Abstract
Fractal geometry is introduced into the analysis of ``two-phase'' magnetic domain patterns. The line-measuring dimension ${D}_{\mathrm{line}}$ is selected to quantitatively describe the ``line structure'' patterns of the multi-branched domains (MBD's) formed in garnet bubble films, and a meaningful ${D}_{\mathrm{line}}$ can be related to the numbers of vertical Bloch lines in their walls, i.e., to the hardness of the MBD's. For quantitatively describing the ``plane-filling'' domain patterns of magnetic materials with uniaxial anisotropy, such as corrugation and spike, even ``flower,'' domains, the box-counting dimension ${D}_{\mathrm{box}}$ is selected. For describing the series of domains of Co and Dy-NdFeB single crystals due to branching process, ${D}_{\mathrm{line}}$ and ${D}_{\mathrm{box}}$ are used in section. Our results show that two phase domain patterns possess fractal natures, and can be described by fractal dimensions.
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