations of the MF₆ and XF₆ octahedrons. Our studies provide deep insights of the underlying mechanism of NTE in M^IIX^IVF₆ fluorides, consequently offering a route for the design of colossal NTE materials.