Interface layer thickness dependence of magnetic properties of SmCo/Fe exchange-spring multilayers: An analytical micromagnetic approach

•Magnetism of SmCo/Fe multilayers are studied by an analytical micromagnetic approach.•The effect of interface layer thickness on demagnetization progress is focused on.•Nucleation field and maximum energy product go up as interface layer thickness rises.•The existence of an interface layer enhances the exchange coupling interaction.•It is consistent with the experiment in [Appl. Phys. Lett. 91, 072509 (2007)]. Experiments have found that the interface layer formed by the interface atomic diffusion in the SmCo/Fe hard/soft exchange-spring system may improve magnetic properties such as the nucleation field and energy product. One-dimensional (1D) analytical micromagnetics can well explain the underlying physics of this phenomenon. In this paper, the magnetic properties of SmCo/Fe exchange-spring multilayers are studied by an analytical micromagnetic approach, focusing on the effect of the interface layer thickness on demagnetization progress. The equations for the angular distribution of the magnetization in all layers and the interface constraint are first derived analytically. The microscopic and macroscopic hysteresis loops, the energy product and angular distribution are calculated, with realistic values for the interface layer thickness considered. It is found that as the interface layer thickness increases, the nucleation field rises, the coercivity increases first and then is almost constant, hence the maximum energy product goes up, while the angular distribution and depinning field decrease. The nucleation field rises with the interface layer thickness for a wide region of the interface exchange energy constant, calculated by a three-dimensional (3D) micromagnetic software (OOMMF), which agrees perfectly with 1D calculated results. Meanwhile, the nucleation field goes up with the interface exchange coupling coefficient for any interface layer thickness. Above results indicate that the existence of an interface layer between the soft and hard layers enhances the exchange coupling interaction between them, which is qualitatively consistent with the experiment in [Appl. Phys. Lett. 91, 072509 (2007)], as confirmed via an in-plane 1D model with interface layer.