On the Magnetization Mechanisms in Polycrystalline Hexaferrites

An attempt was made to adapt the domain-wall size model to the explanation of magnetization mechanisms in real polycrystalline hard ferrites (SrFelzOle). Some new data concerning the total anisotropy specifically for polycrystals were discussed and its value deduced from natural spin resonance measurements. It was observed that samples with different Heg grain size and shape, can present different hysteresis loops. To explain these differences, we applied the theoretical expressions for the magnetization curve and the hysteresis loop developed earlier. In spite of the quickly broadening area of application of polycrystalline highly anisotropic femtes, the theory still lags behind in explaining their specific magnetization behavior [I]. A good description of the magnetization processes from the viewpoint of the grain size in isotropic ferrite structures is provided by the Globus-Guyot model 121, which considers the single crystallite as a sphere divided by a Bloch domain wall @W) moving under the action of an external magnetic field. Magana et al. [3] made the first attempt to apply this model to structures with non-spherical grains. The present work reports on studies of the magnetization processes in real highly anisotropic polycrystalline Srhexaferrites with various size of the grains (crystallites) and aims at applying the DW-size theory to explain the discrepancies observed. We investigated the magnetization processes, the hysteresis BH-curves and the variation of the effective anisotropy field Hen as functions of the grain shape and size in the case of a highly anisotropic polycrystalline Sr hexaferrite (SrFel2OI9). The samples were prepared by following the ceramic technology of "wet" pressing in an external magnetic field. The crystallite size was controlled by means of chosing appropriate temperatures and final isothermic delay. Using systematic optical microscopy observations and statistical analysis, we selected a series of samples with different grain sizes and a maximal degree of texturing. Since the most energetically favorable location of the DW in texturized hexaferrites is along the weak magnetization axis, which we assume to be parallel to the texturing axis (c), all further discussion will imply a (c) sample cross-section. Thus, the crystallite can be approximated by an ellipsoid of revolution with serniaxes (a) and (c), and the ratio P= a/c be defined. The samples studied had a quasi-constant P (P= 0.6 + 0.25) and average grain size as follows (ak , pm) (see Fig.2by:Sample S1 1.111.86; S2 1.212; S3 518; S4 8/13; and S5 40165. The size variance did not exceed 25 %, while the degree of texturing was more than 95 % in samples S1, S2 and S3, and less than 78 % in samples with advanced recrystallization (S4 and S5). The magnetic measurements were carried out using a computerized BH tracer developed at Laboratoire de Magnetisme et Materiaux Magnetiqnes CNRS, France. It allowed us to follow the hysteresis-curve evolution at external magnetic fields of up to 30 kOe. The Hefl measurements were performed by means of an MW technique described in [4]. Based on the results obtained on the magnetization process and on the BH-curves of the series of Sr-ferrite samples investigated, we calculated the data for the pinning force f and DW energy per unit area y from the experimental curves making use of the following expression [2]: where E B H are the losses per unit volume (BH loop surface) and D = 2aZlc reflects the averaged data for the grain size in cross-section c. Following the classical model, we plotted the BH-energy as a function of in, for all five sanlples (Fig. 1.a). This reduced tine is independent of the grain size so that it is possible to determine the parameter f = 2.85 x lo3 erg/cm2. Magana et al. (31 adopted the condition of the DW-size model, namely, that the value of y is independent of the applied magnetic field, and derived an expression for the reduced magnetization: Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jp4:1997175 C1-202 JOURNAL DE PHYSIQUE IV where M and M, are the produced and saturation magnetization of a single grain, and A = p(x1I2n); 6 = y 12c; ,L3 = a I c, with x' and y being the coordinates of the DW bowing and displacement with respect to equilibrium, respectively (Fig.2.b). Using mathematical transformations related to the ellipsoid geometry, dependences were derived in 13) that can be employed to construct a universal hysteresis curve, where the coercitive field H,and the remanence B, are functiol~s of ,L3= a/c (which accounts for the grain shape) and 71 =f/y, the latter reflecting the material's properties. Fig. 1.b. shows a sequence of loops for two typical samples from the series S2 (small grains) and S4 (recrystallized grains). The theoretical values for the same samples are represented by the dashed lines. The discrepancy is easily seen between the experimental and theoretical curves for H, which we relate to the fact that calculating yfrom (I) leaves out the specific characteristics of the highly anisotropic material. namely, the role of the crystallite shape.