Er_3Ga_5O～(12)材料磁光法拉第效应的理论研究
|
摘要
1998年，M.Guillot等人对单晶Er_3Ga_5O_(12)(简写为ErGG)石榴石的磁特性作了实验研究，描述了强磁场下ErGG特有的一些磁性现象，引起了相当的关注。近年来，刘公强、徐游等人对掺轻稀土的材料的磁特性及磁光效应从理论上进行了定量的计算，张锡娟等人对掺镍的铁氧体的磁光效应亦进行了较细致的理论研究，他们的离子内跃迁模型在一定程度上均较好地解释了实验现象，得到了较好的结果。由于重稀土Er~(3+)离子复杂的微观结构，使理论研究有相当的难度，所以迄今为止尚未见到对其详细的量子理论的定量计算的研究报道。本论文经过详细理论推导和计算，第一次用量子理论定量计算了强磁场作用下单品ErGG石榴石的法拉第旋转角，并计算得出了ErGG石榴石在低温4.2K、强磁场作用下与实验基本吻合的磁性各向异性现象。
按照传统的理论，法拉第旋转角主要是由于电偶极跃迁所形成的。刘公强、徐游等人的研究表明，对于Ce~(3+)，Pr~(3+)等稀土离子，由基组态向激发组态之间的跃迁(4f~n→4f~(n-1)5d)是对法拉第旋转的主要贡献。对于我们所研究的Er~(3+)离子，激发组态与基组态之间的能量差大约在6万cm~(-1)以上，且具体的谱项未能有资料提供。同时考虑到一个4f电子跃迁到5d上去，5d电子的自旋有两种取向。当5d电子的自旋取4f中的7个电子自旋平行时，形成高自旋态(HS)；当自旋反平行时，形成低自旋态(LS)。根据Hund法则，同一个电子组态形成的能级中，总自旋越大，能量越低。因此高自旋态的能量低于低自旋态的能量，而由跃迁选择定则可知低自旋态的跃迁是允许的，也就是说Er~(3+)离子从4f~(11)跃迁到4f~(10)5d上去必须越过高自旋念才能到达自旋允许的激发组态。因此，电子Er~(3+)离子4f~(11)→4f~(10)5d的跃迁是困难的。我们根据Judd and Ofelt两人分别提出的由5d电子态的相反宇称态的波函数与4f态混合，使f→f的禁戒跃迁部分解除的理论，我们认为ErGG石榴石的法拉第旋转是由于奇宇称晶场所引起的4f~(11)组态内电
扬州人学硕士学位论文
子跃迁形成的，并第一次通过编程计算了磁场沿ErGG的[100〕方向时，考虑
f分f「卜的4气今‘I叹的电偶极跃迁，得出了一与实验吻合较好的结果。同时我们
还计一算了法拉第旋转角与磁化强度之间的唯象关系。在计算磁化强度时我们发现，
当外磁场不为零时，晶场的大小对磁化强度有较大的影响。同时稀土离子的间接
交换作用对磁性的影响也是至关重要的。当磁场大于150KOe以上时，我们认为间
接交换作用的大小与外磁场的大小有关，我们拟合得到了和外磁场有关的系数，
使计算的磁化强度特性曲线与实验值符合情况有所改善。我们还计算了温度的变
化对ErGG磁化的贡献，发现温度的变化对不1司方向磁化的影响是不同的。
In 1998, M.Guillot et.al reported the magnetic properties and faraday effects in single crystal erbium gallium gallate (ErGG ),which showed some specific properties, and attracted more attentions.In recent years Liu gongqiang and Xu you made the quantitative calculation in magnetic properties and MO effects of the material with doped rare earth ions in theory.Because of the complex microscopic structure of Er3+ ions, so to date, the quantitative calculations by quantum theory reported little.After detail deduction and calculations, we fistly gave the quantitative calculation on faraday rotation angle of the single crystal ErGG under high magnetic field,and gained the magnetic anisotropy.
