A comprehensive study of the temperature ($T$) and magnetic field ($H$) dependence of magnetic entropy change ($\Delta S_M$) for different materials exhibiting inverse magnetocaloric effect (IMCE) is reported. We show that $\Delta S_M$ follows a power-law dependence of $H$ ($\Delta S_M$ ∼ $H^n$; $n$ is an exponent) for these compounds. In contrast to conventional magnetocaloric effect (CMCE), $n$ is independent of $H$ and $T$ in the case of IMCE. As a result, a universal master curve can be constructed to describe $\Delta S_M\left(T\right)$ of the IMCE systems for different $H$ without rescaling the temperature axis. This is completely different from that reported for CMCE, where the rescaling of the temperature axis with the introduction of at least one reference temperature is needed for constructing a universal curve. The different universal behavior of IMCE is attributed to the constant value of $n$ in any field and temperature, which is a generic feature of IMCE systems irrespective of their magnetic state and nature of phase transition. From the proposed phenomenological universal curve, one can extrapolate the magnetocaloric properties of IMCE systems in any temperature and magnetic field range, which would be helpful in designing controlled active magnetic refrigeration devices.

Transport and magnetic properties have been studied in two sets of sol-gel prepared ${\mathrm{Pr}}_{1∕2}{\mathrm{Sr}}_{1∕2}\mathrm{Mn}{\mathrm{O}}_3$ nanoparticles having an average particle size of $30$ and $45\mathrm{nm}$ . Our measurements suggest that the formation of a charge-ordered state is largely affected due to lowering of the particle size, but the ferromagnetic transition temperature $\left(T_C\right)$ remains unaffected.

Observation of charge ordering in single crystalline and bulk polycrystalline systems of various rare-earth based manganites is well documented. However, there is hardly any manifestation of the same when the grain size is reduced to nanoscale. We have observed charge ordering in the case of nanocrystalline ${\mathrm{Pr}}_{0.65}{\mathrm{Ca}}_{0.35}{\mathrm{MnO}}_3$ of average particle size $40\mathrm{nm}$. This phenomenon is attributed to the primary role played by the martensitic character of the charge order transition in the material.