Magnetic correlation length in hard/soft core–shell magnetic nanoarchitectures

Abstract

The magnetic behavior of the hard/soft CoFe2O4@NiFe2O4 system is discussed within the framework of two established models for magnetic nanoparticle ensembles, the Langevin model and the Random Anisotropy Model (RAM), both of which assume coherent and spatially uniform magnetization within the magnetic volume. The proposed approach allows us to quantify how magnetic coherence develops across the structurally distinct core and shell regions and to identify the regime in which these models remain valid, as well as the conditions under which their interpretative limits emerge. In the superparamagnetic state at 300 K, the magnetic sizes extracted from Langevin fitting (∼5.5 nm for the core and ∼8.1 nm for the core–shell particles) are smaller than the geometric diameter, indicating partial spin disorder. Field-dependent blocking temperatures fitted using RAM yield correlation lengths Lcorr,0 ≈ 9–10 nm and intrinsic effective anisotropy constants Keff ≈ 3.2 × 105 J m−3 for both systems. These results reveal an intrinsic limitation of coherent-rotation models when applied to core–shell architectures: the effective energy barrier represents a composite parameter that includes contributions from the core, shell, surface, and interfacial regions, which cannot be individually disentangled within a macrospin framework.