Formation of multi-branched domains and the calculation of their fractal dimension

A "low-bias-field method" was proposed to form single multi-branched. domains( MBDs) in garnet bubble films. The formation of MBDs is related to the nucleation of vertical Bloch lines (VBL) in their domain walls. With the decrease of the static bias-field H-b from. the "critical static bias field for multi-branched expansion" H[d], the corresponding MBDs formed become more and more complex, accompanying the appearance of several kinds of hard domains. The fractal geometry uas introduced into the study of MBDs. The curved and branched patterns of MBDs have been quantitatively described by the "line-measuring dimension" D-line which is associated with the nucleation of VBL in their domain walls.