Relaxation calorimetry at very low temperatures for systems with internal relaxation

We present the detailed introduction of our relaxation calorimetry designed for tiny samples down to very low temperatures of 0.03 K. In particular, we discuss how to analyze the data that are modified by an internal thermal relaxation in the sample or in the sample stage of the specific heat cell. We demonstrate that the correct heat capacity is obtained even when the relaxation curve has a triple exponential decay, rather than a double exponential decay which has usually been discussed. As an example, we discuss the measurements performed for α-YbAlB₄ in a magnetic field of 5 T, where we found the triple exponential decay due to a thermal relaxation between electron and nuclear contributions at relatively high temperature well above 0.1 K. Our modified analysis provides the best solution in such a case.