Magnetization Processes and the Phase Distribution

On the origin of the possibility of controlling the demagnetization behavior are the particularities of the demagnetization process. In the particular case of a poly-crystalline material, demagnetization takes place in a complex way (Fig. 10), involving some (or all) of the stages in the sequence nucleation-expansion-propagation-pinning-depinning [94]. We will describe these stages, as well as their dependence on the extrinsic characteristics of the materials.

The nucleation process corresponds to the first (occurring at a smaller demagnetizing field) irreversible departure of the distribution of the magnetic moments present in a certain region (typically a grain) of a material from the configuration associated to the remanent state. That departure, depending on the main phase properties, could involve either the formation of a reversed region limited

Grain boundaries

Applied demagnetizing field

Grain boundaries

Applied demagnetizing field

Figure 10. Schematic illustration of the intragrain demagnetization sequence (nucleation-nucleus expansion-propagation-pinning stages).

by a domain wall or that of an extended inhomogeneous local magnetization distribution, which corresponds to the onset of the global reversal process and takes place preferentially at (i) points where local demagnetization fields are more intense (as the edges and corners in well-crystallized, polyhedral grains) and (ii) points where the local anisotropy and/or exchange are significantly reduced with respect to their values in a free-from-defects area of the main phase (to be effective, these sites of preferential nucleation should have transverse dimensions of the order of the magnetic moments structures formed upon nucleation). In the most general case, the occurrence, at a given field value, of nucle-ation does not have as a consequence the complete reversal of the magnetization of the sample. This is so just because the growth in size of the total or partly reversed regions requires the input of energy in the system due to the fact that, in general, the moments in those regions do not point along easy axes (as required to minimize the anisotropy energy) and/or are not fully parallel (which is the configuration minimizing exchange and dipolar energies). It is thus necessary to increase the magnitude of the demagnetizing field in order to balance the increase of the energy of the distribution of magnetic moments required by the growth in size of the localized reversed region from which the global reversal proceeds. This process is denominated by nucleus expansion and takes place, reversibly, up to an applied field value for which the nucleus can steadily grow in size (that field is called the propagation field). In the particular case of the hard magnetic materials, the nucleation and propagation fields can be significantly different.

Once the condition of steady expansion of the reversed nucleus is achieved, the magnetization reversal can only be stopped if the structures involved in the propagation (e.g., a domain wall limiting the reversed area) get trapped in regions where they have an energy lower than that corresponding to the previously swept areas. Those pinning centers are associated with secondary phases of deteriorated crystallinity regions where the anisotropy and/or the exchange energies are lower than those of the well-crystallized main phase (planar structures as second phase precipitates are especially effective as pinning centers). If a propagating nucleus gets trapped in one of these pinning points, in order to proceed with the reversal process, it is necessary to increase the applied demagnetizing field in the magnitude required to unpin the propagating structure (the depinning field is related to the characteristics of the difference on the anisotropy, exchange and dipolar energies between the pinning center, and the well-crystallized areas).

From this discussion, it is clear that the field required to fully reverse the magnetization of a grain in a polycrystalline hard material coincides with the maximum of the nucleation, propagation, and depinning fields.

As for the complete reversal of the magnetization of a polycrystalline material, the crucial role corresponds to the intergranular regions (Fig. 11). Those intergranular regions (grain boundaries separating main hard-phase grains) could have a differentiated structure (thus, being a secondary phase) or could just correspond to the main phase structure accumulating defects and additive elements so as to provide the transition between the crystallographic orientations of different main-phase grains. In both cases, the most important points are (i) the occurrence and type of the exchange interactions in the intergranular structure and (ii) the thickness of the grain boundary. These two points will be analyzed in detail in the next section but, for the moment, we can say that:

(a) If the main phase grains are perfectly exchange coupled through the grain boundaries, the global coercive force will correspond to the coercivity of the grain having the smallest reversal field (the structures propagating in the reversal of that grain will not have any hindrance to propagate across the sample). This is a particularly undesirable case, since the coercivity is linked to the region in the material having the most deteriorated magnetic properties.

(b) If the main phase grains are partially exchange coupled (either if they are uniformly coupled through an

Strongly exchange coupled grains

Partly exchange coupled grains

Exchange decoupled grains

Partly exchange coupled grains

Exchange decoupled grains

Freely propagating wall

Wall pinned inside a low anisotropy grain boundary

Partly pinned wall

Wall pinned outside a high anisotropy grain boundary

Figure 11. Domain wall propagation across differently exchange coupled grains.

