Spatial Modulation and Thermal-Induced Spin Phase Transition on the Negative Thermal Expansion of ScF₃ with Metal Dopants

Negative thermal expansion (NTE) is an intriguing physical property of solids, which is often related to the lattice, phonons, charges, and spin. However, most of the studies are mainly focused on the phonons, and the spin-related mechanism in open framework compounds remains unclear owing to the lack of more experimental pieces of evidence. Here, based on the first-principles calculations combined with the quasi-harmonic approximation, we carried out studies of the NTE properties of ScF3 with metal dopants to reveal the roles in NTE of both the spatial effects and spin states. For most of the dopants, the NTE coefficient decreases with the decrease of ionic radius, obeying a linear scaling relationship. Interestingly, for magnetic impurities with a spin phase transition from a high spin state to a low spin state, we show that they will exhibit a Jahn–Teller distortion behavior and enhance the longitudinal vibration mode. In turn, the longitudinal vibration mode has a large positive Grüneisen parameter, which can offset the NTE obviously. This work not only proposes a new insight into the NTE mechanism about impurities in ScF3 but also provides an approach to tailor the NTE properties for fluorides with magnetic impurities as well as oxides