Modern rare-earth-containing magnetocaloric materials: Standing on the shoulders of giant Gd5Si2Ge2

The magnetocaloric effect (MCE) is a phenomenon where varying magnetic fields cause temperature changes in magnetic materials, primarily near their thermomagnetic phase transitions. Its first observation was the induced temperature change of 0.7 K (for 1.5 T at 630 K) in a nickel sample near its thermomagnetic phase transition, but the heart of modern magnetocaloric materials research was shaped by Vitalij K. Pecharsky's and Karl A. Gschneidner Jr.'s discovery of the giant magnetocaloric effect (GMCE) in the famous Gd5Si2Ge2. Significant MCE values are achieved when structural transformations coincide with magnetic transitions. This chapter focuses on rare-earth (RE)-containing magnetocaloric compounds that stand on the shoulders of the "giant Gd5Si2Ge2", i.e., whose MCE values meet the GMCE threshold and pays attention to their material criticality assessment. It highlights recent breakthroughs related to first-order thermomagnetic phase transitions (FOMT) and magnetocalorics, including the quantitative criteria to identify FOMT and the critical point at which FOMT crossovers to second-order thermomagnetic phase transition (SOMT). The chapter examines the massive magnetocaloric materials library, including lanthanide metals, binary lanthanide-metalloid compounds, binary lanthanides-transition metals, ternary intermetallics, RE oxides, and alloys with multiple principal elements (known as high entropy alloys). The book chapter also discusses a directed search strategy for designing intermetallics with multi-principal elements exhibiting FOMT and GMCE, which can largely balance criticality and enable a combination of properties with mechanical stability if it is properly applied when searching for and developing modern magnetocaloric materials containing highly critical rare-earth elements.