Measurement of specific heat is a powerful technique for the investigation of novel materials. Superconducting and magnetic systems, in particular, can be thoroughly characterized by studying their electronic contribution to the specific heat. To investigate their behavior in magnetic fields, single crystals need to be used, since the magnetic properties are dependent on the crystalline orientation. Crystal quality is often enhanced when sizes are reduced down to below the 100 μm scale, which is lower than the limit of conventional calorimeters. Nanocalorimetry allows to detect the weak electronic signature in the specific heat for such small samples with a preserved combination of high resolution and good accuracy. This is achieved by miniaturizing the device using microsystems technology and by a proper optimization of the measurement conditions.

In this thesis, a nanocalorimeter designed for the study of samples with masses from sub-μg  to 100 μg in the temperature range 1-350 K is used for studying three different systems, yielding insights into their physical properties.

In the magnetocaloric compound Fe₂P a deep thermodynamic understanding of the first-order magnetic phase transition at the Curie temperature T_C ≈ 217 K is lacking. The nanocalorimeter is used to map the magnetic phase diagram for fields applied parallel and perpendicular to the easy axis of magnetization. Two different phase diagrams are obtained depending on the applied field orientation. The first-order magnetic phase transition is characterized by specific and latent heat, providing a textbook example of thermodynamic properties around such a transition. The results are complemented with a combined nanocalorimetry - x-ray diffraction study and by magnetization measurements.

The iron-based high-temperature superconductor BaFe₂(As_1-xP_x)₂ shows several anomalous physical properties which have been associated to the presence of a quantum critical point. High-resolution specific heat measurements are an important piece of the puzzle in understanding the behavior of this material. The specific heat is measured as a function of phosphorus doping x in the superoptimally substituted range and several superconducting parameters are extracted. An evolution from a single-gap to a two-gap is seen with doping, as well as a decrease of the London penetration depth close to optimum doping, without signs of divergence.

The superconducting properties are as well investigated in the metastable β phase of gallium. β-Ga is obtained in-situ from the stable α-Ga by increasing the temperature about 10 K above the melting point. This novel method to produce β-Ga allows more reproducible and reliable measurements in comparison to traditional methods. A thorough thermodynamic characterization of the metastable phase is obtained, giving insights into the conditions for a strongly enhanced superconductivity in β-Ga in comparison to α-Ga. β-Ga is found to be a strong-coupling superconductor, with a 2.55 higher density of states at the Fermi energy in comparison to α-Ga.

These measurements demonstrate how several problems in condensed matter physics can be addressed through nanocalorimetry, which allows mapping various phase diagrams and obtaining fundamental thermodynamic properties on high-quality samples in magnetic fields.