According to traditional theory that faraday rotation angle was mainly due to the electric-dipole transition.Liu gongqiang and Xu you's research showed that the
transition from the ground state(GS) to the excited state(ES) (4fn -4fn-15d) of
Ce3+,Pr3+ions was dominant to the faraday rotation angle.But to Er3+ions there was
an energy gap above 60000cm-1 between GS and ES, and the excited spectrum can't be obtained till now.At the same time we considered that when one electron was transited to the 5d ,it can orient its spin in two ways,either parallel with the 7 remaining
4f electrons ,giving rise to a high-spin(HS) state,or antiparallel yielding a low-spin(LS) state.According to Hund's rule,the HS state would be lower in energy.Thus the transition from the GS to the lowest 4f105J state would be forbidden and therefore be
relatively weak compared to the higher energy 4f105d excitation which was spin allowed.In 1960s' Judd and Ofelt proposed the theory that the 4fn configuration
mixed with opposite parity 5d configuration would induce f -f forbidden transition deduction.Based on these consideration,we believed that the faraday rotation angle of ErGG was arisen from the f - f transition. We calculated the transition of
4S3/2-4I15/2 when magnetic field was applied in [100] crystallographic direction and
gained the result which basically familiar with experiment.
In addition we calculated the superficial relationship between the faraday rotation angle and magnetization. We found that (1) the crystal field has a big influence on the magnetization;(2) the indirect exchange of rare earth ion greatly affected on the magnetization.Then we simulated the coefficient relevant to the applied field and gained the better agreement between theory and experiment;(3) finally the effects of temperature on magnetic depended on magnetic direction.
按照传统的理论，法拉第旋转角主要是由于电偶极跃迁所形成的。刘公强、徐游等人的研究表明，对于Ce~(3+)，Pr~(3+)等稀土离子，由基组态向激发组态之间的跃迁(4f~n→4f~(n-1)5d)是对法拉第旋转的主要贡献。对于我们所研究的Er~(3+)离子，激发组态与基组态之间的能量差大约在6万cm~(-1)以上，且具体的谱项未能有资料提供。同时考虑到一个4f电子跃迁到5d上去，5d电子的自旋有两种取向。当5d电子的自旋取4f中的7个电子自旋平行时，形成高自旋态(HS)；当自旋反平行时，形成低自旋态(LS)。根据Hund法则，同一个电子组态形成的能级中，总自旋越大，能量越低。因此高自旋态的能量低于低自旋态的能量，而由跃迁选择定则可知低自旋态的跃迁是允许的，也就是说Er~(3+)离子从4f~(11)跃迁到4f~(10)5d上去必须越过高自旋念才能到达自旋允许的激发组态。因此，电子Er~(3+)离子4f~(11)→4f~(10)5d的跃迁是困难的。我们根据Judd and Ofelt两人分别提出的由5d电子态的相反宇称态的波函数与4f态混合，使f→f的禁戒跃迁部分解除的理论，我们认为ErGG石榴石的法拉第旋转是由于奇宇称晶场所引起的4f~(11)组态内电
扬州人学硕士学位论文
子跃迁形成的，并第一次通过编程计算了磁场沿ErGG的[100〕方向时，考虑
f分f「卜的4气今‘I叹的电偶极跃迁，得出了一与实验吻合较好的结果。同时我们
还计一算了法拉第旋转角与磁化强度之间的唯象关系。在计算磁化强度时我们发现，
当外磁场不为零时，晶场的大小对磁化强度有较大的影响。同时稀土离子的间接
交换作用对磁性的影响也是至关重要的。当磁场大于150KOe以上时，我们认为间
接交换作用的大小与外磁场的大小有关，我们拟合得到了和外磁场有关的系数，
使计算的磁化强度特性曲线与实验值符合情况有所改善。我们还计算了温度的变
化对ErGG磁化的贡献，发现温度的变化对不1司方向磁化的影响是不同的。
In 1998, M.Guillot et.al reported the magnetic properties and faraday effects in single crystal erbium gallium gallate (ErGG ),which showed some specific properties, and attracted more attentions.In recent years Liu gongqiang and Xu you made the quantitative calculation in magnetic properties and MO effects of the material with doped rare earth ions in theory.Because of the complex microscopic structure of Er3+ ions, so to date, the quantitative calculations by quantum theory reported little.After detail deduction and calculations, we fistly gave the quantitative calculation on faraday rotation angle of the single crystal ErGG under high magnetic field,and gained the magnetic anisotropy.
