Influence of Er substitution on frustrated magnetism, Co oxidation state, and spin dynamics of Ca ₃ Co ₂ O ₆

Frustrated quasi-one-dimensional spin-chain systems provide an ideal platform for exploring competing magnetic interactions and slow spin dynamics. In this work, we examine the influence of Er substitution at the Ca site in Ca_3-<i>x</i>Er<i>_x</i>Co₂O₆(<i>x</i>= 0.0-0.40), motivated by the role of rare-earth doping in controlling magnetic frustration. A combined experimental and theoretical approach involving structural characterization, DC magnetization, magnetic relaxation, magnetocaloric analysis, and density functional theory (DFT) is employed. Magnetic measurements reveal a monotonic decrease in the Weiss temperature (<i>θ</i>p) with increasing Er content, suggesting enhanced AFM superexchange interactions between Co²⁺and Co³⁺ions. Er substitution induces a spin-state transition of Co ions at trigonal prismatic sites from<i>S</i>= 2→<i>S</i>= 3/2, while Co at octahedral sites remains unaffected (<i>S</i>= 0). Field-induced magnetization transition from ferrimagnetic to ferromagnetic weakens with increasing Er content, indicating reduced magnetic frustration. Spin relaxation exhibits non-exponential behavior well described by the Weron model (<i>β</i>∼ 0.45, k > 0). Magnetocaloric measurements reveal a positive magnetic entropy change at low temperatures for<i>x</i>= 0.0 and 0.10, associated with competing magnetic states, which diminishes for higher Er concentrations. DFT (GGA +<i>U</i>) calculations provide Co valence electron redistribution and suggest a tendency toward half-metallic behavior driven by Co 3d-O 2p hybridization. These results demonstrate that Er substitution provides an effective route to tune magnetic frustration, spin dynamics, and spin-state transitions in frustrated low-dimensional oxides.