Static Negative Susceptibility in Ferromagnetic Material Induced by Domain Wall: Possibility to Achieve Gigantic Diamagnetism

This article analyzes the local spatial behavior of magnetization ( M ) and demagnetization field ( <tex-math notation="LaTeX">Hdem</tex-math> ) in a multidomain magnetic film. In the transient region (domain wall width), local magnetization and demagnetization fields exhibit opposite slopes, corresponding to a negative susceptibility value ( <tex-math notation="LaTeX"></tex-math> 2.3.). Due to the negative value of susceptibility, a local relative permeability <tex-math notation="LaTeX">< 1</tex-math> ( <tex-math notation="LaTeX"></tex-math> 6.) is observed in the domain wall region. An enhancement in domain wall width decreases the susceptibility, leading to a further reduction in the relative permeability. Additionally, the domain's magnetization gradient significantly alters the local distributions of M and <tex-math notation="LaTeX">Hdem</tex-math> , causing spatial variations in the local permeability. To capture such nanoscale variations in the spatial demagnetized field, we solve 2-D Poisson's equation, including 2-D gradients in the magnetization (caused by multidomain). The domain period, domain wall width, and wall angle are obtained by minimizing the total energy (exchange energy <tex-math notation="LaTeX">$+$</tex-math> demagnetization energy <tex-math notation="LaTeX">$+$</tex-math> anisotropy energy <tex-math notation="LaTeX">$+$</tex-math> Zeeman energy <tex-math notation="LaTeX">$+$</tex-math> DMI energy).