According to traditional theory that faraday rotation angle was mainly due to the electric-dipole transition.Liu gongqiang and Xu you's research showed that the
transition from the ground state(GS) to the excited state(ES) (4fn -4fn-15d) of
Ce3+,Pr3+ions was dominant to the faraday rotation angle.But to Er3+ions there was
an energy gap above 60000cm-1 between GS and ES, and the excited spectrum can't be obtained till now.At the same time we considered that when one electron was transited to the 5d ,it can orient its spin in two ways,either parallel with the 7 remaining
4f electrons ,giving rise to a high-spin(HS) state,or antiparallel yielding a low-spin(LS) state.According to Hund's rule,the HS state would be lower in energy.Thus the transition from the GS to the lowest 4f105J state would be forbidden and therefore be
relatively weak compared to the higher energy 4f105d excitation which was spin allowed.In 1960s' Judd and Ofelt proposed the theory that the 4fn configuration
mixed with opposite parity 5d configuration would induce f -f forbidden transition deduction.Based on these consideration,we believed that the faraday rotation angle of ErGG was arisen from the f - f transition. We calculated the transition of
4S3/2-4I15/2 when magnetic field was applied in [100] crystallographic direction and
gained the result which basically familiar with experiment.
In addition we calculated the superficial relationship between the faraday rotation angle and magnetization. We found that (1) the crystal field has a big influence on the magnetization;(2) the indirect exchange of rare earth ion greatly affected on the magnetization.Then we simulated the coefficient relevant to the applied field and gained the better agreement between theory and experiment;(3) finally the effects of temperature on magnetic depended on magnetic direction.
引文
[1] 戴道生，铁磁学，科学出版社(2000)
[2] 稀土氟化物PrF3的磁光效应与磁性 段明谦、徐游 南京大学学报 vol．29 no．1，Jan，1993
[3] BaM中钴离子基组态的晶场能级 汪颖梅、张锡娟 扬州师院学报 vol 17，No 4．Dec．1997
[4] Ce_xT_(3-x)Al_5O_(12)中Ce_(3+)的4f多重态耦合对其磁矩和磁光性能的影响 杨杰慧，徐游 物理学报
vol．46，no.1，January．1997
[5].Many-body energy-transfer proesses between Er~(3+) ions in yttrium aluminum garnet A.Lupei,V.Lupei,S.Georgescu,and l.Ursu PHYSICS REVIEW B VOLUME 41,NUMBER 16.1 JUNE 1990
[6] What is the role of spin-orbit interaction in magneto-opticaleffect? You Xu, Jiehui Yang, Maurice Guillot JOURNAL OF APPLIED PHYSICS.Vol .85,No.8,15 April 1999
