PHYSICAL REVIEW E 91, 042317 (2015) Magnetic and structural study of electric double-layered ferrofluid with MnFe 2 O 4 @γ -Fe 2 O 3 nanoparticles of different mean diameters: Determination of the magnetic correlation distance E. S. Gonc ¸alves, * D. R. Cornejo, C. L. P. Oliveira, and A. M. Figueiredo Neto Instituto de F´ ısica, Universidade de S ˜ ao Paulo, S˜ ao Paulo, Brazil J. Depeyrot Instituto de F´ ısica, Universidade de Bras´ ılia, Bras´ ılia, Brazil F. A. Tourinho Instituto de Qu´ ımica, Universidade de Bras´ ılia, Bras´ ılia, Brazil R. Aquino Faculdade UnB Planaltina, Universidade de Bras´ ılia, Bras´ ılia, Brazil (Received 13 February 2015; published 30 April 2015) Magnetic fluids based on manganese ferrite nanoparticles were studied from the structural point of view through small angle x-rays scattering (SAXS) and from the magnetic point of view through zero-field cooling and field cooling (ZFC-FC) and ac susceptibility measurements (MS). Three different colloids with particles mean diameters of 2.78, 3.42, and 6.15 nm were investigated. The size distribution obtained from SAXS measurements follows a log-normal behavior. The ZFC-FC and MS results revealed the presence of an important magnetic interaction between the nanoparticles, characterized by a magnetic correlation distance . The colloidal medium can be pictures as composed by magnetic cluster constituted by N interacting particles. These magnetic clusters are not characterized by a physical aggregation of particles. The energy barrier energy obtained is consistent with the existence of this magnetic clusters. Besides the magnetic interaction between particles, confinement effects must be included to account for the experimental values of the magnetic energy barrier encountered. DOI: 10.1103/PhysRevE.91.042317 PACS number(s): 83.80.Hj, 75.75.−c, 75.50.Mm, 61.05.cf I. INTRODUCTION The study of magnetic properties of granular materials is an interesting subject of research in the field of condensed matter physics [1,2]. Due to their technological applications, in particular in information-storage devices, much effort has been devoted to understanding the magnetic behavior of these systems under the action of external magnetic fields. In the case of this type of device, grains are embedded in a solid nonmagnetic matrix and only the grains’ magnetic moments respond to the external field, since they do not rotate or diffuse in the matrix. Different characteristics of the granular medium are responsible for their magnetic properties, e.g., the size distribution of grains, their shape, typical dimension, magnetic moment, and magnetic anisotropy. On the other hand, magnetic nanofluids or ferrofluids, are colloidal dispersions of magnetic nanoparticles in a liquid carrier [3,4]. The great interest in investigating the magnetic properties of ferrofluids is due not only to their fundamental aspects but also to their technological applications, e.g., heat transfer [5] or sealing [6], as well as biological applications, including cancer treatment by magnetic hyperthermia [7], drug delivery [8], and contrast for magnetic resonance imaging (MRI) [9]. In the case of magnetic fluids, particles are free to rotate in the liquid medium, and different physical processes may occur as a function of the external magnetic field. The magnetic moment of the particle may align parallel to the external field, without the physical rotation of the particle * eduardos@if.usp.br (N´ eel rotation), or the particle rotates itself to align the magnetic moment parallel to the field (Brownian rotation) [10]. The different response time depends on parameters of the particle, e.g., volume, magnetocrystalline anisotropy, and of the fluid carrier, e.g., its viscosity. Among the experimental techniques used to investigate the magnetic properties of granular materials, the analysis of the magnetization under conditions of zero-field cooling (ZFC) and field cooling (FC) is widely used, as well as the ac magnetic susceptibility (MS) of the system [11–13]. The ZFC-FC technique allows us to determine the average blocking temperature (T B ) of the system, while the MS allows us to reveal the behavior of that parameter under time-dependent fields. Interestingly, from the magnetization measurements and appropriate modeling, it is possible to extract the blocking temperature distribution, which reveals the particles’ size-distribution function [1]. Nanostructured magnetic materials are often studied whether to determine the complex ac susceptibility [14] or the field dependence of the blocking temperature [15], and the coercive field [16] as a function of temperature and changes in the anisotropy constant [17,18] were investigated as well. Inter- actions between nanoparticles were investigated [1,17,19,20] also by calculations of dipole-dipole-coupled nanoparticles’ relaxation times [21] and through mean-field theory [22]. The analysis of the ZFC-FC magnetization curves is highly improved if a complementary experimental technique is employed. Among these techniques, small-angle x-ray scattering (SAXS) is one of the most adequate. The advantage of SAXS is that one can obtain directly from the scattering intensity curve the size-distribution function of particles in ferrofluids, and also evaluates the presence of clusters [23,24]. 1539-3755/2015/91(4)/042317(7) 042317-1 ©2015 American Physical Society