B-Site Cu²⁺Substitution and Strain-Mediated Magnetic Evolution in La₂CoRuO₆Double Perovskite: Insights from Experiment and DFT + U-Corrected Calculations

Understanding the magnetic ground states of double perovskites remains complex due to competing exchange interactions, spin–orbit coupling, and structural disorder. This study explores the substitution of Cu²⁺ for Co²⁺ in La₂CoRuO₆ (LCRO), integrating experimental and DFT methods to probe the structural and electronic effects influencing magnetism. Pristine LCRO exhibits a monoclinic P2₁/c phase with dominant antiferromagnetic (AFM) Co²⁺–O–Ru⁴⁺ interactions. Low-level Cu²⁺ substitution (x = 0.05 and 0.3) induces a strain-driven transformation to a tetragonal I4/m phase, introducing structural inhomogeneity and mixed valence states. These lead to competing ferromagnetic (FM) interactions (Cu²⁺–O–Ru⁴⁺/Cu²⁺), while AFM order partially persists at x = 0.3 due to orbital asymmetry and strain effects. Magnetic measurements and DFT calculations show a Néel temperature (T_N) shift from 28.7 to 39.8 K (x = 0.05), and emerging FM behavior at 19.2 K. At x = 0.3, AFM suppression and a Curie temperature (T_C) of 36.5 K reveal dominant FM pathways. Finite-size corrected Curie–Weiss analysis highlights the role of strain and particle size in modulating magnetic properties and restoring intrinsic behavior in larger particles.