Micromagnetic analysis of the exchange-coupled hard-soft planar nano-composites

A complete magnetic phase diagram for exchange-coupled planar hard-soft nanocomposites has been obtained in the frame of a one-dimensional micromagnetic model describing the dependence of the properties along the growth direction. The phase diagram in terms of layer thicknesses provides information on the type of demagnetization processes and the critical fields at which nucleation and reversal take place. The basic criterion to this purpose is the analytical expression we have obtained of the critical susceptibility at the nucleation field. The phase diagram is divided into three regions: the exchange-spring magnet (ES), the rigid composite magnet (RM), and the decoupled magnet (DM). The main boundary line is an U-shaped line corresponding to divergence of the critical susceptibility. The diagram also reports the isocritical field lines both for the nucleation and the reversal field. These lines bifurcate along the RM boundary line. The essential characteristics of the phase diagram are directly connected with the intrinsic properties of the chosen soft and hard materials. With increasing ratio between the anisotropy constants of soft to hard phases the ES region is reduced until it disappears at a critical value. The model includes as limiting cases the classical problems of the planar soft inclusion in a bulk magnet and of the domain-wall depinning at the hard-soft interface