Modified Heisenberg model of spin clusters to relate to the spontaneous magnetization reversal

In this paper we utilize the Landau-Lifshitz equation and its properties to derive a scalar equation of motion and analyze a chain of spins and model clusters of spins in materials that in principle not are ferromagnetic, such as aluminum and others. By calculating the total energy of the system of all interactions between the spins, the Landau-Lifshitz equation governs the local behavior of spins or a chain of spins. This model is well known and so called Heisenberg model. We used the Heisenberg model to write the Hamiltonian of the system and got there the equation of that govern the spin chain dynamics. However, in some systems the approximation of a single magnetic phase may not reflect observations. For example, the observation of superparamagnetism and spontaneous magnetization reversal can be better explained through the interaction between magnetic phases. Such behavior has been observed in both nanoparticles and thin films, and can result in novel behavior such as inverted hysteresis loops. A revised Heisenberg model is proposed to describe this behavior. We also discuss the description of the pattern of the magnetization scalar field through the use of the Schrödinger-like equation, which may contribute to modeling the behavior of the magnetization field at the interface of hybrid materials.