Static negative susceptibility in ferromagnetic material induced by domain wall motion: an aspect of superconductor state

Abstract

Domain wall motion in magnetic materiel induces the negative susceptibility leading to a perfect diamagnetism state. The local susceptibility is calculated by the derivative of magnetization ($\vec{M}$) vector w.r.t. magnetic field strength ($\vec{H}$) vector. In the transient region from the upward domain to the downward domain (domain wall width), local $\vec{M}$ and $\vec{H}$ vectors exhibit opposite slopes, which leads to a negative susceptibility value. A negative susceptibility value induces the diamagnetism effect leading to a relative permeability value $<$ 1 $\left(\mu _r < 1\right)$. This diamagnetism sate originates due to the domain wall motion, which is an entirely different mechanism from the electron motion's induced diamagnetism. Furthermore, the strength of the diamagnetism state can be enhanced by tuning the gradient energy of a domain that may correspond to a perfect diamagnetism state $\left(\chi _v \approx -1 \Rightarrow \mu _r \rightarrow 0\right)$. Besides, we believe that there may be a possibility of sustaining such a diamagnetic state (domain wall induced) in a ferromagnetic material that is utterly contradictory to the conventional theory.