Quantitative Understanding of Superparamagnetic Blocking in Thoroughly Characterized Ni Nanoparticle Assemblies

Thanks to advances in chemical synthesis that enable control over the size, structure, properties, and functionalization, magnetic nanoparticles (NPs) present unique opportunities in areas as diverse as data storage, cancer treatment, and biomedical imaging. While superparamagnetism dominates the properties of magnetic NPs, a quantitative understanding of superparamagnetic blocking in NP assemblies remains elusive. We address this challenge here via comprehensive magnetic characterization and analysis of soft ferromagnetic NP ensembles based on Ni. NPs were synthesized by the injection of a Ni-oleylamine (OAm) complex into 200 °C trioctylphosphine (TOP), with size control achieved via the TOP:OAm ratio, reaction time, and differential centrifugation. X-ray diffraction, electron microscopy, and various spectroscopies reveal polycrystalline/twinned face-centered-cubic Ni NPs with mean diameters from 4 to 22 nm, dispersities down to 10%, and TOP and OAm ligands. Superparamagnetic blocking temperatures are carefully determined, quantitatively accounting for the substantial yet frequently ignored effects of dispersity, resulting in mean blocking temperatures spanning 5 K to >300 K. Even accounting for an ∼1 nm-thick magnetically dead/canted shell (deduced from magnetization) and the temperature dependence of the Ni magnetocrystalline anisotropy, these mean blocking temperatures cannot be quantitatively reproduced. Remarkably, this discrepancy is substantially resolved by accounting for shape anisotropy effects that result from even modest average deviations from spherical shapes. A quantitative understanding of the size-dependent blocking temperature of soft ferromagnetic metallic NP assemblies is thus achieved, with no adjustable fitting parameters, by quantitatively accounting for the size distribution, effective ferromagnetic volume, temperature-dependent magnetocrystalline anisotropy, and random shape anisotropy. While frequently ignored, the characterization of such factors is thus vital, paving the way to quantitative understanding of superparamagnetism in other magnetic NP systems.