adiabatic demagnetization · gadolinium · large-spin molecules · magnetocaloric effect · molecular magnetismThe exploitation of magnetic materials is ubiquitous in our everyday life, with the most recent applications ranging from medicine to tribology. One peculiar feature of magnetic materials is the temperature change following a variation of the applied magnetic field in adiabatic conditions, and the first observation of this effect in metallic iron dates back to 1881. The first investigations of this phenomenon, known as the magnetocaloric effect (MCE) in paramagnetic salts to achieve low temperatures are part of the Nobel lecture of William F. Giauquem, who was awarded with the Nobel Prize in Chemistry in 1949.MCE, which results in a temperature drop during an adiabatic demagnetization, is a valid alternative to gas decompression for cooling.[1] It can be exploited in cyclic magnetization and demagnetization processes by switching on and off the thermal link with the bath (Carnot cycle). The lack of mechanical moving parts makes this approach energetically more efficient and easier to use compared to standard cryogenerators or 3 He-4 He dilution fridges. Its use is particularly appealing for very demanding conditions, such as aerospace applications.MCE is indeed based on very basic principles of thermodynamics, that is, the entropy change DS m of a magnetic system once it is exposed to a magnetic field that, in general, polarizes the magnetic moments, thus reducing the degrees of freedom of the system. When the field is brought back to zero, the magnetic contributions to the entropy increase (Figure 1). If the process of demagnetization occurs without any heat flow from the environment to the magnetic system, that is, in adiabatic conditions, a drop in temperature of the magnetic system DT ad occurs. These two parameters, DS m and DT ad , characterize the magnetocaloric properties of a material. To understand which are the key parameters to adjust during the design of an optimized MCE material, it is useful to recall some basic thermodynamic relations:where H is the applied magnetic field and M and C are the field-and temperature-dependent magnetization and specific heat, respectively. The first requirement for a large magnetocaloric efficiency is therefore a strong temperature dependence of the magnetization. This is observed close to the ordering temperature for a ferromagnet, while for a paramagnet it can only be achieved at low temperature. Thus ferromagnetic materials that are mainly based on lanthanide alloys or, more recently, on manganites, are investigated for cooling around room temperature, while paramagnetic demagnetization is used for cryogenic temperatures. Nuclear spins, which are polarized by a magnetic field only at lower temperatures, are employed to attain submillikelvin temperatures.Research on high-temperature magnetocaloric materials to replace standard refrigeration has to face problems related mainly to thermal hysteresis of magnetically ordered materials. On the other hand, the use of...