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International journal of innovation and applied studies

Non linear effects in the magnetization and the magnetic susceptibility of a set of spin one particles interacting with an oscillating field

Chadia Qotni, Az-Eddine L. Marrakchi, Salaheddine Sayouri, Y. Achkar

Published Aug 30, 2016• 0 citations
OpenAlex

Abstract

We study a set of particles of spin 1 subjected to an oscillating field. We calculate the steady states of this system using the Floquet theorem and the method of resonant medium developed to the third order with respect to the oscillating field intensity. The calculation of the magnetization of the overall system allows one to show the saturation of absorption, and gives, to order three, asymptotic terms of both the dispersion and the absorption where nonlinear effects appear.

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We study a set of particles of spin 1 subjected to an oscillating field. We calculate the steady states of this system using the Floquet theorem and the method of resonant medium developed to the third order with respect to the oscillating field intensity.
The calculation of the magnetization of the overall system allows one to show the saturation of absorption, and gives, to order three, asymptotic terms of both the dispersion and the absorption where nonlinear effects appear.
As a continuation of our previously published work, we propose a theoretical framework for the determination of steady-state kinetics in a spin-1 Ising model by the path probability method. The framework is based on the principles of non-equilibrium statistical physics and is quite different from the phenomenological approach. We construct a set of linear kinetic equations for the order parameters using the non-linear dynamic (or rate) equations in the presence of external magnetic field. From the steady-state solutions of the linear equations, an expression for the complex (or dynamic) magnetic susceptibility [Formula: see text] is derived. The temperature dependence of the magnetic dispersion relation [Formula: see text] and magnetic absorption factor [Formula: see text] has been studied in the ferromagnetic (FM) and paramagnetic (PM) phases as well as near the critical regime.
A theoretical analysis is made of the nonlinear (in respect of the radiation intensity) rotation of the plane of polarization occuring in an atomic medium subjected to a static magnetic field near one-photon (two-level atoms) and two-photon (three-level atoms) resonances. A study is also made of the influence of a strong monochromatic pump wave on the propagation of a weak nonmonochromatic wave. The wave functions and quasienergies are calculated for a three-level system in static magnetic and monochromatic electromagnetic fields near a two-photon resonance. It is shown that the Verdet constant and the refractive index of such a system depend on the magnitude and relative sign of the frequency detuning from resonance. Proximity to a two-photon resonance destroys the polarizability of a medium for either sign of the detuning.
The nonlinear rate equations based on the path probability method is used to derive the dynamic (or complex) susceptibility ( ? ) for a spin-1 Ising model with bilinear and biquadratic interactions when the external magnetic field exists. Firstly, the rate equations are linearized. Then, these are solved in the presence of an oscillating external magnetic field. From the real and imaginary parts of ? , the magnetic dispersion and absorption factors are found. Temperature dependence of these quantities in the ferromagnetic and paramagnetic phase regions (as well as their critical properties) are presented. Finally, the theoretical results are compared with those obtained using irreversible thermodynamics
A diagrammatic approach to the theory of nonlinear susceptiblities is developed. Including damping, the steady state nonlinear response functions to several simultaneously applied monochromatic electromagnetic fields are obtained in terms of linear response functions in the weak coupling system. Saturation phenomena in microwave resonance and in parametric processes can be understood as lower order responses in the system with higher spin temperature. The condition for the Raman emission is discussed in some details. Results are compared with previous theories, in particular with that of Bloembergen and Shen. The theory is extended to the case where the spacially inhomogeneous perturbation is imposed.