Correlation between critical magnetic behavior and griffiths phase in ferromagnetic La_0.7Sr_0.3Mn_1-xFe_xO_{3 (x=0.05) nanoparticle}

The magnetic behavior of the La0.7Sr0.3Mn0.95Fe0.05O3 nanoparticles was investigated. X-ray diffraction analysis revealed that this sample exhibited rhombohedral symmetry with R (3) over barc space group. The sample underwent a ferromagnetic-paramagnetic transition at approximately 290 K, characterized by a second-order phase transition. Interestingly, the state above the transition temperature is not purely paramagnetic but rather exhibits a short-range ferromagnetic order or Griffiths phase, which becomes more pronounced as the temperature increases up to the Griffiths transition temperature (similar to 345 K). The values of the critical exponents obtained in this study, beta = 0.671, gamma = 1.087, and delta = 2.612, with T-C = 290.09 K, are distinct from those of any known universality class, and are confirmed by a single scaling equation of state. This unusual behavior is ascribed to the existence of the Griffiths phase, which reflects the unconventional critical behavior of magnetic susceptibility. In addition to conventional magnetic measurements, detailed studies of isothermal magnetization and magnetocaloric effects have been performed, and theoretical analyses have been utilized to further explore the Griffiths phase. Furthermore, a correlation between the Griffiths phase and the anomalous critical parameters was established.