Low-temperature experimentation is crucial to discovery in condensed matter Physics. Novel phenomena often appear at high pressure, which provides unique technical challenges to these measurements. This is especially true for calorimetry studies, for which the ambient pressure technique is predicated on the sample being in quasi-adiabatic conditions. We pioneer a new capability to perform calorimetry studies on samples that are embedded in a thermally conductive medium. With a framework that only requires one lock-in, the 3ω technique goes beyond standard methods by replacing DC thermometry with AC resistance techniques. We focus on the situation of materials at high-pressure in a piston cylinder cell, comparing various possible measurement strategies. Detailed calculations of the thermodynamic variables pave the way for further development and optimisation for future projects studying materials under pressure and beyond.

We apply this technique to study the heat capacity of CeSb₂ at pressures up to 26kbar, temperatures down to 300mK and fields up to 9T. At ambient pressure, CeSb₂ is a Kondo lattice heavy fermion material with a ferromagnetic ground state and various magnetic transitions at low temperatures. Between 6kbar and 16kbar, CeSb₂ undergoes a structural transformation that destroys the ferromagnetism, but reveals a new transition to a magnetically ordered state. Further pressure pushes this magnetic transition to a quantum critical point (QCP) and the material becomes an unconventional superconductor. Applying the new calorimetry technique, we discover two magnetic transitions in this phase. We track these transitions as further pressure pushes them together and towards the QCP. The field response of these transitions suggest that both persist close to the vicinity of the QCP which could be the key to understanding the details of its unconventional superconductivity, and understanding superconductivity in heavy fermion materials more broadly.