Magnetic Properties Of Rare-Earth Garnet Under High Magnetic Field And Low Temperatures

This paper mainly studies the magnetic properties of Praseodymium Gallium Garnet, Dysprosium Gallium Garnet and Yttrium Iron Garnet through semi-classical phenomenological theory and quantum theory under the extreme conditions (high magnetic field and low temperatures)During recent years, much attention has been paid to the study of the magnetic properties of rare-earth garnet materials in the high magnetic field and low temperatures or other extreme conditions. Within the maximum degree that can be met with in the laboratory under a variety of extreme conditions, the scientists who experimentally study magnetic properties on the rare earth magnetic garnets. It is shown that the magnetic properties of some magnetic materials are different between extreme conditions and non-extreme conditions. Under the extreme conditions (strong magnetic fields and low temperatures), the relationships of magnetization and external magnetic field in some rare-earth magnetic materials present a complex non-linear characteristics. Meanwhile, with the increasing of external magnetic field, the saturation and the anisotropic properties of the magnetization in some rare earth garnets are gradually increased. In addition, the analyses of the effect of crystal field and the exchange interaction on the magnetic properties of the rare-earth magnetic garnet are discussed.On the other hand, based on the classical phenomenological theory and the quantum theory, this paper will further study the magnetic properties of rare-earth garnet. Further, the calculated results are compared with the experimental results of the rare-earth magnetic materials under extreme conditions (strong magnetic fields and low temperatures).Here, taking the crystal field, external magnetic field and exchange interaction into account, a deep theoretical calculation on the magnetic properties of PrGaG, DyGaG and YbIG, by the classical phenomenological theory and quantum theory, are presented. Here, our calculations are based on the crystal field theory, the Zeeman effect theory, the quantum theory of magnetic anisotropy and the theory of Kramers theorem at the situation of extreme conditions. Firstly, the magnetic anisotropy, magnetic saturation and the temperature characteristics of magnetic susceptibility have been discussed by analyzing the crystal structure of PrGaG, DyGaG and YbIG in the basis of crystal field theory. Moreover, with the special consideration of crystal field effect and the exchange interaction, the coefficient associated with the molecular field and exchange interaction field, the magnetic anisotropy and the magnetization of PrGaG, DyGaG and YbIG are studied in detail.In the research of magnetic properties of the paramagnetic rare earth gallium garnet (PrGaG and DyGaG) and the ferrimagnetic rare-earth iron garnet (YbIG), it is found that the crystal field parameters can directly affect the lowest magnetic energy levels and wave functions. Therefore, what can be seen is that the determination of crystal field parameters has great effects on the theoretical calculation of its magnetic properties. The method used in the paper is to select the most suitable set of crystal field parameters first, then study further about the magnetic properties of rare earth garnet materials theoretically, with the combination of crystal field and exchange interaction, under the extreme conditions (strong magnetic fields and low temperatures). Then, the effects of the external magnetic fields and exchange interaction field on the magnetic behaviors under extreme conditions are discussed through the application of classical theory and quantum theory. The theoretical results show that the field-dependence and temperature-dependence of the magnetization perfectly fit with the experimental curves, which further proves the correctness of our theoretical calculations. Meanwhile, it further illuminates that the un-neglected effects of exchange interaction during the calculations of the magnetic properties of rare earth garnets. In the mean time, a further discuss in detail on the magnetization, the coefficient of molecular field, the coefficient of exchange interaction that related on molecular field and magnetic anisotropy of PrGaG, DyGaG and YbIG has been hold. Here, it should be pointed out that this study can present a guidance of experimental research of magneto-optical rare-earth garnets under extreme conditions. Additionly, our theoretical analyses of rare-earth garnets will further help to explore the magnetic theory under extreme conditions.