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Interacting tails of asymmetric domain walls – theory and experiments
Lukas Döring, Claudia Hengst, Felix Otto and Rudolf Schäfer
In this paper, we address the structure and interaction of neighboring asymmetric Néel and Blochwalls in soft ferromagnetic films.
First, we review a recent reduced model for the structure of parallel systems of asymmetric walls with potentially interacting tails. The reduced model has the form of a minimization problem in two parameters that describe the amount of rotation in a stray-field free wall-core and the average hardaxis magnetization in each domain, respectively. Starting from the micromagnetic torque equation, we provide a new derivation of this reduced model that uses the method of matched asymptotic expansions instead of the original variational approach. The theoretical results apply to any soft thin-film material and cover also isolated domain walls, in the limiting case of large domain widths. With only little numerical effort, we then obtain detailed quantitative information on the structure of asymmetric domain walls. In particular, we predict the hard-axis magnetization curves for asymmetric Bloch and interacting asymmetric Néel walls.
In the second part of the paper, we report on experimentally observed domain-wall transitions in Co40Fe40B20 films of lateral dimensions 60μm × 9500μm and thicknesses 102nm, 153nm, and 212nm. Upon the wall transition, the average hard-axis magnetization in the domains increases significantly. The increase depends on the width of the domains and ranges from 0.1Ms to 0.25Ms for domain widths between 18μm and 6μm. For the thicknesses 102nm and 153nm, the predicted hard-axis magnetization jump excellently agrees with the experimental data. We conclude that interacting tails of neighboring asymmetric Néel walls cause the observed additional rotation of the magnetization towards large hard-axis fields.
Hence, our results contribute to a quantitative understanding of isolated and interacting asymmetric domain walls in soft ferromagnetic films.