Understanding phase transitions in low dimensional systems by highly sensitive specific heat measurements

During the last 20 years, the possibility of fabricating nanoscale samples has opened the possibility to study critical phenomena in reduced dimension systems. This includes strong thermal fluctuations, fluctuations of the order parameter, the weakening of the interactions involved and the onset of a competition between surface and volume effects; the major pending question being the existence of singularities of thermodynamic functions at the phase transition in 0D, 1D or 2D magnetic or superconducting systems. Thanks to innovative experimental development based on suspended sensors made at Institut Néel, a very sensitive thermal experiment permits the measurement of specific heat signatures of very small mass sample (down to the nanogram) [1].

In this presentation, I will detail recent experiments demonstrating the power of the specific heat tool to study phase transitions at low dimension. Various illustrations will be given starting from magnetic materials like CoO down to very small thickness (few nm) where a significant reduction in the Néel temperature of CoO ultra-thin films has been revealed. It is found that the films consist of weakly coupled antiferromagnetic (AF) grains. The T_N reduction from large to small grain samples scales with the grain size reduction, according to the Binder theory of critical phenomena in systems of reduced dimensions.

Then, I will present measurements performed on submicron mesoscopic superconductors (ring, disk) where phase transitions between different vortex states have been evidenced as a function of applied magnetic field [2,3]. Finally, I will review recent experimental development allowing the measurement of in situ cold deposited superconducting thin films close to the insulating regime. A quench condensed apparatus has been mounted permitting the deposition of the sample directly on the Si membrane sensors at low temperature. Heat capacity measurement can be done continuously as a function of the thickness in granular or ultra-thin film through the insulator to superconducting transition [4]. This innovative equipment paves the way to new measurement of specific heat anomaly in low dimensional systems, in the presence of fluctuations or close to a Quantum Phase Transition.