  Magnetocaloric properties of an inhomogeneous magnetic system of a 7.6 nm
La${}_{0.7}$Sr${}_{0.3}$MnO${}_{3}$ consisting of superparamagnetic (SPM) with
blocking temperature ( $T_B$ = 240 K) and ferromagnetic (FM) phases ( $T_C$ =
290 K) is studied by dc magnetization measurements. Isothermal magnetization
versus applied magnetic field is carried out from 100 K to 320 K in magnetic
fields up to 4 kOe to determine changes in the magnetic entropy ($-\Delta S_M$)
and the relative cooling power (RCP). Due to the co-existence of SPM and FM
phases, there are two peaks in the temperature dependence of$-\Delta S_M$ in
different applied magnetic fields from 1.3 kOe to 4 kOe. The peaks are at 220 K
and 270 K which are close $T_B$ and $T_C$ of the film. The highest RCP occurs
at 270 K (which is in $T_B$ $\mathrm{<}$ $T$ $\mathrm{<}$ $T_C$) in H = 4 kOe
with the value of 0.19 (J/kg K). The $-\Delta S_M$ vs T data are fit to the
exponent power law, $-\Delta S_M=a H^n$ where it shows good fits for the whole
measured temperature range. This analysis reveals a deviation of n from $n$ =
2/3 which is likely due to the presence of SPM spin clusters in the dead layer
for $T$ $\mathrm{<}$ $T_C$. Results show that the thin film of
La${}_{0.7}$Sr${}_{0.3}$MnO${}_{3}$ can be a good candidate for magnetic
refrigeration devices with multiple RCP peaks in low and high temperatures.
