Pinning frequencies of the collective modes in $\alpha$-uranium

TL;DR

This study compares the specific heat of single-crystal and polycrystalline $ ext{U}$-uranium, attributing differences to collective mode excitations and pinning frequencies of charge-density waves, clarifying longstanding discrepancies in Debye temperature measurements.

Contribution

It introduces a model linking excess heat capacity to collective mode excitations with two cutoff frequencies, explaining differences in Debye temperatures from various measurement techniques.

Findings

Excess heat capacity in single crystals at specific temperatures.

Polycrystals show thermally broadened heat capacity without excess.

The model explains the longstanding Debye temperature discrepancy.

Abstract

Uranium is the only known element that features a charge-density wave (CDW) and superconductivity. We report a comparison of the specific heat of single-crystal and polycrystalline $\alpha$-uranium. \red{Away from the the phase transition the specific heat of the polycrystal is larger than that of the single crystal, and the aim of this paper is to explain this difference.} In the single crystal we find excess contributions to the heat capacity at 41 K, 38 K, and 23 K, with a Debye temperature, $\Theta_D$ = 256 K. In the polycrystalline sample the heat capacity curve is thermally broadened ($\Theta_D$ = 184 K), but no excess heat capacity was observed. The excess heat capacity, $C_\phi$ (taken as the difference between the single crystal and polycrystal heat capacities) is well described in terms of collective-mode excitations above their respective pinning frequencies. This attribution is represented by a modified Debye spectrum with two cutoff frequencies, a pinning frequency, $\nu_o$, for the pinned CDW (due to grain boundaries in the polycrystal), and a normal Debye acoustic frequency occurring in the single crystal. We explain the 50-year-old difference in Debye temperatures between heat capacity and ultrasonic measurements.