Unusual enhancement of effective magnetic anisotropy with decreasing particle size in maghemite nanoparticles

In magnetic nanoparticles (NPs), the observed increase in the effective magnetic anisotropy Keff with the decrease in particle size D is often interpreted, sometimes unsuccessfully, using the equation Keff = Kb + (6KS/D), where Kb is the bulk-like anisotropy of the core spins and KS is the anisotropy of spins in the surface layer. Here, we test the validity of this relation in γ-Fe2O3 NPs for sizes D from 15 nm to 2.5 nm. The samples include oleic acid-coated NPs with D = 2.5, 3.4, 6.3, and 7.0 nm investigated here, with results on 14 other sizes taken from literature. Keff is determined from the analysis of the frequency dependence of the blocking temperature TB after considering the effects of interparticle interactions on TB. For the γ-Fe2O3 NPs with D \u3c 5 nm, an unusual enhancement of Keff with decreasing D, well above the magnitudes predicted by the above equation, is observed. Instead the variation of Keff vs. D is best described by an extension of the above equation by including Ksh term from spins in a shell of thickness d. Based on this core-shell-surface layer model, the data are fit to the equation Keff = Kb + (6KS/D) + Ksh{[1−(2d/D)]−3−1} with Kb = 1.9 × 105 ergs/cm3, KS = 0.035 ergs/cm2, and Ksh = 1.057 × 104 ergs/cm3 as the contribution of spins in the shell of thickness d = 1.1 nm. Significance of this result is discussed