Energy barrier and exchange coupling in spring-magnets

Abstract

The exchange-coupled nanocomposite magnets have potential for high energy products because materials with this configuration may take the advantages of high magnetization of the soft magnetic constituents and the high coercivity of the hard constituents. From the physical point of view, the energy-barrier, EB, the minimum energy required for magnetization reversal, is the key issue in controlling the magnetic properties. In this paper, a modeling analysis of exchange coupling between the soft and hard magnetic layers, and the energy-barrier EB-S, EB-H is presented. We have derived the energy-barrier EB-S and EB-H as follows: EB-S= KStS{1-[H-(J/MStS)]/HK-S}2 (HK-S =2KS/MS; H < HC-S); EB-H =KHtH{1-[H+(J/MHtH)]/HK-H}2 (HK-H=2KH/MH; HC-S < H<HC-H); where M, K, t, and Hc are the magnetization, anisotropy constant, layer-thickness and coercivity, respectively, and the subscript S and H denote the soft and hard constituents. J is the exchange-coupling constant between the hard and the soft phase layers. It is seen from these equations that the energy-barrier of the soft-layer EB-S increases with J and the energy-barrier of the hard-layer EB-H decreases with J.