The magnetic correlations in double perovskites $\mathrm{L}{\mathrm{a}}_2\mathrm{M}{\mathrm{n}}_{2-x}\mathrm{N}{\mathrm{i}}_x{\mathrm{O}}_6$ ($x=0.5$, 0.75, 1.0, 1.25, and 1.5) have been systematically investigated across macroscopic, mesoscopic, and microscopic length scales using temperature-dependent bulk DC magnetization, neutron depolarization, and neutron powder diffraction measurements, respectively. The magnetic properties evolve from a long-range ferromagnetic (FM) order to a cluster ferromagnetic/spin-glass (FM/SG) behavior as the Ni concentration increases. This evolution is directly linked to changes in the crystal structure, transitioning from pure orthorhombic ($x=0.5$) to mixed orthorhombic and monoclinic ($x=0.75-1.0$), and eventually to mixed trigonal and monoclinic ($x=1.25-1.5$) symmetries. Ni substitution enhances the magnetic ordering temperature from 170 K ($x=0.5$) to 280 K ($x=1.0$), but this is accompanied by a reduction in both magnetization and ordered magnetic moment. Beyond $x=1.0$, any long-range magnetic ordering is absent. Additionally, all compositions exhibit a reentrant spin-glass-like phase at low temperatures (below $\sim 50$ K). Neutron diffraction analysis confirms that long-range FM order occurs only in the orthorhombic phase, while the monoclinic and trigonal phases lack such magnetic ordering. The temperature-dependent magnetic correlations are closely connected to variations in crystal structural parameters, including lattice constants and unit-cell volume. The electrical conductivity behavior, following the variable range hopping (VRH) model, highlights the role of multivalent Mn and Ni ions on the electrical properties. This study elucidates the microscopic mechanisms behind the tunable magnetic and electrical properties of $\mathrm{L}{\mathrm{a}}_2\mathrm{M}{\mathrm{n}}_{2-x}\mathrm{N}{\mathrm{i}}_x{\mathrm{O}}_6$, offering valuable insights for the design of advanced materials for spintronic applications.

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• Magnetic order
• Magnetic phase transitions
• Magnetism
• Ferromagnets
• Magnetic insulators
• Crystal structures
• Magnetization measurements
• Neutron diffraction