Wall pinning

D. Sander, R. Skomski, C. Schmidthals, A. Enders, and J. Kirschner, Film Stress and Domain Wall Pinning in Sesquilayer Iron Films on W(110) , Phys. Rev. Lett. 77, 2566(1996). 

Figure 9. Magnetic hysteresis origin and phenomenology of hysteresis. The coercivity of the particles shown in this figure is caused by domain-wall pinning at the grainboundary phase.

The exponent m cannot be regarded as a fitting parameter but depends on the symmetry of the system. In most cases, m = 3/2 [16, 140, 158, 166, 167, 174, 175], but m = 2 for highly symmetric systems, such as aligned Stoner-Wohlfarth particles. In particular, the m = 3/2 law is realized for misaligned Stoner-Wohlfarth particles and for most domain-wall pinning mechanisms [5], Experimental values of m tend to vary between 1.5 to 2 [136, 158]. Linear laws, where m = 1, are sometimes used in simplified models, but so far it hasn t been possible to derive them from physically reasonable energy landscapes [5, 16, 176]. The same is true for dependences such as /H- l/H0 [177], where series expansion yields an m = 1 power law. 

Domain walls pinned by planar defects having magnetic properties different from the matrix were considered by Friedberg and Paul (1975). Hirosawa et al. (1986) and Sagawa et al. (1987a) used the formalism derived by these latter authors to analyze the coercive force in a variety of materials after correcting the latter... 

A very important step forward was the discovery that the addition of small quantities of zirconium, in Sm(Co, Fe, Cu, Zr)z, coupled with a relatively complex heat-treatment, yielded coercivities of 6.5 kOe (520 kA/m) by general wall pinning in alloys with more Fe, less Cu and higher z-values than previously possible (Kaneko et al. 1977, Ojima et al. 1977, Yoneyama et al. 1978). The best energy... 

Fig. 4.3S. Magnetisation by reversible domain wall bowing (a) a rectangular wall pinned on two edges (b) a circular wall in a spherical grain, pinned on its perimeter.

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