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A general method for the quantification of dipolar interactions in assembliesof nanoparticles has been developed from a model sample constituted bymagnetite nanoparticles of 5 nm in diameter, in powder form with oleic acid asa surfactant so that the particles were solely separated from each otherthrough an organic layer of about 1 nm in thickness. This quantification isbased on the comparison of the distribution of energy barriers formagnetization reversal obtained from time-dependent relaxation measurementsstarting from either (i) an almost random orientation of the particlesmagnetizations or (ii) a collinear arrangement of them prepared by previouslyfield cooling the sample. Experimental results and numerical simulations showthat the mean dipolar field acting on each single particle is significantlyreduced when particles magnetizations are collinearly aligned. Besides, theintrinsic distribution of the energy barriers of anisotropy for thenon-interacting case was evaluated from a reference sample where the samemagnetic particles were individually coated with a thick silica shell in orderto make dipolar interactions negligible. Interestingly, the results of thenumerical simulations account for the relative energy shift of the experimentalenergy barrier distributions corresponding to the interacting andnon-interacting cases, thus supporting the validity of the proposed method forthe quantification of dipolar interactions.

Quantification of dipolar interactions in Fe$_{3-x}$O$_4$ nanoparticles