Analytical modeling of magnetocaloric effect in dense nanoparticle systems

Determining the magnetocaloric effect (MCE) in dense nanoparticle systems (DNSs) poses a challenge due to the increased complexity of matter at the nanoscale. Given the interparticle magnetic interactions, diverse particle size and shape distributions, and the presence of inhomogeneous magnetic phases, selecting a suitable phenomenological model is essential to describe the temperature dependence of magnetic behavior in DNSs. Herein, we chose a cost-effective Ni100-xCrx DNS with adjustable magnetic transitions to showcase the resilience of the MCE across a broad temperature range (147-614 K). While the hyperbolic tangent model appears more fitting for materials with a single Curie temperature (T-C), such as its parent bulk alloys, in the presence of a T-C distribution a Gaussian distribution model proves to be better suited for DNSs. The latter model yields a magnetic entropy change, Delta S-max = 0.09-0.15 J kg-K-1 in the DNS at a tiny field of 0.1T. The correlations between the broadening of the MCE peak and T-C distribution are attributed to the particle size distribution and chemical inhomogeneity present in the DNS, paving the way for fine-tuning MCE-related properties such as the relative cooling power (13.17-33.45 J kg(-1)) and adiabatic temperature change (0.03-0.17 K). Our methodology not only enhances the potential for designing innovative MCE materials with broader operating ranges but also validates the universality of our phenomenological model for other families of nanocrystalline/nanogranular oxides/alloys thin films.