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

TL;DR

This study investigates how optical phonons influence the uniaxial negative thermal expansion in transition-metal zirconides TrZr2, revealing that low-energy optical phonons are crucial for the NTE phenomenon along the c-axis.

Contribution

It demonstrates the role of low-energy optical phonons in causing negative thermal expansion in TrZr2 compounds through combined experimental and theoretical analysis.

Findings

Ni substitution decreases oscillator strength of Einstein modes

Low-energy optical phonons are present in NTE compounds but absent in positive expansion NiZr2

Enhanced phonon density of states correlates with NTE behavior

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$_{2}$.