Lay summary
Perovskite materials have attracted very much attention in the last 15 years, since they represent some of the most likely alternatives to standard materials commonly used nowadays. The most famous examples are given by the high-temperature cuprate superconductors that allow transporting electricity without losses, giant magneto-resistance manganates or ferro-electric titanates that could be used for data storage devices. Recently, another very interesting class of materials showing giant magneto-resistance (MR) and metal-insulator (MI) transitions has been discovered: the cobalt perovskites with general formula R[1-y](Sr,Ba)[y]Co[2]O[5+x]. In addition, at high temperatures, the cobaltites are interesting for their large ionic conduction, thus showing potential for applications as gas sensors, oxidation catalysts, or electrode materials for fuel cells.Little is known about the correlation between the spin and charge degrees of freedom in perovskite cobaltites under extreme conditions, i.e. whether and to what extent the spin-state transitions affect the metal-insulator,charge- and spin-ordering transitions. Besides, the effective dimensionality of the cobaltites is known to directly affect their magnetic and electronic properties. In order to optimise these complex materials for industrial applications, it is crucial to understand the basic interactions that control their electronic and magnetic properties over a large range of magnetic fields, pressure and temperature.External pressure gives the possibility to change the spin-state of the Co ions by changing bond lengths and/or bond angles. In this respect, external pressure provides a unique tool to tune electronic and magnetic properties by changing the delicate energy balance between the crystal-field and the intra-atomic exchange energies.Temperature between hundreds and thousand K allows reproducing practical temperature range of gas sensors, electrode materials, etc. In this broad interval of pressure and temperature, the properties of the matter could be strongly modified, some of these modifications being non reversible.The great interest of some of these compounds also deals with the fact that a quantum critical point (QCP) can possibly be produced by tuning an external control parameter, such as hydrostatic pressure, chemical composition, or magnetic field. The proximity to a QCP is known to give rise to novel ground states, such as quantum magnetism and unconventional forms of superconductivity. Since quantum criticality is becoming increasingly recognized as a universal phenomenon in condensed matter physics, it is of paramount importance to understand how QCPs might stabilize new phases.