Insulating phase in Sr$_2$IrO$_4$: An investigation using critical analysis and magnetocaloric effect

The nature of insulating phase in 5$d$ based Sr$_2$IrO$_4$ is quite debated as the theoretical as well as experimental investigations have put forward evidences in favor of both magnetically driven Slater-type and interaction driven Mott-type insulator. To understand this insulating behavior, we have investigated the nature of magnetic state in Sr$_2$IrO$_4$ through studying critical exponents, low temperature thermal demagnetization and magnetocaloric effect. The estimated critical exponents do not exactly match with any universality class, however, the values obey the scaling behavior. The exponent values suggest that spin interaction in present material is close to mean-field model. The analysis of low temperature thermal demagnetization data, however, shows dual presence of localized- and itinerant-type of magnetic interaction. Moreover, field dependent change in magnetic entropy indicates magnetic interaction is close to mean-field type. While this material shows an insulating behavior across the magnetic transition, yet a distinct change in slope in resistivity is observed around $T_c$. We infer that though the insulating phase in Sr$_2$IrO$_4$ more close to be Slater-type but the simultaneous presence of both Slater- and Mott-type is the likely scenario for this material.