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摘要

对顺磁性材料磁光特性和维尔德常数的研究通常采用量子理论, 但传统的量子理论仅考虑了电子跃迁偶极矩的影响, 难以对维尔德常数进行全面系统的描述. 本文在考虑跃迁偶极矩影响的基础上, 以受迫振动对电偶极矩修正的方式计入外磁场与光电场对电子运动的影响. 首先从微观层面分析了顺磁性材料磁光效应及维尔德常数的内在机理, 而后通过经典电子动力学理论和量子理论分别分析了电子的能级跃迁和外场作用下非跃迁位移对电偶极矩的贡献, 进而推导得到顺磁性材料的极化率, 构建了维尔德常数的解算模型. 以典型顺磁性磁光材料铽镓石榴石为例, 量子计算了Tb ³⁺离子在自旋-轨道耦合、晶场及有效场作用下的能级及波函数, 最终分别定量求解得到传统量子理论和本文方法下的维尔德常数. 对比分析发现: 相比传统量子理论, 利用本文方法计算得到的结果与实验数据更为吻合, 具有一定的优越性.

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Abstract

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 Tb ³⁺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.

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作者及机构信息

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通信作者:许友安,408091240@qq.com

基金项目:国家自然科学基金(批准号: 61505254)资助的课题

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Corresponding author:Xu You-An,408091240@qq.com

Funds:Project supported by the National Natural Science Foundation of China (Grant No. 61505254)

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参考文献

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施引文献

下载: 全尺寸图片幻灯片

		1	2	3	4	5	6	7	8
Tb³⁺	E_m₁	41.6	49.7	84.9	89.2	267.5	272	303.2	310.5
Tb³⁺	E_n₁	–863.2	–336.4	–56.3	784.6	1446.7	1996.2

下载: 导出CSV

	1	2	3	4
Tb³⁺	($ \pm 2.342 \mp 0.9516\nu \chi $)	($ \pm 0.46 \mp 0.1422\nu \chi $)	($ \pm 0.897 \mp 0.3641\nu \chi $)	($ \pm 1.49 \mp 0.6561\nu \chi $)

下载: 导出CSV

λ/nm	457.9	532	632.8	830	1064	1300
V_e	–305.7	–190	–134.4	–61	–40.2	–20
V_t	–351.9	–236.2	–157.8	–83.2	–50.3	–32.9
V_w-t	–314.6	–198.7	–144.3	–68.9	–43.7	–23.1
注:V_t为Van Vleck-Hebb传统量子理论的计算值,V_w-t为本文方法的计算值,V_e为实验数据^[19—22].

下载: 导出CSV

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