Domain wall nucleation

For large sizes the particles are multi-domain becoming more bulk-like with increasing size. The mechanism of magnetization reversal is domain wall nucleation and motion for the multi-domain case [1], As the particle size is reduced the increase of energy due to domain wall formation dominates over the decrease in energy attributed to the formation of domains. Thus, below a critical particle size domain walls will no longer... 

The rare earth-cohalt magnets are discussed here with a fairly applied bias. Relevant fundamental subjects are treated exhaustively elsewhere in this handbook series basic magnetic properties of the RE-elements by Legvold (1980), those of RE-TM intermetallics by Buschow (1980), and the theory of hard-magnetic behavior - small-particle magnetization reversal, domain-wall nucleation and motion, and the role of anisotropy in these - by Zijlstra (1982). Buschow (1988) discusses the various mechanisms thought to be controlling the coercivity in all REPM, and the... 

The hystersis loops of fig. 30.16 and 30.17 improperly imply that the switching process for strain or polarization reversal is instantaneous and complete once the threshold field, Eo or stress tq is exceeded. This switching occurs by domain wall nucleation and movement which is not particularily fast for the /3 -molybdates. Much of the applied research on these materials concerns this switching process as summarized in ch. 30 section 3.6. 

The spontaneous strain ( t i2)s may be reversed, as discussed earlier, with fig. 30.17, by applying a compressional stress along the orthorhombic h-axis. At very small applied stress, the crystal responds with a small elastic deformation until the critical threshold stress (to) is exceeded at which time domain walls nucleate and move until the region subjected to the stress has been switched to the opposite strain state. Decreasing this applied stress to zero leaves the crystal in the positive , Xs spontaneous strain state. 

In Figure 13 the relation between the intrinsic coercivity Ha and the particle diameter dis given. The figure is based on a described model (35). The maximum is found around the critical particle diameter. In general the particle diameter and size is not very well defined. For the multidomain particles (d > dcritical ) the Ha is smaller than the intrinsic anisotropy field of the particle. Nucleation effects cause a decrease in FF. as the d increases. This behavior is understood only qualitatively for a full description see Reference 36. Low noise media should consist of single-domain particles reversal by domain walls is slow and introduces noise. 

Summary. On the basis of phenomenological Ginzburg-Landau approach we investigate the problem of order parameter nucleation in a ferromagnetic superconductor and hybrid superconductor - ferromagnetic (S/F) systems with a domain structure in an applied external magnetic field H. We study the interplay between the superconductivity localized at the domain walls and between the domain walls and show that such interplay determines a peculiar nonlinear temperature dependence of the upper critical field. For hybrid S/F systems we also study the possible oscillatory behavior of the critical temperature TC(H) similar to the Little-Parks effect. 

For ferroelectrics, mainly two possible mechanisms for irreversible processes exist. First, lattice defects which interact with a domain wall and hinder it from returning into its initial position after removing the electric field that initiated the domain wall motion ( pinning ) [16]. Second, the nucleation and growth of new domains which do not disappear after the field is removed again. In ferroelectric materials the matter is further complicated by defect dipoles and free charges that also contribute to the measured polarization and can also interact with domain walls [17]. Reversible contributions in ferroelectrics are due to ionic and electronic... 

Figure 11. Pinning and nucleation. Pinning means that coercivity is created by trapping the domain wall at pronounced inhomogenities (pinning centers). In the absence of pinning centers, the coercivity is determined by the reversal field at which the original magnetization configuration becomes unstable (nucleation).

When the anisotropy energy within the hard layer cannot be considered as infinite as compared to the Zeeman energy, the nucleation field depends on the hard layer magnetic properties [122], However, as long as <7hard > 34ard ( hard and 4ard are the hard layer thickness and domain wall width respectively), Hn does not depend much on dhard. For 10 nm, the room temperature nucleation field jU()Hn is typically 1 T. 

As mentioned above, domain switching in ferroelectrics is accompanied by domain nucleation, moving domain walls and restructuring of dipoles and charges. A characteristic feature of this irreversible process is the appearance of a hysteresis loop in the dependence of dielectric displacement... 

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