Hole-doped perovskite-type manganites have received intensive attention due to their intriguing physical phenomena such as giant magnetocaloric effect and magnetic-phase transitions. However, the mechanism of internal ferromagnetic interaction still needs to be further explored due to the complex natures of competing double-exchange (DE) and super-exchange (SE) interaction, Jahn-Teller (JT) polaron localization, charge ordering, and phase separation scenarios. Critical exponent analysis near magnetic phase transition is a powerful tool to investigate the details of the ferromagnetic interactions and has been used frequently in various magnetocaloric materials. In this article, the critical behavior analyses of perovskite manganites in recent years are comprehensively reviewed. A large number of studies have shown that even in single-phase materials with uniform structure and composition, the critical behavior can be affected by multiple factors such as grain boundary density and the degree of disorder, making them difficult to fully describe the intrinsic ferromagnetism. In this review, firstly, the critical behaviors of typical manganites with different bandwidths in single crystal and polycrystalline are discussed. In a double-exchange dominated system such as La-Sr-Mn-O, short-range 3D-Heisenberg model is basically in good accordance with optimally-doped single crystal sample. However, it would be replaced by long-range mean-field critical behavior in polycrystalline sample when the correlation length exceeds the crystallite size. In a typical intermediate bandwidth system such as La-Ca-Mn-O exhibiting a complex phase diagram described by competing SE/DE interactions, JT polaron localization/delocalization, and Griffith phase disorder, the critical exponent can vary from 3D-Heisenberg model to tricritical mean-field model, for the crossover from first to second order phase transition. Secondly, the studies of elements doping and different fabrication methods indicate that the critical behavior of manganites can be effectively modulated, and vary between different theoretical models including even nonuniversal exponent for highly disordered magnetic system. In the following part, the influence of magnetic field on the critical behavior and field induced crossover phenomena of La-Ca-Mn-O system near tricritical point is analyzed and discussed in detail. Furthermore, the magnetocaloric effects of materials near the tricritical point collected in many studies are listed and compared with each other. Excellent magnetocaloric properties with high magnetic entropy change and relative cooling power in plenty of researches indicate that ideal magnetocaloric material would be very likely to be found in the materials near the tricritical point, which lay at the borderline between first-order and second-order phase transition. Consequently, it is suggested that perovskite manganites are still quite promising in the potential magnetic refrigeration applications, and need to be further developed.
