Demagnetization Process And Hysteresis Loops In Antiferromagnetically Exchange Coupled Hard/Soft Ferromagnetic Trilavers

Exchange-coupled hard/soft composites, are widely regarded as the best available permanent magnetic materials. The demagnetization processes and hysteresis loops have been investigated in detail within a self-contained micromagnetic model, for hard/soft trilayers with an antiferromagnetic exchange-coupling in the interface. In addition, The analytical formulas for the nucleation fields have been derived for both coherent and incoherent modes in a hard/soft multilayer system with anisotropy perpendicular to the film plane. The results are as follows:1.Every demagnetization process is composed of two independent processes, corresponding to the magnetic reversal of the soft and hard phases, linked by an intermediate antiparallel state. Each of the two processes can be divided into three steps, namely nucleation, evolution and pinning of the domain walls. The implicit formulas for both the nucleation fields of the soft and hard phases have been derived, as functions of the exchange coupling strength as well as the thicknesses of the layers. The first nucleation field HN1is more sensitive to the value of the antiferromagnetic interface coupling constant J than to the thicknesses of the layers. Therefore, in most cases a simplified formula for HN1could be used where it changes with the interface coupling constant J only. On the other hand, the second nucleation field HN2does not change with the soft layer thickness Ls at all in all realistic cases so that the formula could be simplified too. Both the nucleation and pinning fields at the first demagnetization process are negative, which fall as J decreases (the absolute value of J increases). In the meantime, the gap in between these fields decrease, accompanied by a change of the phase diagram from the rigid composite to the exchange springs. The micromagnetic and macroscopic hysteresis loops, as well as the angular distributions of the magnetization between the nucleation and pinning fields have been obtained numerically. It is found that the evolution of the interface spins within the hard phases is not monotonic. These spins rotate toward an opposite direction as that in the soft layer following the first nucleation and then spring back near the first pinning. The magnetic reversal in the hard phase is completed at the second pinning field, which is larger than the anisotropy field of the hard phase. The macroscopic hysteresis loops with antiferromagnetic interface coupling are characterized by a negative coercivity at large soft layer thickness, accompanied by a small rectangle near the center of the loop. In addition, the first demagnetization process from nucleation to pinning is slow accompanied by a deterioration of the squareness of the hysteresis loops, especially for the case with a strong interface coupling. The second demagnetization process, however, is very fast, leading to a simultaneous nucleation and pinning as well as rectangular hysteresis loop.2.Both the coherent and incoherent nucleation fields decrease as the soft layer thickness Ls increases, whereas they increase with the hard layer thickness Lh. However, Lh has obvious influence on the incoherent nucleation field HNin only when Lh is smaller than its domain wall width, while it always has apparent effect on the coherent nucleation field HNco. In addition, enhancement of the exchange coupling at the hard/soft interface leads to the increase of the HNin, whereas it has no effect on the HNco. Comparison of the nucleation fields for different modes shows that the incoherent nucleation field is always smaller than the coherent one, suggesting that the dominant nucleation mode in the composite materials is the incoherent one.