Surface anisotropy broadening of the energy barrier distribution in magneticnanoparticles

Abstract

The effect of surface anisotropy on the distribution of energy barriers in magneticfine particles of nanometer size is discussed within the framework of theTln(t/τ0) scaling approach. The comparison between the distributions of the anisotropyenergy of the particle cores, calculated by multiplying the volume distributionby the core anisotropy, and of the total anisotropy energy, deduced by derivingthe master curve of the magnetic relaxation with respect to the scaling variableTln(t/τ0), enables the determination of the surface anisotropy as a function of the particle size. Weshow that the contribution of the particle surface to the total anisotropy energy can be welldescribed by a size-independent value of the surface energy per unit area which permits thesuperimposition of the distributions corresponding to the particle core and effectiveanisotropy energies. The method is applied to a ferrofluid composed of non-interactingFe3−xO4 particles of 4.9 nmaverage size and x about 0.07. Even though the size distribution is quite narrow in thissystem, a relatively small value of the effective surface anisotropy constantKs = 2.9 × 10−2 erg cm−2 gives rise to a dramatic broadening of the total energy distribution. The reliability of theaverage value of the effective anisotropy constant, deduced from magnetic relaxation data,is verified by comparing it to that obtained from the analysis of the shift of the acsusceptibility peaks as a function of the frequency.