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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. -
Keywords:
- paramagnetic /
- Verdet constant /
- energy level transition /
- electric dipole moment
[1] Zhang F, Tian Y, Yi Z, Gu S H 2016 Chin. Phys. B 25 094206
Google Scholar
[2] Tian Y, Tan B Z, Yang J, Zhang Y, Gu S H 2015 Chin. Phys. B 24 063302
Google Scholar
[3] Yasuhara R, Furuse H 2013 Opt. Lett. 38 1751
Google Scholar
[4] 李长胜 2015 物理学报 64 047801
Google Scholar
Li C S 2015 Acta Phys. Sin. 64 047801
Google Scholar
[5] Becquerel H 1897 J. Phys. Theor. Appl. 6 681
[6] 刘公强, 龚挺 1985 上海交通大学学报 19 81
Liu G Q, Gong T 1985 J. Shanghai JiaoTong Univ. 19 81
[7] 刘公强, 乐志强, 沈德芳 2001 磁光学(上海: 科学技术出版社) 第30—34页
Liu G Q, Le Z Q, Shen D F 2001 Magnetooptics (Shanghai: Science and Technology Press) pp30–34 (in Chinese)
[8] 蔡伟, 邢俊辉, 杨志勇 2017 物理学报 66 187801
Google Scholar
Cai W, Xing J H, Yang Z Y 2017 Acta Phys. Sin. 66 187801
Google Scholar
[9] van Vleck J H, Hebb M H 1934 Phys. Rev. 46 17
Google Scholar
[10] Suits J 1972 IEEE Trans. Mag. 8 95
Google Scholar
[11] 刘公强, 黄燕萍 1988 物理学报 37 1626
Google Scholar
Liu G Q, Huang Y P 1988 Acta Phys. Sin. 37 1626
Google Scholar
[12] Scott G B, Lacklison D 1976 IEEE Trans. Mag. 12 292
Google Scholar
[13] Slezák O, Yasuhara R, Lucianetti A, Mocek T 2016 Opt. Mater. Express 6 3683
Google Scholar
[14] Taskeya H 2017 Int. J. Electromagn. Appl. 7 17
[15] Wittekoek S, Popma T J A, Robertson J M, Bongers P F 1975 Phys. Rev. B 12 2777
Google Scholar
[16] Zhu N F, Li Y X, Yu X F 2008 Mater. Lett. 62 2355
Google Scholar
[17] Vasyliev V, Villora E G, Nakamura M, Sugahara Y, Shimamura K 2012 Opt. Express 20 14460
Google Scholar
[18] Löw U, Zvyagin S, Ozerov M, Schaufuss U, Kataev V, Wolf B, Lüthi B 2013 Eur. Phys. J. B 86 87
Google Scholar
[19] Chen Z, Yang L, Wang X Y, Hang Y 2016 Opt. Mater. 62 475
Google Scholar
[20] Villaverde A B, Donatti D A, Bozinis D G 1978 J. Phys. C: Solid State Phys. 11 L495
Google Scholar
[21] Kaminskii A A, Eichler H J, Reiche P, Uecker R 2005 Laser Phys. Lett. 2 489
Google Scholar
[22] Raja M Y A, Allen D, Sisk W 1995 Appl. Phys. Lett. 67 2123
Google Scholar
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图 1 顺磁性磁光材料中的能级跃迁
Figure 1. Energy level transition in paramagnetic magneto-optical materials.
图 2 电子运动及受力分析
Figure 2. Electronic motion and force analysis.
图 3 总电偶极矩
Figure 3. Total electric dipole moment.
图 4 Tb3+离子的能级分裂过程
Figure 4. Energy level splitting process of Tb3+ ions.
图 5 维尔德常数随波长变化情况
Figure 5. Verdet constant varies with wavelength.
表 1 晶场及自旋轨道作用下的能级位移(单位为cm–1)
Table 1. Energy level shift under the action of crystal field and spin orbit (in cm–1).
