Lattice enthalpies and magnetic loops in lanthanide iron garnets, Ln₃Fe₅O₁₂

Highlights: • The lattice enthalpies Δ_LH^θ of Ln₃Fe₅O₁₂ are determined by the Born–Haber cycle. • The obtained values are compared with those evaluated by other two methods. • (∂Δ_LH^θ/∂V_m) corresponds to an upper limit of the shear moduli (rigidity) of LnIGs. • The magnetic entropy = f (effective magnetic moment) for LnIGs represents a loop. • This effect of magnetic loop is new for the lanthanide series. - Abstract: Experimental lattice enthalpies Δ_LH^θ of lanthanide iron garnets Ln₃Fe₅O₁₂ (LnIGs) with Ln = Ce − Lu, have been determined from the Born–Haber thermochemical cycle. The results have been compared with those reported by other authors using numerical simulation or an empirical equation. The lattice enthalpy of PmIG has been predicted by linear interpolation between Δ_LH^θ of the adjacent NdIG and SmIG. It has been found that the partial derivative (∂Δ_LH^θ/∂V_m) for the series of LnIGs corresponds by magnitude and dimension to an upper limit of their rigidity. New effect of magnetic loops has been noted in the same series in the dependence of the lattice magnetic entropies on the effective magnetic moments (theoretical and experimental values)