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The microscopic mechanism of the zero-field splitting parameters (ZFS) including D and (a-F) for 6 S(3d5) state ion in trigonal-symmetry crystal field have been investigated using the complete diagonaliztion method (CDM) by taking into account the spin-spin (SS), the spin-other-orbit (SOO) and the orbit-orbit (OO) magnetic interactions besides the well-known spin-orbit (SO) magnetic interaction. It was found that the contribution to the ZFS parameters D and (a-F) arising from the spin-orbit (SO) magnetic interaction is the most important in most of the crystal field (CF) ranges,but the contribution to the zero-field splitting (ZFS) parameter D and (a-F) from the other three mechanisms, including the SS mechanism, SOO mechanism and OO mechanism, cant be ignored. The ZFS parameters D and (a-F) arise from the net spin quartet states as well as the combined effects of the spin doublet states and the spin quartets states, and the contribution to the ZFS parameters from the net spin doublet states are zero. Our investigation shows that the rank-2 ZFS parameter D primarily results from the net spin quartet states whereas the rank-4 ZFS parameter (a-F) primarily results from the combined effect of the spin doublet states and the spin quartet states. An illustrative evaluation is performed for the typical crystal material Fe3+: Al2O3. Good agreement between the theoretical values and the experimental finding are obtained.
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Keywords:
- 6 S(3d5) state ion /
- zero-field splitting (ZFS) parameter /
- magnetic interaction /
- complete diagonalization method (CDM)
[1] Droubay T C, Keavney D J, Kaspar T C, Heald S M, Wang C M, Johnson C A, Whitaker K M, Gamelin D R, Chambers S A 2009 Phys. Rev. B 79 155203
[2] Shen Y B, Zhou X, Xu M, Ding Y C, Duan M Y, Linghu R F, Zhu W J 2007 Acta Phys. Sin. 56 3440 (in Chinese) [沈 益、 周 勋、 徐 明、 丁迎春、 段满益、 令狐荣锋、 祝文军 2007 物理学报 56 3440]
[3] Chikoidze E, Dumont Y, Von Bardeleben H J, Gleize J, Jomard F, Rzepka E, Berrerar G, Ferrand D, Gorochov O 2007 Appl. Phys. A 88 167
[4] McCarty A D, Hassan A K, Brunel L C, Dziatkowski K, Furdyna J K 2005 Phys. Rev. Lett. 95 157201
[5] Yang Z Y 2009 Chin. Phys. B 18 1253
[6] Yang L, Yin C H, Jiao Y, Zhang L, Song N, Ru R P 2006 Acta Phys. Sin. 55 1991 (in Chinese) [杨 柳、 殷春浩、 焦 扬、 张 雷、 宋 宁、 茹瑞鹏 2006 物理学报 55 1991]
[7] Rudowicz C, Gnutek P 2009 Physica B 404 3582
[8] Yang Z Y , Hao Y 2005 Acta Phys. Sin. 54 2883 (in Chinese)[杨子元、 郝 跃 2005 物理学报 54 2883]
[9] Yang Z Y 2010 Spectrochimica Acta Part A 75 277
[10] Qi L, Kuang X Y, Chai R P, Duan M L, Zhang C X 2009 Chin. Phys. B 18 1586
[11] Lu H P, Yin C H, Wei X S, Niu Y X, Song N, Ru R P 2007 Acta Phys. Sin. 56 6608 (in Chinese) [吕海萍、 殷春浩、 魏雪松、 钮应喜、 宋 宁、 茹瑞鹏 2007 物理学报 56 6608]
[12] Blume M, Orbach R 1962 Phys. Rev. 127 1587
[13] Macfarlane R M 1967 J. Chem. Phys. 47 2066
[14] Yu W L, Wang J Z 1993 Phys. Stat. Sol. 176 433
[15] Febbraro S 1987 J. Phys. C 20 5367
[16] Wang J Z, Yu W L, Fang K 1991 Phys. Rev. B 43 2575
[17] Barnes J A, Carroll B L, Flores L M, Hedges R M 1970 Atomic Data 2 1
[18] Blume M, Watson R E 1963 Proc. Roy. Soc. (London)A 271 565
[19] Blume M, Watson R E 1962 Proc. Roy. Soc. (London)A 270 127
[20] Marvin H H 1947 Phys. Rev. 71 102
[21] Yang Z Y 2007 J. Lum. 126 753
[22] Bramley R, Strach S J 1983 Chem. Rev. 83 49
