Magnetic coupling among spinel iron oxide microparticles by Mössbauer spectroscopy

2014 Mössbauer spectra of hydrous spinel iron oxide colloids and their evolution with thermal treatment have been interpreted using a modified Weiss local field model. It is found that interparticle interactions overcome the single particle anisotropy energy. Existence of a crystalline texture within aggregates is suggested. J. Physique Lett. 46 (1985) L-437 L-443 15 mm 1985, Classification Physics Abstracts 76.80 75.60J 75.30G 75.30K Mossbauer spectra of magnetic microcrystals are usually interpreted (see reviews [1,2]) in terms of non interacting particles with thermal fluctuations of their magnetization vector (M) among the easy directions of magnetization (superparamagnetic relaxation, SR) or about an easy direction in a pre-relaxation process (collective magnetic excitations, CME). Uniaxial magnetic anisotropy is generally assumed so that the anisotropy energy is taken as : where K is the anisotropy energy constant, V is the particle volume and 0 is the angle between M and the symmetry axis. K values thus obtained are much larger than bulk magnetocrystalline data, and size dependent, what is attributed to surface effects. Corresponding models applied to patterns of hydrous spinel iron oxide colloids worked correctly except for particles about 8 nm in size, at room temperature. It led us to account explicitly for magnetic coupling between the particles. This is reported here. Materials were obtained by alkalizing mixtures of FeCl2 and FeCl3 by soda (samples A, B, C) or ammonia (samples D, E) and drying the precipitate in an evacuated dessicator with P205. (*) Laboratoire associe au CNRS, n° 302. Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyslet:019850046010043700 L-438 JOURNAL DE PHYSIQUE LETTRES Detailed preparation conditions and physico-chemical properties have been already reported [3-5]. All materials were of a defect spinel-type [6] with lattice constant (0.835 nm) in between that of Fe304 and that of y-Fe203, the Fe2 + concentration determined by chemical analysis was always less than 0.10. Size distributions were evaluated from electron micrographs and fitted to Log-normal laws : where the median diameter Do and the standard deviation Q were the two adjustable parameters. Sizes Dx evaluated from X-ray diffraction (XRD) line widths using the Scherrer method were coherent with these distributions. We found Dx "-I Do exp(2.5 (12) (ratio of the third to second moment of f(D)) in agreement with the meaning of Dx. Moderate thermal treatments (24 h) were performed. XRD profiles proved that the size of the spinel domains scattering coherently was not altered even when partial conversion to a-Fe203 had occurred, and that (x-domains were always much larger than the spinel ones. All observations about the y ~ a transformation, its spreading over a temperature range, size and preparation dependent, agreed with known features [7-8]. Mossbauer spectra were recorded with a conventional spectrometer operating in the constant acceleration mode using a 57Co/Rh source. Absorbers, with a thickness in the range 10-15 mg Fe/ cm2 were made up of powders embedded in an acrylic resin. Dilution in the resin was checked to have no effect on the spectra. Typical patterns are given in figure 1. Large particles gave a pattern identical to that of y-Fe203 [9]. The size effect prominent at room temperature (RT) was much weakened on cooling giving more or less asymmetrically broadened six-line patterns (Fig. 2A) at 80 K (NT) and the spectrum of bulk y-Fe203 at 4 K. All patterns but one (Fig. IC) could be correctly fitted using the SR-CME models [1,10-12] based on the volume weighted size distributions F(D) = D 3 f (D), and assuming a single K value per sample. Corresponding K values were in the range 104-105 J/m3, increasing with decreasing particle size, and coherent with data already reported [13-15]. Thermal treatments induced no significant modification in the RT pattern of as-prepared Na containing materials (sample B) up to appearance of a-Fe203, but progressive changes (Fig. 2) were observed for samples either prepared with ammonia (series D) or freed from Na + ions by acid treatment (series A, C) [5]. When involved, cx-Fe203 always gave a narrow-line XRD pattern Fig. 1. Mössbauer spectra of hydrous spinel iron oxide colloids with various sizes (Dx) at 295 K. L-439 MAGNETIC COUPLING AMONG MICROPARTICLES and a narrow-line RT Mossbauer sextuplet, indicating large particle sizes. Clearly it is absent from the materials studied here (Fig. 2). Size effect being ruled out by X-ray diffraction, the data evolution with the annealing tended to indicate an increase in K. Patterns with typical « udder »like shape (Fig. 2A 1, A2, Cl) proved inconsistent with the SR-CME model. Size dependence of K, release of the standard deviation of the size distribution, cubic instead of uniaxial anisotropy, produced no significant improvement in the fits. Such patterns with better resolution of the inner lines actually are in conflict with the SR-CME model which leads to a collapse of these lines first They involve hyperfine field (HF) distributions which extend much lower than what is predicted [ 16, 17 ]. Reduced hyperfine fields may be connected with surface effects [1 ] such as progressive decoupling of surface spins from the core, or existence of a perturbed layer. The surface field may not be significantly smaller than that of the bulk at low temperature, but distinct temperature dependences may be thought of, leading to notable reduction at the surface, at room temperature. Evolution of the data with annealing may support the existence of a hydrous layer whose dehydration results in progressive ordering of surface spins, that ordering being hindered by Na + ions. No analysis has however been attempted in this way, mainly because independent characterization of the layer was lacking. We have exploited an alternative to the HF reduction, which resides in magnetic interactions between the particles [18]. This viewpoint was supported by the existence of aggregates in solution [5] and by the well-known texture of polycrystalline acicular y-Fe2 O 3 particles [19]. A few publications dealing with similar features in other materials have been reported recently. The HF distributions have been either computed from the spectra [16,17] or adjusted by trial and error [20]. We have adopted another way. Following Morup’s paper [18], magnetic interactions between the particles were taken into account using a modified Weiss mean field model. Within the approximations that all particles are nearly identical with nearly identical surroundings, and ignoring time dependent phenomena, average values can be used. Then the anisotropy energy due to interaction between particle i with magnetization Mi and its surroundings may be written : where H~ is the mean field proportional to the average magnetization ( M > of the ni neighbouring particles. Assuming for simplicity that Hm is parallel to the anisotropy axis of the crystallite, the anisotropy energy (1) for particle i becomes : where Ms is the saturation magnetization per unit volume. This is formally equivalent to the energy of an isolated particle in the presence of an external field applied along the easy direction. Neglecting any dynamical effect, the probability that the direction of Mi is in the range (0, 0 + dO) is : where k is the Boltzmann constant and T is the temperature. Hence, since the magnetic hyperfine field is proportional to magnetization, as far as the correlation time of the thermal fluctuations is short compared to the Larmor precession period LN of the nuclear moment (typically a few 10 9 s), the magnetic splitting of component i can be expressed in terms of an average hyperfine field given by : L-440 JOURNAL DE PHYSIQUE LETTRES where Ho is the hyperfine field in the absence of fluctuations and cos 8 ~ is the thermal average ofcos9. ~ For h = Hm Ms/2 K ~ 1, i.e. for dominant interaction anisotropy, E(0) has one minimum at 0 = 0 and cos 0 > is given by [21 ] :