[7] PrCo_5的磁晶各向异性起源 孙峪怀Journal of Southwest Nationalities college Natural Science Edition Aug．19978．
[8] Magneto-optical effects of Rh~(3+) and Rh~(?) doped yttrium iron garnet M.Kucera and J.Kunes R.Gerber JOURNAL OF APPLIED PHYSICS .Vol.85,No.8,15 April 1999
[9] Temperature dependence of the Faraday roation for CdMnCoTe films J.Y.Ahn,M.Tanaka,and M.Imamure JOURNAL OF APPLIED PHYSICS VOLUME 89MBYNE\BER H , 1 JUNE 2001
[10] 奇宁称晶场和自旋-轨道耦合对钡铁氧体中Ni~(2+)离子磁光效应的影响 张锡娟、徐游 科学通报 第43卷 第23期
[11] Faraday rotation in a study of charged excitions in Cd_(1-x)Mn_xTe W.Maslana, W.Mac,J.A.Gaj,P.Kossacki,and A.Golnik PHYSICS REVIEW B VOL 63,165318.2001
[12] Mechanism for strong nonlinearities in the Faraday rotation and absorption in the ferromagnetic semeconductor CdCr_2Se_4 L.Lgolik,Z.E.Kun'kova,and C.Heide JOURNAL OF APPLIED PHYSICS VOL87,NUM 9.1 MAY 2000
[13].The Role of the Spin-Orbit Coupling Strength in the MO Effects of Magnetic Insulators You xu,Jiehui yang,Xijuan Zhang,Fang Zhang ,and M.Guillot IEEE TRANSACTIONS ON MAGNETICS VOL.37,NO.4,JULY 2001
[14] 稀土古榴石的磁光效应与L-S耦合的影响及温度的依赖性 张锡娟 邵争鸣 汪颖梅 Journal of Liaoning Normal University(Natural Science)Vol．21 No．1 1998
[15] Ce：YIG自旋-轨道耦合对磁光效应的影响 杨杰慧，潘留占，徐游，物理学报 Vol．49，no．4，April．2000
[16] Guabt Faraday rotation of blue light in epitaxial Ce_xY_(3-x)Fe_5O_(12) films grown by pulsed laser deposition Hyonju Kim,Alex Grishin,and K.V.Rao JOURNAL OF APLIED PHYSICS VOL.89,NO.8,15 APRIL 2001
[17] What is the role spin-orbit interaction in magneto-optical effect? You Xu ,Jiehui Yang, Maurice Guillot JOURNAL OF APPLIED PHYSICS VOLUME 85 .NUMBER 8 15 APRIL 1999
[18] 对Pr：YIG中Pr~(3+)离子激发态能级的研究 张芳 赵治国 杨杰慧Journal o Henan University (Natural Science)Vol．30 No．3 Sep．2000
[19] Pr：YIG中Pr~(3+)离子磁光效应的研究 张芳，杨杰慧，潘留占，韩运侠 河南师范大学学报(自然科学版) vol．27 no．3 Aug．1999
[20] Sm_2Fe_(17)C_x化合物磁晶各向异性计算 恩克 特占斯 那顺 松林李新文 巴图 Journal of Inner Mongolia Normal University(Natural Science Edition)No．2 1997
[21] Sm_2Fe_(17-x)Ca_xC_y化合物磁晶各向异性的晶场分析 松林 达古拉 娜仁其木格 哈斯巴根 那顺 富泉 特古斯 恩克 徐游Journal of Inner Mongolia Normal University(Natural Science Edition)Vol．29 No．4 Dec．2000
[22].Magnetic properties of Sc-substituted erbium iron garnet single crystals in high magnetic field J.Osterero M.GuillotJOURNAL OF APPLIED PHYSICS.Vol .85,No.8,15 April 1999
[23].Faraday Rotation in Co~(3+) -substituted Magnetic Garnets A.Takeuchi,K.Ando,K.Shinagawa,T.Saito,and T.Tsushima IEEE TRANSACTIONS ON MAGNETICS VOL.35,NO.5,SEPTEMBER 1999
