Two La0.5Ag0.1Ca0.4MnO3 Manganite Nanoparticles Synthesized via Sol–Gel and Solid-State Methods–Structural, Magnetic, and Magnetocaloric Properties

La0.5Ag0.1Ca0.4MnO3 manganite nanoparticles are synthesized via two different ways, namely, a solid-state reaction (S1) and the sol–gel process (S2). Their structural, magnetic, and magnetocaloric properties are reported. The powder X-ray diffraction (PXRD) and Rietveld refinement analyses confirm fully crystalline single-phase orthorhombic nanoparticles, even with different conditions of synthetic processes. Moreover, considering the magnetic phase transition of both samples through Banerjee’s criterion revealed a second-order paramagnetic–ferromagnetic phase transition. The influence of elaboration process on magnetic and magnetocaloric behaviors has been investigated. The solid-state sample exhibits a lower magnetic entropy change (Δ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\Delta$$\end{document} SM) value in comparison to that obtained by sol–gel reaction. Besides, the effect of magnetoelastic coupling and electron interaction in magnetocaloric properties was evidenced via Landau theory.