Advancements in technology are increasingly driven by the development of new functional materials. One such family is the heavy fermions, obtained by combining rare-earth elements with metallic host material. These heavy fermions display exotic quantum mechanical properties at low temperatures. Key techniques that measures properties such as specific heat, magnetic susceptibility, and nuclear spin-lattice relaxation provide valuable insights of the interactions within these systems, enabling the exploration of their unique characteristics  and guiding the discovery of new related materials.

In this thesis, AC calorimetry is used to measure specific heat as a primary tool to characterize these materials. Specific heat contains all the contributions associated with different subsystems in the material. Accurate measurement and careful interpretation of the measurements are essential, as these materials comprise of multiple subsystems such as electronic, nuclear, and magnetic, having different time scales. Due to multiple time scales involved, traditional calorimetry methods become challenging. To solve this issue we here develop a new experimental technique based on AC calorimetry that can disentangle different contributions to specific heat at low temperatures. The technique, that we call Thermal Impedance Spectroscopy (TISP), allows independent measurement of the electronic and nuclear specific heat at low temperatures. This is because the relaxation time of the nuclear subsystem to equilibrate with the lattice (electrons and phonons) is slow and can be captured by the frequency response of the calorimeter-sample assembly. This relaxation time, known as the nuclear spin-lattice relaxation time T₁, provides an additional probe for the electronic subsystem. The method's effectiveness is demonstrated using indium, a known metallic system, with results aligning well with expectations and prior Nuclear Magnetic Resonance (NMR) studies.

TISP was applied to investigate several quantum materials, including heavy fermions close to or at a quantum critical point. The role of the magnetic field on the quantum criticality of these systems was investigated using TISP, and complementary techniques such as magnetic susceptibility and X-ray measurements were employed to further investigate these materials.