Thermometry of microscopic samples at ultra-low temperatures and high magnetic fields.

Measuring heat capacity and thermal conductivity of small crystals in the ultra-low temperature regime (< 20 mK) along with high magnetic fields (> 14 T) is challenging due to a lack of suitable thermometers and the small thermal masses of samples. Quartz tuning forks have been shown to be a viable method of temperature measurement of viscous fluids and in particular liquid helium-3 in this extreme regime [1]. This method has been realized for relatively large thermal baths incompatible with measuring thermal effects of small samples. We have designed small capsules of helium-3 to serve as miniaturized and self contained thermometers. Such thermometers provide a way to make local measurements for thermal conductivity or transport. We will discuss techniques for measuring resonance properties in a wide range of conditions from gas to a highly viscous liquid. The simplest method is to measure a resonance curve with a frequency sweep and fit the width of the lorentzian. However, we are exploring alternative techniques such as resonance tracking of the amplitude and ring down measurements and their applicability in different conditions. Our goal is to show that these thermometers and techniques will allow for experiments of thermal properties with novel materials in this difficult to probe regime.