Research in spintronics has attracted much attention in the last few years due to the technological progress in generating and manipulating spin currents in miniaturized devices. Notwithstanding dissipative effects are inherent to experiments, in many theoretical works the damping of spin waves is included later by phenomenological arguments or even disregarded. Among the many techniques that have been used to treat magnetic models, bosonic representations is one of them. In this work, we chose the Holstein-Primakoff bosonic formalism to treat a ferromagnetic model with a priori inclusion of the damping term. Damping is included through a non-Hermitian term in the Hamiltonian and we showed that the well-known coherent state formalism can be generalized to properly represent the dissipative magnon model. The obtained results are then used to describe the precession magnetization in spintronic experiments, as the spin pumping process.
Almost all traditional physical formalisms are developed by using conservative forces, and the microscopic implementation of dissipation involves a sort of unusual process, mainly in quantum systems. In this work, we study the quantum harmonic model endowed with a non-Hermitian term responsible for dissipation. In addition, we also include an oscillating field that drives the model to a coherent state, which is dominated by fluctuation in a specific frequency, while regular thermal states are lowly occupied. The usual coherent state formalism at zero temperature is extended to treat dissipative models at finite temperature. We define a generating function that is used in the evaluation of the most relevant statistical averages, such as the particle distribution. Then, we successfully employ the developed formalism to discuss two well-known applications; the damped quantum harmonic oscillator, and the precession magnetization in a ferromagnetic sample.
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