Study Of The Effective Field Base On Exchange Interaction In Pr:YIG And Gd₃Ga₅O₁₂ At Low Temperature

The rare-earth garnets have attracted a great deal of attention during the past several decades due to their technical applications in optical isolators, magnetic field sensors, magnetic refrigeration and so on. The excellent properties of the crystals are induced by the crystal field effect, the exchange interaction between electrons in different magnetic ions and the spin fluctuations of magnetic ions. However, the exchange interaction in the crystals can not be well understood yet because of the complexity of the crystal structure. The main purpose of this article is to research the effective field based on exchange interaction in rare-earth garnets at low temperature and to provide theoretical help for the technical applications of the materials.The first accomplished work is about the effect of spin fluctuations on the exchange field in Pr: YIG crystal at low temperature. In general magnetic materials, the temperature dependence of the spin fluctuations corresponds to that of the coefficient of the exchange field. Therefore, we make use of the thermal variation of the spin fluctuations to improve the exchange field in Pr:YIG crystal. The improved exchange field is Hin=nO(1+γT+β-ωT)MYIG·. In order to examine the correctness of the exchange field, the magnetic and magneto-optical properties are calculated in the temperature range of4.2-300K, our theoretical prediction is much better agreement with the experimental data.The second accomplished work is to study the effective field based on the exchange interaction in Gd3GasO12(GGG) under low and moderate magnetic field at low temperature. In this work, the crystal field levels and wave functions of GGG are calculated. Through to analyze the magnetic character of GGG under low and moderate magnetic field at low temperature, the effective field based on the exchange interaction is given as Hin=(θp)/(T-θp)He+1.11/(T2+29.77)He2.The expression showed that both temperature and external magnetic field have important influence on the exchange interaction in GGG crystal. Using the effective field, the Zeeman splitting levels of the six nonequivalent crystal sites, the average magnetic moment, the isothermal magnetic entropy change ΔSM and the adiabatic temperature change ΔT are calculated. The calculated results are in good consistence with the experimental data. Therefore, the correctness of the effective field is proven. The results redound to the technical applications of the materials.