Dynamics of a ferromagnetic domain wall: avalanches, depinning transition and the Barkhausen effect

We study the dynamics of a ferromagnetic domain wall driven by an external magnetic field through a disordered medium. The avalanche-like motion of the domain walls between pinned configurations produces a noise known as the Barkhausen effect. We discuss experimental results on soft ferromagnetic materials, with reference to the domain structure and the sample geometry, and report Barkhausen noise measurements on Fe$_{21}$Co$_{64}$B$_{15}$ amorphous alloy. We construct an equation of motion for a flexible domain wall, which displays a depinning transition as the field is increased. The long-range dipolar interactions are shown to set the upper critical dimension to $d_c=3$, which implies that mean-field exponents (with possible logarithmic correction) are expected to describe the Barkhausen effect. We introduce a mean-field infinite-range model and show that it is equivalent to a previously introduced single-degree-of-freedom model, known to reproduce several experimental results. We numerically simulate the equation in $d=3$, confirming the theoretical predictions. We compute the avalanche distributions as a function of the field driving rate and the intensity of the demagnetizing field. The scaling exponents change linearly with the driving rate, while the cutoff of the distribution is determined by the demagnetizing field, in remarkable agreement with experiments.Comment: 17 RevTeX pages, 19 embedded ps figures + 1 extra figure, submitted to Phys. Rev.

Preoptic Aromatase Cells Project to the Mesencephalic Central Gray in the Male Japanese Quail (Coturnix Japonica)

Previous tract-tracing studies demonstrated the existence of projections from the medial preoptic nucleus (POM) to the mesencephalic central gray (GCt) in quail. GCt contains a significant number of aromatase-immunoreactive (ARO-ir) fibers and punctate structures, but no ARO-ir cells are present in this region. The origin of the ARO-ir fibers of the GCt was investigated here by retrograde tract-tracing combined with immunocytochemistry for aromatase. Following injection of fluorescent microspheres in GCt, retrogradely labeled cells were found in a large number of hypothalamic and mesencephalic areas and in particular within the three main groups of ARO-ir cells located in the POM, the ventromedial nucleus of the hypothalamus, and the bed nucleus striae terminalis. Labeling of these cells for aromatase by immunocytochemistry demonstrated, however, that aromatase-positive retrogradely labeled cells are observed almost exclusively within the POM. Double-labeled cells were abundant in both the rostral and caudal parts of the POM and their number was apparently not affected by the location of the injection site within GCt. At both rostro-caudal levels of the POM, ARO-ir retrogradely labeled cells were, however, more frequent in the lateral than in the medial POM. These data indicate that ARO-ir neurons located in the lateral part of the POM may control the premotor aspects of male copulatory behavior through their projection to GCt and suggest that GCt activity could be affected by estrogens released from the terminals of these ARO-ir neurons