Evidence of Griffiths-like clustered phase and nonuniversal critical behavior in the double perovskite Er 2 NiMnO 6

The Griffiths phase (GP), a state of magnetic disorder persisting above the Curie temperature $({T}_C)$, is frequently observed in rare-earth and transition-metal oxides, often leading to anomalous quantum critical fluctuations near ${T}_C$. In this study, we investigate the ordered double perovskite ${\mathrm{Er}}₂{\mathrm{NiMnO}}₆$ (ENMO), uncovering similar critical instabilities through detailed magnetic, magnetocaloric, and heat capacity measurements and analysis. The derived critical exponents near the critical region, ${T}_C$ $[\ensuremath{\alpha}=\ensuremath{-}0.942(1),$ $\ensuremath{\beta}=1.081(8),$ $\ensuremath{\gamma}=0.765(6), \text{and} \ensuremath{\delta}=1.731(7)]$ deviate significantly from all known universality classes of magnetism, yet they satisfy the magnetic scaling equation of state. Complementary magnetocaloric effect (MCE) analysis confirms these critical exponents while revealing a substantial low-temperature magnetic entropy change and adiabatic temperature values ($\ensuremath{-}\mathrm{\ensuremath{\Delta}}{S}_{\text{max}}$ $\ensuremath{\approx}$ 15 J/kg K and $\mathrm{\ensuremath{\Delta}}{T}_{\text{ad}}$ $\ensuremath{\approx}$ 15 K for $\mathrm{\ensuremath{\Delta}}H=70$ kOe), further supported by heat capacity data. The anomalous critical behavior is attributed to quantum GP formation above ${T}_C$, consistent with predictions from both the Bray model and Yang-Lee zeros theory. Additionally, ENMO maintains a robust insulating character across the measured temperature range, well-described by polaron hopping mechanisms. These findings challenge conventional models of magnetic phase transitions in disordered systems, emphasizing the necessity for new theoretical frameworks to account for clustered-phase dynamics and the development of revised universality classes to explain such unconventional critical phenomena.