三价镨离子掺杂对铽镓石榴石晶体磁光性能影响的量子计算  

Quantum calculation of the influence of trivalent praseodymium ions doping on the magneto-optical properties of terbium gallium garnet crystal

作　　者：蔡伟 许友安 杨志勇 Cai Wei;Xu You -An;Yang Zhi -Yong(Armament Launch Theory and Technology Key Discipline Laboratory of China,RocketForce University of Engineering,Xi′an 710025,China;Science and Technology on Electro-optic Control Laboratory,Luoyang 471000,China)

机构地区：[1]火箭军工程大学,兵器发射理论与技术国家重点学科实验室,西安710025 [2]光电控制技术重点实验室,洛阳471000

出　　处：《物理学报》2019年第13期262-269,共8页Acta Physica Sinica

基　　金：国家自然科学基金(批准号:61505254)资助的课题~~

摘　　要：在铽镓石榴石(TGG)晶体中掺杂Pr^3+离子能够有效提升材料的磁光性能,但目前缺乏系统的理论计算阐明此问题.本文根据量子理论,分析了掺杂Pr^3+离子的影响机理并进行了定量计算.根据微扰理论解算久期方程,得到自旋-轨道耦合、晶场、有效场及离子之间的超交换作用下,Tb^3+,Pr^3+离子的能级位移及波函数;进一步解算出Tb^3+,Pr^3+离子自基态4f至5d的跃迁电偶极矩、各能级上的分布概率及平均磁矩;获得了的进一步分裂,导致Pr:TGG晶体维尔德常数明显提升;掺杂Pr^3+离子后,晶体内部有效磁矩增高,磁化率增大,且温度依赖性降低;维尔德常数数与Pr^3+离子掺杂量成分段线性关系,当晶体内部的Tb^3+离子和Pr^3+离子含量相等时,达到最大值.本文的计算结果与已有的实验数据符合较好.Compared with those materials with superior magneto-optical properties,such as YIG,Ce:YIG and Ba3Tb(PO4)3,pure terbium gallium garnet(TGG)crystal has comparative low Verdet constant and cannot meet the requirements of some high-power devices.Doping Pr^3+ions in TGG crystal can remarkably enhance its magneto-optical properties and expand its application scope,but there are still lack of systematic theoretical calculations to clarify this phenomenon.Based on the quantum theory,this paper presents the influence of doping Pr^3+ions on the magneto-optical performance and the corresponding quantitative calculation results.Firstly,taking various effects on Tb^3+ions and Pr^3+ions in the crystal into consideration,the Hamiltonian is modeled and discussed in detail.The secular equations are solved by applying the perturbation method,and then the energy level shifts and wave functions of the Tb^3+ions and Pr^3+ions are worked out,where the spinorbit coupling,crystal field,effective field and super-exchange interaction between the two types of ions are considered.Furthermore,the transition dipole moments of Tb^3+ions and Pr^3+ions from the 4f ground state to higher level 5d,together with the distribution probability at each energy level and the average magnetic moment,are resolved.Finally,the Verdet constants and magnetic susceptibilities of pure TGG crystal and Pr:TGG crystal are calculated and compared with each other.Moreover,the relationship between the Verdet constant of Pr:TGG crystal and the Pr^3+-doping amount is derived.The results show that the Faraday rotation angle caused by Pr^3+ions is larger than that of Tb^3+ions,meanwhile,the strong super-exchange between Tb^3+ions and Pr^3+ions causes further splitting of the 4f energy level,resulting in a significant increasement of the Verdet constant of the Pr:TGG crystal,which reaches 313.4 rad/m·T,191.2 rad/m·T and 60.4 rad/m·T at the wavelengths of 532 nm,632.8 nm and 1064 nm,respectively.In addition,doping Pr^3+ions inside the crystal improves the internal effect

关 键 词：法拉第旋转 量子理论 维尔德常数 磁化率 

分 类 号：O73[理学—晶体学]