Investigation of magneto-transport properties of the co-doped La1.6-xPrxCa1.4-xBaxMn2O7 (x = 0.2 and 0.4) double-layered manganite

Structural and magneto-electrical transport properties of double-layered La1.6-xPrxCa1.4-xBaxMn2O7 (x = 0.2 and 0.4) manganite compounds were studied. X-ray diffraction patterns refinement shows that the samples crystallize in a tetragonal I4/mmm structure, whereas a rhombohedral structure phase with R3-c\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$R\stackrel{-}{3}c$$\end{document} space group is detected as a secondary phase. The electrical resistivity under 0 and 1 T exhibited a metal–insulator transition at TMI. It is found that the ρ(T) decreases with increasing Pr-Ba contents. Magnetoresistance (MR%) curves displayed a maximum value of ∼51.69% at 63 K for the x = 0.2 sample and decreases with increasing Pr-Ba concentrations to ∼33.44% at 64 K for x = 0.4 under 1 T. The obtained values of the temperature coefficient of resistivity for both samples have similar trend as TMI. Below TMI\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$T_{{MI}}$$\end{document}, ρT=ρ0-ρ0.5T0.5+ρ2T2+ρ5T5\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$~\rho \left( T \right) = \rho ~_{0} - \rho _{{0.5}} T^{{0.5}} + \rho _{2} T^{2} + \rho _{5} T^{5}$$\end{document} model fits well the resistivity curves which reflect a combination of the grain boundary effects, weak localization, electron–electron, and electron–phonon scattering to the electrical resistivity. Above TMI, the non-adiabatic small polaron hopping model describes the electrical resistivity behavior in T>θD/2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$T > ~\theta _{D} /2$$\end{document} region. The Mott’s 3D variable range hopping mechanism (3D-VRH) was found to be the most suitable mechanism for describing the high-temperature resistivity behavior between TMI and θD/2. The density of states near the Fermi level N(EF)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$N(E_{F} )$$\end{document}, mean hopping distance, (Rh)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$(R_{h} )$$\end{document} and mean hopping energy (Eh)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$(E_{h} )$$\end{document} of the charge carriers have been calculated from the experimental curves using Mott’s 3D-VRH model. The experimental and fitting curves of the resistivity and the related results are discussed in detail.