[24] Red Shift of Faraday Rotation in Thin Fihns of Completely Bishmuth-Substituted Iron Garnet Bi_3Fe_5O_(12) Ming-Yan chern,Fang-Yuh Lo,Da-ren liu,Kuang Yang and Juin-Sen Liaw Jpn.J.Appl.Phys.vol.38(1999)Pt, 1,no. 12A
[25] 紫蓝磁光材料量子法拉第效应 张怀武，刘颖力，王豪才 电子科技大学学报 vol，26 no．6 Dec．1997
[26] Therretical calculation of the optical properties of Y_2Fe_5O_(12) W.Y.Ching,Zong-quan Gu,and Yong-Nian Xu JOURNAL OF APPLIED PHYSICS VOL.89.No, 11, IJUNE 2001
[27] Faraday rotation and magnetic properties of erbium gallium gallate under high magnetic field. M.Guillot T.Schmiedel and You Xu JOURNAL OF APPLIED PHYSICS.Vol .83,No.11,1 April 1998
[28] Magnetooptical properties of Sc-substituted erbium-iron-garnet single crystals J.Ostorero M.Guillot JOURNAL OF APPLIED PHYSICS.Vol .83,No. 11,1 April 1999
[29] Faraday rotation and magnetic properties of neodynium trifluoride under high magnetic field M.Guillot T.Schmiedel You xu JOURNAL OF APPLIED PHYSICS.Vol .85,No.8,15 April 1999
[30] Giant Faraday rotation spectra of Zn_(1-x)Mn_xSe observed in high magnetic fields up to 150 T T.Yasuhira, K.Uchida, Y.H.Matsuda,and N.Miura PHYSICS REVIEW B VOL.61,NUM.7,15 FEBRUARY 2000-1
[31] Analysis of the Solid -State Spectra of Trivalent Neodymium and Erbium. B.G.Wybourne
THE JOURNAL of Chemical Physics vol.32,no3.1960
[32] Composition of the Electronic States of Nd(Ⅳ) and Er(lv) B.G.Wybourne EMISSION SPECTRA OF THULIUM 33.Er2(Fe_(1-x)Co_x)_(15)Ga_2化合物的磁晶各向异性 张立刚 物理学报 Vol.47 No.5 May,1998
[33] P.Weiss,J.Phys.Redium.,6(1907),445
[34] W.Heisenberg, Z.Phys,49(1928),31
[35] T.Moriya & A.kawabata, J.Phys.Soc.Japan,34(1973),639;35(1973),35.
[36] T.Moriya&Y.Takahashi,J.Phys.Soc.Japan,45(1978),397;J.de Phys.,39( 1978),C6-1466
[37] 张锡娟，徐游，科学通报，43 (23)(1998), 2503
[38] You Xu,Tu Ba, Yinglie Liu,J.Appl.Phys.,73(10)(1993),6937
[39] You Xu,Guoying Zhang,Mingqian Duan,J.Appl.Phys.,73(10)(1993),6133
[40] You Xu,Mingqian Duan,Phys.Rev.B.,46(18)(1992), 11636
[41] You Xu,Jiehui Yang,Xijuan Zhang,et aI,IEEE Trans Magn,37(4)(2001),2411
[42] Liu Gongqiang,Huang Yanping,and Yu Zhiqiang, Phys.Rev.B.,41(1)(1990),749
[43] Liu Gongqiang, Yu Zhiqiang,Le Zhiqiang,J.Magn.Magn.Mat.,96(1991), 155
[44] Liu Gongqiang,Zuo Wende,Le Zhiqiang,J.Appl.Phys.,69(3)(1991), 1591
[45] Liu Gongqiang,Zuo Wende,Phys.Rev, B 44(2)(1991),699
[46] 磁光学Magnetooptics 刘公强 乐志强 沈德芳著 科学前沿丛书。
[47] 李荫远、李国栋，铁氧体物理学，科学出版社(1976)
[48] 陆学善，激光基质钇铝石榴石的发展，科学出版社(1972)
[49] Geller, S.,and Gilleo.M.A., Acta Crystallog., 10(1957),239.
[50] Espinosa,G.P., J.Chem.Phys.,37(1962),2344-2347.
