A continuum theory for stripe-shaped magnetic domains in thin films

Starting from a potential-based kinematical description of continuously distributed stripe-shaped domain walls, a mesoscopic potential is derived through an averaging procedure. The resulting mesoscopic theory is formulated in terms of a few fields with physically meaningful microscopic interpretation. Based on a phenomenological closure-domain extension, a constrained energy minimization principle is introduced. A monolithic finite-element based numerical solution algorithm is proposed. Based on a consistent linearization of the numerical algorithm, quadratic convergence is obtained for the nonlinear solution procedure. A first simple examination of the theory is undertaken by simulating a thin film with spatially and temporally non-constant effective anisotropy. The results are found to be consistent with analytical predictions.

Automated summary

This paper presents a potential-based kinematical description of continuously distributed stripe-shaped domain walls, and derives a mesoscopic potential through an averaging procedure. The resulting mesoscopic theory is formulated in terms of a few fields with physically meaningful microscopic interpretation. A constrained energy minimization principle is introduced based on a phenomenological closure-domain extension. A monolithic finite-element based numerical solution algorithm is proposed, with quadratic convergence achieved for the nonlinear solution procedure through consistent linearization. A first simple examination of the theory is undertaken by simulating a thin film with non-constant effective anisotropy, and the results are consistent with analytical predictions.