Paramagnon heat capacity in (Ti,Zr,Hf)NiFexNiSn half-Heusler composites

As a measure of the temperature response of the energy of matter, the heat capacity C-p is a fundamental thermodynamic property. Its dependence on magnetic field, especially at low temperatures, yields insight into the electronic, phononic, and magnetic states of condensed matter. Here, we present a set of paramagnetic and ferromagnetic (Ti, Zr, Hf )NiFexSn half-Heusler composites that exhibit low-field (<3 T) maxima in C-p and higher-field magnetic quenching of the heat capacity at temperatures below 10 K. Using rigorous statistical analysis, we attribute the effect to the existence of paramagnons within the compounds. To explain the lowest-temperature (<4 K), low-field declines in C-p, we derive a magnon model up to fourth order in dispersion. While the combined paramagnon and magnon model matches the data well, the fit parameters are significantly underdetermined. We provide a qualitative explanation of the secondary effect based on superconducting phases within the composites. Overall, our work highlights the insight of field-dependent heat capacity studies at fixed temperatures that cannot be as easily gleaned from the temperature-dependent heat capacity at fixed magnetic fields.