[51] Tbshihiro Shintaku and Takechiko Uno,Jpn.J.Appl.Phys.,35( 1996),4689-4691
[52] Hyonju Kim,A.M.Grishin,et aI.IEEE Trans. Magn.35(5)(1999),3163-3165
[53] C.Leycuras and H.Le Gall et al.L.,appl.Phys.,55(6)(1984),2161
[54] Akira Yanase, J.Phys.Soc.Japan,,42(5)(1977), 1680
[55] Yoshinobu Maeda,J.Appl.Phys.72(8)(1992),3835
[56] 段明谦，徐游，南京大学学报，29(1)(1993)，41
[57] A.Lupei,V.Lupei,S.Georgescu,and I.Ursu,et al,Phys.Rev. B.,41 (16)(1990), 10923
[58] Yoshinobu Maeda,Jpn.J.Appl.Phys.,37(1998),3676-3681
[59] Y.Shimony, et al,J.Appl.Phys.,68(6)(1990),2966
[60] M.Guillot,T.Schmiedel and You Xu,J.Appl.Phys.,85(8)(1999),5097
[61] M.Guillot,T.Schmiedel,and You Xu, J.Appl.Phys.83(11)(1998),6762
[62] 晶体生长科学与技术 下册张态从主编 科学出版社 P71
[63] Faraday rotation and magnetic propertyes of erbium gallium gallate under high magnetic field M.Guillot,T.Schmiedel,and You Xu JOUNAL OF APPLIED PHYSICS VOL83,NO11
[2] 稀土氟化物PrF3的磁光效应与磁性 段明谦、徐游 南京大学学报 vol．29 no．1，Jan，1993
[3] BaM中钴离子基组态的晶场能级 汪颖梅、张锡娟 扬州师院学报 vol 17，No 4．Dec．1997
[4] Ce_xT_(3-x)Al_5O_(12)中Ce_(3+)的4f多重态耦合对其磁矩和磁光性能的影响 杨杰慧，徐游 物理学报
vol．46，no.1，January．1997
[5].Many-body energy-transfer proesses between Er~(3+) ions in yttrium aluminum garnet A.Lupei,V.Lupei,S.Georgescu,and l.Ursu PHYSICS REVIEW B VOLUME 41,NUMBER 16.1 JUNE 1990
[6] What is the role of spin-orbit interaction in magneto-opticaleffect? You Xu, Jiehui Yang, Maurice Guillot JOURNAL OF APPLIED PHYSICS.Vol .85,No.8,15 April 1999
[7] PrCo_5的磁晶各向异性起源 孙峪怀Journal of Southwest Nationalities college Natural Science Edition Aug．19978．
[8] Magneto-optical effects of Rh~(3+) and Rh~(?) doped yttrium iron garnet M.Kucera and J.Kunes R.Gerber JOURNAL OF APPLIED PHYSICS .Vol.85,No.8,15 April 1999
[9] Temperature dependence of the Faraday roation for CdMnCoTe films J.Y.Ahn,M.Tanaka,and M.Imamure JOURNAL OF APPLIED PHYSICS VOLUME 89MBYNE\BER H , 1 JUNE 2001
[10] 奇宁称晶场和自旋-轨道耦合对钡铁氧体中Ni~(2+)离子磁光效应的影响 张锡娟、徐游 科学通报 第43卷 第23期
[11] Faraday rotation in a study of charged excitions in Cd_(1-x)Mn_xTe W.Maslana, W.Mac,J.A.Gaj,P.Kossacki,and A.Golnik PHYSICS REVIEW B VOL 63,165318.2001
[12] Mechanism for strong nonlinearities in the Faraday rotation and absorption in the ferromagnetic semeconductor CdCr_2Se_4 L.Lgolik,Z.E.Kun'kova,and C.Heide JOURNAL OF APPLIED PHYSICS VOL87,NUM 9.1 MAY 2000
[13].The Role of the Spin-Orbit Coupling Strength in the MO Effects of Magnetic Insulators You xu,Jiehui yang,Xijuan Zhang,Fang Zhang ,and M.Guillot IEEE TRANSACTIONS ON MAGNETICS VOL.37,NO.4,JULY 2001
[14] 稀土古榴石的磁光效应与L-S耦合的影响及温度的依赖性 张锡娟 邵争鸣 汪颖梅 Journal of Liaoning Normal University(Natural Science)Vol．21 No．1 1998
[15] Ce：YIG自旋-轨道耦合对磁光效应的影响 杨杰慧，潘留占，徐游，物理学报 Vol．49，no．4，April．2000
