Using dilute silver erbium alloys as a paramagnetic temperature sensor in metallic magnetic calorimeters (MMCs) has the advantage of the host material not having a nuclear quadrupole moment, in contrast to the alternative of using gold erbium alloys. We present numerical calculations of the specific heat and magnetization of Ag:Er, which are necessary for designing and optimizing MMCs using this type of alloy as sensor material. The parameter ranges we consider are temperatures between $$1\,{\text {{mK}}}$$ 1 mK and $$1\,{\text {{K}}}$$ 1 K , external magnetic fields of up to $$20\,{\text {{mT}}}$$ 20 mT , and erbium concentrations of up to $$2000\,{\text {{ppm}}}$$ 2000 ppm . The system is dominated by an interplay of crystal field effects, Zeeman splitting, and the RKKY interaction between erbium ions, with certain specific constellations of erbium ions having noticeable effects on the specific heat. Increasing the external magnetic field or assuming a decreased strength of the RKKY interaction leads to a higher magnetization and a narrowing of the main Schottky peak, while changes in the erbium concentration can be well described by parameter scaling.

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 $$^{163}{{\text {Ho}}}$$ 163 Ho , such as the ones developed for the neutrino mass experiment ECHo. We investigate alloys with atomic concentrations of $$x_{{{\text {Ho}}}}=0.01{-}4\%$$ x Ho = 0.01 - 4 % at temperatures between 10 and $$800\,{{{\hbox {mK}}}}$$ 800 mK . Due to the large total angular momentum $$J=8$$ J = 8 and nuclear spin $$I=7/2$$ I = 7 / 2 of $${{\text {Ho}}}^{3+}$$ Ho 3 + 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 $$T\approx 250\,{{{\hbox {mK}}}}$$ 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 $$T\le 20\,{{{\hbox {mK}}}}$$ T ≤ 20 mK , silver holmium alloys with $$x_{{{\text {Ho}}}}\gtrsim 1\%$$ x Ho ≳ 1 % are suited best.

When considering fine details, X-ray emission spectra present a structure that is quite complex over a quite wide energy window. Its systematic exhaustive study, until recently, has been hindered in...