Modeling Stray Field Distribution Generated by Domain Walls in Rare-Earth Substituted Iron Garnets

Rare-earth substituted iron garnets (REIGs) are interesting materials which may present large in-plane magnetization. In correspondence of defects, domain walls (DWs) undergo nucleation, segmentation, and pinning. In such cases, the Néel spike domain structure may appear, and its DWs can produce not negligible stray fields above the REIG. Experimental characterization through quantitative magneto-optical imaging with an indicator film showed that stray fields are detectable above the surface of Lu and Bi substituted iron garnets in correspondence of DWs delimiting a Néel spike that is generated by a microcrack. These DWs are interesting for both fundamental studies and innovative applications, and therefore carrying out a quantitative analysis is crucial. To understand how the externally detected stray fields are correlated with the pattern of the internal magnetization, here we propose 2-D and 3-D models based on FEM developed through the COMSOL Multiphysics software. These models consider the in-plane magnetization of the REIG and the magnetic microstructure of the Néel spike. They provide a good reproduction of the magnetic fields and allow describing the corresponding magnetic microstructure. It turns out that the results are both in agreement with the experiments.