Quantifying superparamagnetic signatures in nanoparticle magnetite: a generalized approach for physically meaningful statistics and synthesis diagnostics

Abstract

Magnetization is a common measurable for characterizing bulk, nanoscale, and molecular materials, which can be quantified to high precision as a function of an applied external field. These data provide detailed information about a material's electronic structure, phase purity, and impurities, though interpreting this data can be challenging due to many contributing factors. In sub-single-domain particles of a magnetic material, an inherently time-dependent rotation of the entire particle spin becomes possible. This phenomenon, known as superparamagnetism (SPM), simultaneously represents a very early size-dependent property to be considered, while being one of the least explored in the current quantum materials era. This discrepancy is, at least in part, due to the need for models with less built-in complexity that can facilitate the generation of comparative data. In this work, we map an extensive dataset of variable-size SPM Fe₃O₄ (magnetite) to an intrinsic statistical model for their field-dependence. By constraining the SPM behavior to a probabilistic model, the data are apportioned to several decorrelated sources. From this, there is strong evidence that standard measures such as saturation magnetization, M_S, are poor comparative parameters, being dependent on experimental knowledge and measurement of the magnetic mass. In contrast, parameters of the intrinsic probability distribution, such as the maximum susceptibility, χ_max, are far better suited to describe the SPM behavior itself and do not propagate unknown magnetic mass error. By confining the data fitting to intrinsic variables of the model distribution, scaling parameters, and linear contributions, we find greater value in magnetic data, ultimately aiding potential synthesis diagnostics and prediction of new properties and functionality.