1 2 3 4 5 6 7 8 Tb3+ Em1 41.6 49.7 84.9 89.2 267.5 272 303.2 310.5 En1 –863.2 –336.4 –56.3 784.6 1446.7 1996.2 
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表 2 有效场作用下的能级分裂(单位为cm–1)
Table 2. Energy level splitting under the action of effective field (in cm–1).
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 $)
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表 3 不同理论下的维尔德常数(单位为
${\rm{rad/(m}} \cdot {\rm{T)}}$ )Table 3. Verdet constant under different theories (in
${\rm{rad/(m}} \cdot {\rm{T)}}$ ).
DownLoad: CSV
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[1] Zhang F, Tian Y, Yi Z, Gu S H 2016 Chin. Phys. B 25 094206
Google Scholar
[2] Tian Y, Tan B Z, Yang J, Zhang Y, Gu S H 2015 Chin. Phys. B 24 063302
Google Scholar
[3] Yasuhara R, Furuse H 2013 Opt. Lett. 38 1751
Google Scholar
[4] 李长胜 2015 物理学报 64 047801
Google Scholar
Li C S 2015 Acta Phys. Sin. 64 047801
Google Scholar
[5] Becquerel H 1897 J. Phys. Theor. Appl. 6 681
[6] 刘公强, 龚挺 1985 上海交通大学学报 19 81
Liu G Q, Gong T 1985 J. Shanghai JiaoTong Univ. 19 81
[7] 刘公强, 乐志强, 沈德芳 2001 磁光学(上海: 科学技术出版社) 第30—34页
Liu G Q, Le Z Q, Shen D F 2001 Magnetooptics (Shanghai: Science and Technology Press) pp30–34 (in Chinese)
[8] 蔡伟, 邢俊辉, 杨志勇 2017 物理学报 66 187801
Google Scholar
Cai W, Xing J H, Yang Z Y 2017 Acta Phys. Sin. 66 187801
Google Scholar
[9] van Vleck J H, Hebb M H 1934 Phys. Rev. 46 17
Google Scholar
[10] Suits J 1972 IEEE Trans. Mag. 8 95
Google Scholar
[11] 刘公强, 黄燕萍 1988 物理学报 37 1626
Google Scholar
Liu G Q, Huang Y P 1988 Acta Phys. Sin. 37 1626
Google Scholar
[12] Scott G B, Lacklison D 1976 IEEE Trans. Mag. 12 292
Google Scholar
[13] Slezák O, Yasuhara R, Lucianetti A, Mocek T 2016 Opt. Mater. Express 6 3683
Google Scholar
[14] Taskeya H 2017 Int. J. Electromagn. Appl. 7 17
[15] Wittekoek S, Popma T J A, Robertson J M, Bongers P F 1975 Phys. Rev. B 12 2777
Google Scholar
[16] Zhu N F, Li Y X, Yu X F 2008 Mater. Lett. 62 2355
Google Scholar
[17] Vasyliev V, Villora E G, Nakamura M, Sugahara Y, Shimamura K 2012 Opt. Express 20 14460
Google Scholar
[18] Löw U, Zvyagin S, Ozerov M, Schaufuss U, Kataev V, Wolf B, Lüthi B 2013 Eur. Phys. J. B 86 87
Google Scholar
[19] Chen Z, Yang L, Wang X Y, Hang Y 2016 Opt. Mater. 62 475
Google Scholar
[20] Villaverde A B, Donatti D A, Bozinis D G 1978 J. Phys. C: Solid State Phys. 11 L495
Google Scholar
[21] Kaminskii A A, Eichler H J, Reiche P, Uecker R 2005 Laser Phys. Lett. 2 489
Google Scholar
[22] Raja M Y A, Allen D, Sisk W 1995 Appl. Phys. Lett. 67 2123
Google Scholar
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