[16] Guabt Faraday rotation of blue light in epitaxial Ce_xY_(3-x)Fe_5O_(12) films grown by pulsed laser deposition Hyonju Kim,Alex Grishin,and K.V.Rao JOURNAL OF APLIED PHYSICS VOL.89,NO.8,15 APRIL 2001
[17] What is the role spin-orbit interaction in magneto-optical effect? You Xu ,Jiehui Yang, Maurice Guillot JOURNAL OF APPLIED PHYSICS VOLUME 85 .NUMBER 8 15 APRIL 1999
[18] 对Pr：YIG中Pr~(3+)离子激发态能级的研究 张芳 赵治国 杨杰慧Journal o Henan University (Natural Science)Vol．30 No．3 Sep．2000
[19] Pr：YIG中Pr~(3+)离子磁光效应的研究 张芳，杨杰慧，潘留占，韩运侠 河南师范大学学报(自然科学版) vol．27 no．3 Aug．1999
[20] Sm_2Fe_(17)C_x化合物磁晶各向异性计算 恩克 特占斯 那顺 松林李新文 巴图 Journal of Inner Mongolia Normal University(Natural Science Edition)No．2 1997
[21] Sm_2Fe_(17-x)Ca_xC_y化合物磁晶各向异性的晶场分析 松林 达古拉 娜仁其木格 哈斯巴根 那顺 富泉 特古斯 恩克 徐游Journal of Inner Mongolia Normal University(Natural Science Edition)Vol．29 No．4 Dec．2000
[22].Magnetic properties of Sc-substituted erbium iron garnet single crystals in high magnetic field J.Osterero M.GuillotJOURNAL OF APPLIED PHYSICS.Vol .85,No.8,15 April 1999
[23].Faraday Rotation in Co~(3+) -substituted Magnetic Garnets A.Takeuchi,K.Ando,K.Shinagawa,T.Saito,and T.Tsushima IEEE TRANSACTIONS ON MAGNETICS VOL.35,NO.5,SEPTEMBER 1999
[24] Red Shift of Faraday Rotation in Thin Fihns of Completely Bishmuth-Substituted Iron Garnet Bi_3Fe_5O_(12) Ming-Yan chern,Fang-Yuh Lo,Da-ren liu,Kuang Yang and Juin-Sen Liaw Jpn.J.Appl.Phys.vol.38(1999)Pt, 1,no. 12A
[25] 紫蓝磁光材料量子法拉第效应 张怀武，刘颖力，王豪才 电子科技大学学报 vol，26 no．6 Dec．1997
[26] Therretical calculation of the optical properties of Y_2Fe_5O_(12) W.Y.Ching,Zong-quan Gu,and Yong-Nian Xu JOURNAL OF APPLIED PHYSICS VOL.89.No, 11, IJUNE 2001
[27] Faraday rotation and magnetic properties of erbium gallium gallate under high magnetic field. M.Guillot T.Schmiedel and You Xu JOURNAL OF APPLIED PHYSICS.Vol .83,No.11,1 April 1998
[28] Magnetooptical properties of Sc-substituted erbium-iron-garnet single crystals J.Ostorero M.Guillot JOURNAL OF APPLIED PHYSICS.Vol .83,No. 11,1 April 1999
[29] Faraday rotation and magnetic properties of neodynium trifluoride under high magnetic field M.Guillot T.Schmiedel You xu JOURNAL OF APPLIED PHYSICS.Vol .85,No.8,15 April 1999
[30] Giant Faraday rotation spectra of Zn_(1-x)Mn_xSe observed in high magnetic fields up to 150 T T.Yasuhira, K.Uchida, Y.H.Matsuda,and N.Miura PHYSICS REVIEW B VOL.61,NUM.7,15 FEBRUARY 2000-1
[31] Analysis of the Solid -State Spectra of Trivalent Neodymium and Erbium. B.G.Wybourne
THE JOURNAL of Chemical Physics vol.32,no3.1960
[32] Composition of the Electronic States of Nd(Ⅳ) and Er(lv) B.G.Wybourne EMISSION SPECTRA OF THULIUM 33.Er2(Fe_(1-x)Co_x)_(15)Ga_2化合物的磁晶各向异性 张立刚 物理学报 Vol.47 No.5 May,1998
[33] P.Weiss,J.Phys.Redium.,6(1907),445
[34] W.Heisenberg, Z.Phys,49(1928),31
[35] T.Moriya & A.kawabata, J.Phys.Soc.Japan,34(1973),639;35(1973),35.
