Specific Heat of Holmium in Gold and Silver at Low Temperatures

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Specific Heat of Holmium in Gold and Silver at Low Temperatures Matthew Herbst1   · Andreas Reifenberger1 · Clemens Velte1 · Holger Dorrer2 · Christoph E. Düllmann2,3,4 · Christian Enss1 · Andreas Fleischmann1 · Loredana Gastaldo1 · Sebastian Kempf1 · Tom Kieck2,5 · Ulli Köster6 · Federica Mantegazzini1 · Klaus Wendt5 Received: 30 December 2019 / Accepted: 13 September 2020 © The Author(s) 2020

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 Ho , such as the ones developed for the neutrino mass experiment ECHo. We investigate alloys with atomic concentrations of xHo = 0.01−4% at temperatures between 10 and 800 mK . Due to the large total angular momentum J = 8 and nuclear spin I = 7∕2 of Ho3+ ions, the specific heat of Au:Ho and Ag: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 setups 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 ≈ 250 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 ≤ 20 mK , silver holmium alloys with xHo ≳ 1% are suited best. Keywords  Heat capacity · Schottky anomaly · Dilute holmium alloys · Metallic magnetic calorimeters · ECHo

* Matthew Herbst [email protected]‑heidelberg.de * Andreas Reifenberger [email protected]‑heidelberg.de * Clemens Velte [email protected]‑heidelberg.de Extended author information available on the last page of the article

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Journal of Low Temperature Physics

1 Introduction Ho is an unstable holmium isotope which undergoes electron capture with the energy QEC = (2.833 ± 0.030stat ± 0.015syst ) keV [1] available for the decay. Based on its half-life of 𝜏1∕2 = 4570 a , 2 × 1012 atoms of 163 Hoyield an activity of 10 Bq  [2]. For more than 30 years, this nucleus is considered to be one of the best candidates to be used in experiments for the determination of the effective electron neutrino mass [3–9]. The best approach for this kind of experiment is to perform a calorimetric measurement of the electron capture spectrum, as was proposed in 1983 by De Rújula and Lusignoli [3, 4]. The current technology is based on low-temperature microcalorimeters [10] where 163 Hoatoms are enclosed in the particle absorber of the detector. Presently, two large experiments, namely ECHo [11] and HOLMES [12], follow this approach. As the name su

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