Specific Heat of Holmium in Gold and Silver at Low Temperatures

TL;DR

This study measures the specific heat of dilute holmium alloys in gold and silver at very low temperatures, revealing a dominant Schottky anomaly and concentration-dependent interactions, aiding the development of low-temperature microcalorimeters for neutrino experiments.

Contribution

The paper provides experimental data on holmium alloy specific heat at millikelvin temperatures, highlighting the dominant hyperfine and crystal field effects relevant for low-temperature detector optimization.

Findings

Specific heat dominated by Schottky anomaly at ~250 mK

Concentration-dependent RKKY and dipole-dipole interactions

Silver holmium alloys with >1% holmium suitable for T ≤ 20 mK

Abstract

The specific heat of dilute alloys of holmium in gold and in silver plays a major role in the optimization of low temperature microcalorimeters with enclosed $^{163}\textrm{Ho}$, such as the ones developed for the neutrino mass experiment ECHo. We investigate alloys with atomic concentrations of $x_\textrm{Ho}=0.01\,\% - 4\,\%$ at temperatures between $10\,\textrm{mK}$ and $800\,\textrm{mK}$. Due to the large total angular momentum $J=8$ and nuclear spin $I=7/2$ of $\textrm{Ho}^{3+}$ ions, the specific heat of $\underline{\textrm{Au}}\textrm{:Ho}$ and $\underline{\textrm{Ag}}\textrm{:Ho}$ depends on the detailed interplay of various interactions, including contributions from the localized 4f electrons and nuclear contributions via hyperfine splitting. This makes it difficult to accurately determine the specific heat of these materials numerically. Instead, we measure their specific heat by using three experimental set-ups optimized for different concentration and temperature ranges. The results from measurements on six holmium alloys demonstrate that the specific heat of these materials is dominated by a large Schottky anomaly with its maximum at $T\approx 250\,\textrm{mK}$, which we attribute to hyperfine splitting and crystal field interactions. RKKY and dipole-dipole interactions between the holmium atoms cause additional, concentration-dependent effects. With regard to ECHo, we conclude that for typical operating temperatures of $T\leq 20\,\textrm{mK}$, silver holmium alloys with $x_\textrm{Ho}\gtrsim 1\,\%$ are suited best.