[36] T.Moriya&Y.Takahashi,J.Phys.Soc.Japan,45(1978),397;J.de Phys.,39( 1978),C6-1466
[37] 张锡娟，徐游，科学通报，43 (23)(1998), 2503
[38] You Xu,Tu Ba, Yinglie Liu,J.Appl.Phys.,73(10)(1993),6937
[39] You Xu,Guoying Zhang,Mingqian Duan,J.Appl.Phys.,73(10)(1993),6133
[40] You Xu,Mingqian Duan,Phys.Rev.B.,46(18)(1992), 11636
[41] You Xu,Jiehui Yang,Xijuan Zhang,et aI,IEEE Trans Magn,37(4)(2001),2411
[42] Liu Gongqiang,Huang Yanping,and Yu Zhiqiang, Phys.Rev.B.,41(1)(1990),749
[43] Liu Gongqiang, Yu Zhiqiang,Le Zhiqiang,J.Magn.Magn.Mat.,96(1991), 155
[44] Liu Gongqiang,Zuo Wende,Le Zhiqiang,J.Appl.Phys.,69(3)(1991), 1591
[45] Liu Gongqiang,Zuo Wende,Phys.Rev, B 44(2)(1991),699
[46] 磁光学Magnetooptics 刘公强 乐志强 沈德芳著 科学前沿丛书。
[47] 李荫远、李国栋，铁氧体物理学，科学出版社(1976)
[48] 陆学善，激光基质钇铝石榴石的发展，科学出版社(1972)
[49] Geller, S.,and Gilleo.M.A., Acta Crystallog., 10(1957),239.
[50] Espinosa,G.P., J.Chem.Phys.,37(1962),2344-2347.
[51] Tbshihiro Shintaku and Takechiko Uno,Jpn.J.Appl.Phys.,35( 1996),4689-4691
[52] Hyonju Kim,A.M.Grishin,et aI.IEEE Trans. Magn.35(5)(1999),3163-3165
[53] C.Leycuras and H.Le Gall et al.L.,appl.Phys.,55(6)(1984),2161
[54] Akira Yanase, J.Phys.Soc.Japan,,42(5)(1977), 1680
[55] Yoshinobu Maeda,J.Appl.Phys.72(8)(1992),3835
[56] 段明谦，徐游，南京大学学报，29(1)(1993)，41
[57] A.Lupei,V.Lupei,S.Georgescu,and I.Ursu,et al,Phys.Rev. B.,41 (16)(1990), 10923
[58] Yoshinobu Maeda,Jpn.J.Appl.Phys.,37(1998),3676-3681
[59] Y.Shimony, et al,J.Appl.Phys.,68(6)(1990),2966
[60] M.Guillot,T.Schmiedel and You Xu,J.Appl.Phys.,85(8)(1999),5097
[61] M.Guillot,T.Schmiedel,and You Xu, J.Appl.Phys.83(11)(1998),6762
[62] 晶体生长科学与技术 下册张态从主编 科学出版社 P71
[63] Faraday rotation and magnetic propertyes of erbium gallium gallate under high magnetic field M.Guillot,T.Schmiedel,and You Xu JOUNAL OF APPLIED PHYSICS VOL83,NO11