Unraveling the correlation between the remanence ratio and the dipolar field in magnetic nanoparticles by tuning concentration, moment, and anisotropy

Well-dispersed, uniform cobalt ferrite (CoFe₂O₄) nanoparticles (NPs) with diameters of 9, 11, 14, and 30 nm were synthesized by thermal decomposition of a metal–organic salt. Multiple variables, including the interparticle distance, moment, and anisotropy, were altered by dilution in a silica matrix and reduction in hydrogen to reveal the intrinsic correlation between the ratio of remanence to saturation magnetization (M_r/M_s) and interparticle dipolar interactions, the strength of which was estimated by the maximum dipolar field H_dip. To date, this correlation has not been systematically investigated experimentally. To prevent the particles from agglomerating, the reduction was performed after dilution. The results revealed that the correlation between M_r/M_s and H_dip roughly followed M_r/M_s ∝ 1/lgH_dip independent of the size, distance, moment, and anisotropy of the magnetic nanoparticles. In particular, the correlation was closer for the nanoparticle systems that had higher concentrations or moments, that is, stronger dipolar interactions. For the single-phase CoFe₂O₄ nanoparticles, deviation from M_r/M_s ∝ 1/lgH_dip can be attributed to the effects of surface spin, and for the slightly reduced nanoparticles, this deviation can be attributed to the pinning effect of CoFe₂O₄ on CoFe₂.