Surface and exchange anisotropy fields in MnFe2O4 nanoparticles: Size and temperature effects

Angular measurements of magnetic resonance are used to investigate the surface anisotropy field as well as the exchange anisotropy field in spherical ${\mathrm{MnFe}}_{\mathrm{2}}{\mathrm{O}}_{\mathrm{4}}$ magnetic nanoparticles as a function of temperature and particle diameter (D). The resonance field is a combination of angular dependent and angular independent fields, both affected by the surface anisotropy field, which in turn follows a $D^{\mathrm{-\alpha }}$ power law, with α very close to unity. The angular dependent component probes the surface anisotropy field while the angular independent component probes the exchange anisotropy field. In the temperature range from 100 to 250 K a negative surface anisotropy field is found, which increases as the particle size is reduced, indicating a radial orientation of the spins at the ${\mathrm{MnFe}}_{\mathrm{2}}{\mathrm{O}}_{\mathrm{4}}$ nanoparticle surface.