Specific heat analyses on optical-phonon-derived uniaxial negative thermal expansion system $Tr$Zr$_{2}$ ($Tr$ = Fe and Co$_{1-x}$Ni$_{x}$) (2406.18291v1)

Abstract: Recently, huge uniaxial negative thermal expansion (NTE) along a $c$-axis has been observed in transition-metal ($Tr$) zirconides $Tr$Zr${2}$ with a tetragonal CuAl${2}$-type structure. In a recent study on FeZr${2}$ [M. Xu et al., Nat. Commun. 14, 4439 (2023)], the importance of optical phonons to the emergence of the $c$-axis NTE in FeZr${2}$ has been proposed. In this study, the physical properties of $Tr$Zr${2}$ ($Tr$ = Fe and Co${1-x}$Ni${x}$) have been studied by specific heat, sound velocity measurements, and theoretical phonon calculations to discuss the importance of optical phonons to the emergence of the $c$-axis NTE in CoZr${2}$ and FeZr${2}$. From analyses of lattice specific heat, we found that Ni substitution results in a systematic decrease in oscillator strength for the Einstein modes with 8.74 meV (CoZr${2}$). From phonon calculations, the low-energy optical phonon branches at the $\Gamma$ point were observed for CoZr${2}$ and FeZr${2}$ with $c$-axis NTE, but not in NiZr${2}$ with positive thermal expansion. The enhancement of phonon density of states near the above-mentioned optical phonon energy in CoZr${2}$ and FeZr${2}$ is consistent with the specific heat analyses. We propose the importance of the low-energy optical phonons to the emergence of the $c$-axis NTE in TrZr${2}$.