Dipolar interaction and demagnetizing effects in magnetic nanoparticle dispersions

FRANCISCO H SÁNCHEZ; PEDRO MENDOZA ZÉLIS; LORENA ARCINIEGAS; GUSTAVO A PASQUEVICH; MARCELA FERNÁNDEZ VAN RAAP

La Plata

Congreso; VI Reunión Nacional Sólidos 2015; 2015

The problem of the influence of dipolar interactions on the magnetic response of nanoparticle (NP) dispersions has been a concern for decades and the subject of numerous papers [1,2,3,4,5]. Although important advances were made, relevant aspects of dipolar interaction influence on NP response are frequently neglected, especially due to the lack of a simple conceptual frame usefulfor the treatment of this problem. Dipolar interactions between the NPs belonging to a solid or liquid dispersion give rise to modifications of susceptibility and NP magnetic moment characteristic time, in comparison to the values of these quantities in the absence of interactions. The appropriate description of this problem is relevant for applications of single domain magnetic NPs, for example in biomedicine. In this talk a useful approximation aimed to describe magnetic susceptibility of NP solid dispersions is introduced, and applied to experimental results. The model is built from conceptsbased on demagnetizing effects of magnetic dipolar interactions. By making reasonable simplifying approximations an expression for the principal components of an effective demagnetizing tensor N is achieved. The model allows for the analysis of the magnetic response of uniform and non uniform space distributions of NPs (i.e., occurrence of clustering). To simplify its formulation meancharacteristic NP (cluster) sizes and mean NPs (clusters) near neighbor distances are represented by single parameters, D( c D ) and d ( c d ), respectively. An expression for N is derived, which is a function of mean relative distances between NPs and between clusters,g = d / D andc c c g = d / D . N depends also on demagnetizing tensors associated with specimen shape, s N , and average cluster shape, c N . It is shown that principal components of N are given by N N N u x y zwherej and c j are packing factors adequately defined to consider NPs and clusters space occupation. Average magnetic dipolar energy per NP is estimated as a function of u N , NP particle volumeV and NP magnetization. Experimental results of M(H,T), non-published and taken from literature, are discussed in theframe of the introduced model. Novel results [6] were obtained from rectangular prism specimens taken from dispersions of polyacrilic acid coated magnetite NPs in PVA hydrogels with NP mass fractions m x ranging from 0.0139 to 0.0934. Results from literature [7, 8] correspond to oleic acid coated magnetite NPs dispersed in PEGDA-600 polymer, for specimens with = 0.0015, 0.003, 0.027 m x .Analyses clearly demonstrate and quantify clustering effects in both cases. Significant structural information is retrieved in both examples. It was found that clusters are randomly oriented and c g varies from 2.2 to 7.5 while g remains almost constant at 1.4 ? 1.6. It is shown that recorded lowfield susceptibility and size of NP magnetic moment retrieved from magnetic measurements is strongly affected by dipolar interactions, and hence by prism relative dimensions. This observation highlights the importance of reporting complete information on measurement geometry when publishing results on NP dispersions magnetic response. Using model expressions, intrinsicproperties corresponding to non interacting NPs, such as magnetic susceptibility and magnetic moment can be retrieved.1 R. López-Ruiz, F. Luis, J. Sesé, J. Bartolomé, C. Deranlot and F. Petroff, Europhysics Letters 89 67011 (2010),doi:10.1209/0295-5075/89/670112 B. Hillebrands, S.O. Demokritov, C. Mathieu, S. Riedling, O. Büttner, A. Frank, B. Roos, J. Jorzick, A.N. Slavin, B.Bartenlian, C. Chappert, F. Rousseaux, D. Decanini, E. Cambril, A. Müller, U. Hartmann, Preprint Server AG Hillebrands:http://www.physik.uni-kl.de/w_hilleb, J. Mag. Soc. Jpn. 23, 670 (1999)3 R. K. Das, S. Rawal, D. Norton, and A. F. Hebard, J. Appl. Phys. 108, 123920 (2010), doi:10.1063/1.35242774 Paolo Allia, Paola Tiberto, J Nanopart Res 13 7277 (2011), DOI 10.1007/s11051-011-0642-25 Gabriel T. Landi, Journal of Applied Physics 113, 163908 (2013); doi: 10.1063/1.48025836 F.H. Sánchez et al., to be published7 Paolo Allia, Paola Tiberto, J Nanopart Res 13 7277 (2011), DOI 10.1007/s11051-011-0642-28 P. Allia, P. Tiberto, M. Coisson, A. Chiolerio, F. Celegato, F. Vinai, M. Sangermano, L. Suber, G. Marchegiani, J NanopartRes (2011) 13:5615?5626, DOI 10.1007/s11051-011-0642-2