Grains coupled through a low anisotropy intergranular phase

Freely propagating wall

Wall pinned inside a low anisotropy grain boundary

Partly pinned wall

Wall pinned outside a high anisotropy grain boundary intergranular exchange constant that is a fraction of that of the main phase, case A, or if they are nonuni-formly coupled, case B), the increase in volume of the reversed regions will find either pinning centers (case A, stopping the walls inside the grain boundaries) or propagation barriers (case B, stopping the grains outside the grain boundaries) at the grain boundaries. The global coercivity will be a convolution of the distribution of grain reversal fields and of the depinning fields of the grain boundary regions (this is a particularly complex case since the reduced exchange at the grain boundaries also can influence the distribution of nucleation fields). (c) If the main phase grains are fully exchange decoupled, the global coercivity directly results from the distribution of grain reversal fields. This case is, in principle, preferred for the optimization of the hard materials since, as we will see in the next section, it is compatible with the state of the art about the control of the properties of the intergranular regions and ensures the achievement of coercivities directly related to the structure and properties of the main phase.

It is clear that the detailed knowledge of the actual demagnetization mechanism taking place in a concrete material is the key to the achievement of a relevant optimization of its hysteretic properties and that the basic mechanism for that purpose is the control of the phase distribution and morphology. This information is, nevertheless, quite elusive to simple and straightforward analysis and, usually, can only be partially obtained. To that purpose, the most commonly analyzed data are those corresponding to the temperature dependence of the coercive force [95], due to the availability of models correlating in simple terms the magnetic properties and some microstructural features. The conclusions of those models [96, 97], initially proposed by Brown, and basically adequate to describe nucleation-ruled magnetization reversal processes, can be summarized in Eq. (9)

Figure 11. Domain wall propagation across differently exchange coupled grains.

where HC(T) is the temperature dependence of the coercivity, a and Neff are parameters fitting the experimental coercivity data, HK(T) is the experimental temperature dependence of the anisotropy field, and MS(T) is the experimental temperature dependence of the magnetization. Equation (9) simply states that at all the temperatures, the coercive force can be obtained from the anisotropy field of the main phase (the maximum observable coercivity in that phase) multiplied by a factor (lower than the unity) that contains all the sources of deterioration of the local coercivity and decreased in the local demagnetizing field at the site of the reversal onset. The fitting parameter a can be factor-ized on the contributions of the texture of the grains of the main phase, the occurrence of either complete intergranular exchange or perfect grain decoupling, and the local reduction of the anisotropy related to the occurrence of poor crys-tallinity or soft regions. As for the Nef parameter, the local demagnetizing factor, it can be larger than the unity since it does not necessarily describe fields originated by uniform magnetization distributions [98].

Despite its simplicity (it reduces the complex influence of the phase distribution to only two parameters), Eq. (9) almost universally describes the temperature dependence of the coercivity [99] and is very useful to analyze the behavior of a series of samples prepared under similar conditions. A typical example of this type of study is the analysis of the influence of additive elements on the grain decoupling that (provided other influencing factors are maintained constant) should correspond to an increase of a with the increase of the decoupling. Also, the achievement of better crystallini-ties, resulting in better defined grain edges and corners can be correlated easily to the increase of Nf.

The occurrence of pinning-depinning processes can be quite unambiguously identified from the measurement (usually carried out in highly textured samples) of the angular dependence of the coercivity [100]. If the main phase grains in these samples are well exchange coupled, the presence of depinning walls can be pinpointed from the observation of a monotonous increase of the coercivity with the increase of the angle $ formed by the direction of the saturation rema-nence and the applied demagnetizing field. That increase is related to the increase of the pressure exerted over the pinned walls by the applied field that is proportional to 1/ cos In contrast with the reversal mechanisms linked to pinning, a nucleation-ruled reversal usually exhibits an angular dependence of the coercivity characterized by an initial decrease with the increase of a minimum and a further increase, a behavior resembling (but, in general, not mimicking) the angular dependence of the coercivity predicted for systems demagnetizing according to coherent rotation mechanisms.

Finally, in what concerns the analysis of the magnetic properties, the measurement of the relaxational properties (those related to the thermally activated magnetization reversal) can yield and estimate (the so-called activation volume) of the size of the region involved in the onset of the reversal process [101]. That estimate can be useful to try to identify the characteristics of the points at which the nucleation occurs but, generally, the discussions based on the measurement of the magnetic viscosity are not very conclusive.

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