6. Static and dynamic properties of topological defects in ultrathin films and dots
Résumé
The magnetic structure of ultrathin films caused by dipolar interactions is studied analytically. A Taylor Maclaurin series expansion of dipolar interactions enables us to consider dipolar interactions as local interactions in function of the spin field and its space derivatives. This allows a fruitful comparison with liquid crystal phenomenological Hamiltonians. Dipolar anisotropy appears at lowest order in the expanded dipolar interaction. The next non zero term favours the appearance of vortices and hyperbolic points in finite ultrathin films while the next one, the fourth order term, controls the competition between vortices, hyperbolic points and other topological defects. The magnetic structure of an ultrathin film depends on the transversal sample size by means of higher order terms. For a very limited ultrathin dot, a structure with just one vortex is stable; for larger samples, networks of vortices, hyperbolic points and other topological defects have a lower energy than a single vortex. For larger and larger samples, more and more complex structures optimize a discrete screening of the dipolar interaction. The dynamical properties of magnetic vortices, hyperbolic points and other defects are also studied with evidence for different classes of eigen modes.
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