Nanoparticle size distribution and surface effects on the thermal dependence of magnetic anisotropy

Standard approaches to investigate the anisotropy of nanoparticle assemblies are either by means of zero-field-cooled-field-cooled DC magnetization curves or by analyzing the coercivity at low temperatures. However, these methodologies are restricted to average values of an anisotropy constant, without probing its temperature dependence or symmetry. In this context, analyzing the thermal dependence of coercivity arises as a more comprehensive approach to assess anisotropic properties. Here, we investigate experimentally the thermal dependence of coercivity for cobalt ferrite nanoparticle samples synthesized by different methods, in a large range of nanoparticle diameters, resulting in samples with different internal structure, surface roughness, and size distribution. Our analysis consists of accounting for the size distribution and thermal dependence of the relevant variables, allowing us to access the anisotropy constant as a function of temperature. The results indicate that the surface plays an important role in the low-field determined anisotropy constants, with the thermal dependence pointing to a combination of types/sources of anisotropy affecting the coercivity. While the cubic magnetocrystalline anisotropy dominates for nanoparticles with higher diameter, the influence of surface contribution increases substantially for smaller sizes. The state of the surface is shown to be key for determining the main source of anisotropy.The authors gratefully acknowledge the financial support of the Brazilian agencies CAPES, CNPq (Grants 465259/2014-6, 202340/2015-5 and 400849/2016-0), INCT-FCx (Grant 2014/50983-3) and FAP-DF (Grants 0193.001569/2017 and 0193.001376/2016). A.L.O. acknowledges support from the Universidad Pública de Navarra (Grant PJUPNA2020). The authors of University of Brasília and Sorbonne Université acknowledge support by contract CAPES/COFECUB no 88881.370915/2019-01 and Ph959/20