Publications

Specific Heat of Holmium in Gold and Silver at Low Temperatures

M Herbst, A Reifenberger, C Velte et al., J Low Temp Phys 202, 106–120 (2021).

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 163Ho, 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 800mK. 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 ≈ 250mK, 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 ≤ 20mK, silver holmium alloys with xHo ≳ 1% are suited best.

Graph of the measured specific heat of five holmium alloys at low temperatures. All samples show a maximum at a few hundred millikelvin.

Numerical Calculation of the Thermodynamic Properties of Silver Erbium Alloys for Use in Metallic Magnetic Calorimeters

M Herbst et al., J Low Temp Phys 209, 1119–1127 (2022).

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 mK and 1 K, external magnetic fields of up to 20 mT, and erbium concentrations of up to 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.

Graph of the simulated temperature dependence of the specific heat of various erbium alloys at low temperatures.

High Resolution Magnetic Micro-calorimeters: Thermodynamics, Cooling Requirements, and Noise

M Herbst, PhD thesis, Heidelberg University (2023).

Magnetic micro-calorimeters (MMCs) are cryogenic particle detectors well suited for high-precision X-ray spectroscopy. They measure the temperature rise caused by an X-ray impact via the change in magnetization of a paramagnetic temperature sensor. Until now, MMCs have been designed to operate at around 20 mK, requiring sophisticated cooling, which limits their application. In this work, we show that magnetic micro-calorimetry is possible at significantly higher temperatures, by developing two novel MMCs with reduced cooling requirements. The first illustrates a new application for MMCs in the field of particle induced X-ray emission spectroscopy. At an operating temperature of 85 mK, this detector has a FWHM energy resolution of 19 eV at 5.9 keV, outperforming current alternatives. Our second MMC is a proof-of-principle detector, which demonstrates that operating temperatures of up to 300 mK are feasible. With a third, stand-alone device, we analyze noise sources affecting superconducting microstructures, such as MMCs. By comparing results from three different operation modes, we are able to disentangle noise components, in particular magnetic flux noise. High-precision measurements of noise originating from the sensor show a previously unobserved Johnson noise component and unexpected variations in the magnetic flux noise, which we relate to the dynamics of the magnetic moments in the sensor. Overall, our results broaden the application range of MMCs, and illustrate how noise analysis can improve the performance of superconducting devices.

Photo of a bound copy of a dissertation. The cover is blue and features the title and two sketches of experiments.

Measuring Magnetic 1/f Noise in Superconducting Micro-structures and the Fluctuation-dissipation Theorem

M Herbst et al., Supercond. Sci. Technol. 36 105007 (2023).

The performance of superconducting devices like qubits, superconducting quantum interference devices (SQUIDs), and particle detectors is often limited by finite coherence times and noise. Various types of slow fluctuators in the Josephson junctions and the passive parts of these superconducting circuits can be the cause, and devices usually suffer from a combination of different noise sources, which are hard to disentangle and therefore hard to eliminate. One contribution is magnetic noise caused by fluctuating magnetic moments of magnetic impurities or dangling bonds in superconducting inductances, surface oxides, insulating oxide layers, and adsorbates. In an effort to further analyze such sources of noise, we have developed an experimental set-up to measure both the complex impedance of superconducting microstructures, and the overall noise picked up by these structures. This allows for important sanity checks by connecting both quantities via the fluctuation-dissipation theorem. Since these two measurements are sensitive to different types of noise, we are able to identify and quantify individual noise sources. Furthermore, our measurements are not limited by the quantum noise limit of front-end SQUIDs, allowing us to measure noise caused by just a few ppm of impurities in close-by materials. We present measurements of the insulating layers of our devices, and magnetically doped noble metal layers in the vicinity of the pickup coils at T = 40mK - 800mK and f = 1Hz - 100kHz.

Schematic of an experiment to measure noise. A central chip is read out by different devices.