Modeling stray field distribution generated by domain-walls in rare-earth substituted iron garnets

Rare heart substituted iron garnets (REIGs) are interesting material 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, Bi) substituted iron garnets in correspondence of DWs delimiting a Néel spike that is generated by a micro-crack. These DWs are interesting both for fundamental studies and for innovative applications, and therefore performing a quantitative analysis is crucial. To understand how the externally detected stray fields are correlated to the pattern of the internal magnetization, here we propose 2D and 3D 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 allows to describe the corresponding magnetic microstructure. It turns out that the results are both in agreement with experiments.