Structural tuning interlinking various optical, dielectric and magnetic trends in annealed Mn0.5Zn0.5Fe2O4 spinel ferrites nanostructures

•Important structural parameters including crystallite size, lattice constant and strain, dislocation and X-ray densities, polaron radius and specific surface area have been studied in spinel Mn0.5Zn0.5Fe2O4 nanoparticles against the variation in annealing temperatures.•Optically, tuning in direct/indirect band gaps, metallization criterion and Urbach energy owing to the alterations in available energy states have been investigated.•Refractive index, dielectric constant (real and imaginary), skin depth, optical density and extinction coefficient have also been studied.•Magnetically, saturation magnetization, coercivity, remnant magnetization, magnetic moment and exchange bias along with others have been investigated thoroughly.