Individual monolayer analysis of anomalous hysteresis loops

Abstract

Based on a quantum spin model and by using the many-body Green's function method, we discuss the mechanism of anomalous hysteretic loops for exchange-coupled ultrathin bilayers by analyzing in detail the spin behavior in all monolayers. Spins in each monolayer can flip abruptly to generate steplike or triplet loops, or they can reverse gradually to generate double loops. Specially, the spins in an interfacial monolayer may be oriented in the opposite direction from those in the other monolayers of a given layer under a strong interfacial antiferromagnetic exchange. This individual monolayer analysis improves the earlier understanding of the anomalous hysteresis loops by phenomenological models.Anomalous hysteresis loops could occur experimentally in ferromagnetic (FM) films. Here we mean the anomalous loops as steplike 1,2 and multiloops. The latter could be either double loops or triplet loops, which also includes the case of inverted loops. 2-7 Phenomenological models have been used to explain the anomalous loops by exchange-coupled bilayers 2,3,6,8,9 or by introducing higher-order anisotropy. 4,10 In exchange-coupled bilayer models, the system consisted of two FM layers. Each FM layer was assigned a magnetization, the magnitude of which was independent of external field, but could rotate under an external field. There was an antiferromagnetic (AFM) exchange between the two magnetizations. The orientations of the magnetizations were not always along the field direction. Hence the magnetizations of both layers had projections on the field direction. The combination of the projections made up the anomalous loops.If one realizes the system from a microscopic view, the physical picture will be different from what the phenomenological model gave. In a microscopic model, each FM layer consists of several monolayers (ML's), and each ML is in turn composed of spins at crystalline sites. Every spin interacts with its neighbors by Heisenberg exchange interaction. As there is a lack of translation invariance along the out-ofplane direction, the behavior of the spins may be different from ML to ML. The interaction between the two FM layers is in fact an AFM interfacial exchange, not just the interaction between the two magnetizations. Thus the behavior of the spins inside each FM layer may not be uniform, and neither can the behavior of each layer be recognized as a single magnetization. Compared with the microscopic model, a phenomenological model seemed too rough. A detailed microscopic explanation based on quantum mechanics should help us to understand the physics of the anomalous loops more clearly. In this paper, we present a monolayer spin-flip or spin-reversal picture of the anomalous loops for ultrathin exchange-coupled bilayer.The Hamiltonian we use includes three parts:H 1 is the Hamiltonian of the first FM layer:The first term is the Heisenberg FM exchange in each ML, where only the nearest-neighbor interaction is considered.Here i and j label sites and the Greek letters label ML's. The second term is the Heisen...

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