The Verdet constant is one of the key parameters to characterize the material magneto-optical properties. The quantum theory is usually used to study magneto-optical properties and calculate the Verdet constant of paramagnetic material. However, the traditional quantum theory only takes into account the influence of the electron transition dipole moments caused by the particle property of light, which therefore cannot formulate the Verdet constant of magneto-optical material accurately.

In view of the shortcomings of the existing theory, in this paper we propose is a wave-transition model of the Verdet constant. Due to the special wave-particle duality of light, the contribution of the non-transition dipole moment to the Verdet constant, caused by the electric field of light wave, should not be ignored.

According to the basic theory of magneto-optical effect, in this paper we first explore the intrinsic mechanism of the paramagnetic material’s Verdet constant at a microscopic level and analyze the deficiency of traditional quantum theory. Furthermore, the classical electronic dynamic theory and quantum theory are used to reveal the contribution of volatility and transition of the light to the electric dipole moment. The density operator and statistical algorithm are introduced to derive the polarizability tensor of the paramagnetic magneto-optical material, thus obtaining the Verdet constant expression of the paramagnetic magneto-optical material, from which the Verdet constant is formulated. Taking the paramagnetic magneto-optical material TGG for example, the splitting energy levels and wave function of Tb³⁺ ions in the spin-orbit coupling, crystal field and effective field are calculated by the quantum method, and finally the Verdet constants under the traditional quantum theory and the volatility transition contribution model are obtained quantitatively. The comparative analysis shows that the results calculated by the wave-transition contribution model are more consistent with the experimental data and more accurate than the results calculated through the traditional quantum theory. The idea and method put forward in this paper will provide reference for further exploring the magneto-optical effect mechanism of paramagnetic magneto-optical materials.