Some Magnetostatic and Micromagnetic Properties of the Infinite Rectangular Bar

Abstract

In estimating the nucleation field of an infinite rectangular bar, Aharoni used a variational method to calculate a lower bound to the magnetostatic energy. He constrained the variable potential to a specified form inside an ellipse circumscribed about the rectangle. In the present article, the method is improved by imposing the constraint only inside the rectangle itself. The resulting potential problem can be reduced to that of a bar of infinite permeability in an applied field of specified form; the final results can be expressed in terms of the demagnetizing factors Dx∞ and Dy∞ of such a bar. Similarly, an upper bound to the energy can be expressed in terms of the demagnetizing factors Dx0 and Dy0 of a bar of zero permeability. For rotation in quasiunison, the new lower bound to the nucleation field is considerably better than the old, but the new upper bound is not as good as that already obtained by constraining the magnetization to uniformity. New tables of Dx∞,Dy∞,Nx∞ (≡4πDx∞), and Ny∞ (≡4πDy∞) as functions of dimension ratio p are included; the demagnetizing factors at infinite and at zero permeabilities satisfy the relations Dx∞+Dy0= Dx0+Dy∞=1.