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 (
${H}_{\text {dem}}$
) 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 (
${\partial {M}}/{\partial {H}_{\text {dem}}} < {0} $
). Due to the negative value of susceptibility, a local relative permeability
${ < } {1}$
(
$\mu _{r} < {1}$
) 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
${H}_{\text {dem}}$
, 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 + demagnetization energy + anisotropy energy + Zeeman energy + DMI energy).