Magnetic domain transtitions are phase transitions, just like the solidifcation of a snowflake. It's not that surprising to me that magnetic domain structure could be fractal, many phase transitions can look fractal in the right conditions, of which water solidifcation into snowflakes is just one example.

Despite the fact that several versions of this story claim this is the "first ever" observation or discovery of fractal domains, it seems to have been reported at least a decade earlier [1], in a similar but somewhat more complex ternary neodynium compound.

[1] https://arxiv.org/abs/0901.3515