[23] Abragam A, Bleaney B 1970 Electron Paramagnetic Resonance of Transition Ions (Clarendon Press, Oxford 1986; Dover, New York)
[24] Rudowicz C and Misra S K 2001 Appl. Spectr. Rev. 36 11
[25] Gnutek P, Yang Z Y, Rudowicz C 2009 J. Phys.: Condens. Matter 21 455402
[26] Lee S, Brodbeck C M, Yang C C 1977 Phys. Rev. B15 2469
[27] Diaconu M, Schmidt H, Pppl A, Bttcher R, Hoentsch J, Klunker A, Spemann D, Hochmuth H, Lorenz M and Grundmann M 2005 Phys. Rev. B 72 085214
[28] Yang Z Y, Hao Y, Rudowicz C, Yeung Y Y 2004 J. Phys.: Condens. Matter 16 3481
[29] Rudowicz C, Yang Z Y, Yeung Y Y, Qin J 2003 J. Chem. Phys. Solids 64 1419
[30] Yeung Y Y, Rudowicz C 1992 Computers Chem. 16 207
[31] Yeung Y Y, Rudowicz C 1993 J. Computational Phys. 109 150
[32] Wybourne B G 1965 Spectroscopic Properties of Rare Earths, John Wiley & Sons, Inc. New York
[33] Powell M J D, Gabriel J R, Johnston D F 1960 Phys. Rev. Lett. 5 145
[34] Fraga S, Karwowski J, Saxena K M S 1976 Handbook of Atomic Data, Elsevier, Amsterdam
[35] Yu W L and Wang J Z 1992 Chinese Science Bulletin 37 1840 (in Chinese)[余万伦、王俊忠1992 科学通报 37 1840]
[36] Zhao M G, Chin M 1995 Phys. Rev. B 52 10043
[37] Lei Y 2001 Mater. Science and Engineer. B 86 206
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[1] Droubay T C, Keavney D J, Kaspar T C, Heald S M, Wang C M, Johnson C A, Whitaker K M, Gamelin D R, Chambers S A 2009 Phys. Rev. B 79 155203
[2] Shen Y B, Zhou X, Xu M, Ding Y C, Duan M Y, Linghu R F, Zhu W J 2007 Acta Phys. Sin. 56 3440 (in Chinese) [沈 益、 周 勋、 徐 明、 丁迎春、 段满益、 令狐荣锋、 祝文军 2007 物理学报 56 3440]
[3] Chikoidze E, Dumont Y, Von Bardeleben H J, Gleize J, Jomard F, Rzepka E, Berrerar G, Ferrand D, Gorochov O 2007 Appl. Phys. A 88 167
[4] McCarty A D, Hassan A K, Brunel L C, Dziatkowski K, Furdyna J K 2005 Phys. Rev. Lett. 95 157201
[5] Yang Z Y 2009 Chin. Phys. B 18 1253
[6] Yang L, Yin C H, Jiao Y, Zhang L, Song N, Ru R P 2006 Acta Phys. Sin. 55 1991 (in Chinese) [杨 柳、 殷春浩、 焦 扬、 张 雷、 宋 宁、 茹瑞鹏 2006 物理学报 55 1991]
[7] Rudowicz C, Gnutek P 2009 Physica B 404 3582
[8] Yang Z Y , Hao Y 2005 Acta Phys. Sin. 54 2883 (in Chinese)[杨子元、 郝 跃 2005 物理学报 54 2883]
[9] Yang Z Y 2010 Spectrochimica Acta Part A 75 277
[10] Qi L, Kuang X Y, Chai R P, Duan M L, Zhang C X 2009 Chin. Phys. B 18 1586
[11] Lu H P, Yin C H, Wei X S, Niu Y X, Song N, Ru R P 2007 Acta Phys. Sin. 56 6608 (in Chinese) [吕海萍、 殷春浩、 魏雪松、 钮应喜、 宋 宁、 茹瑞鹏 2007 物理学报 56 6608]
[12] Blume M, Orbach R 1962 Phys. Rev. 127 1587
[13] Macfarlane R M 1967 J. Chem. Phys. 47 2066
[14] Yu W L, Wang J Z 1993 Phys. Stat. Sol. 176 433
[15] Febbraro S 1987 J. Phys. C 20 5367
[16] Wang J Z, Yu W L, Fang K 1991 Phys. Rev. B 43 2575
[17] Barnes J A, Carroll B L, Flores L M, Hedges R M 1970 Atomic Data 2 1
[18] Blume M, Watson R E 1963 Proc. Roy. Soc. (London)A 271 565
[19] Blume M, Watson R E 1962 Proc. Roy. Soc. (London)A 270 127
[20] Marvin H H 1947 Phys. Rev. 71 102
[21] Yang Z Y 2007 J. Lum. 126 753
[22] Bramley R, Strach S J 1983 Chem. Rev. 83 49
[23] Abragam A, Bleaney B 1970 Electron Paramagnetic Resonance of Transition Ions (Clarendon Press, Oxford 1986; Dover, New York)
[24] Rudowicz C and Misra S K 2001 Appl. Spectr. Rev. 36 11
[25] Gnutek P, Yang Z Y, Rudowicz C 2009 J. Phys.: Condens. Matter 21 455402
[26] Lee S, Brodbeck C M, Yang C C 1977 Phys. Rev. B15 2469
[27] Diaconu M, Schmidt H, Pppl A, Bttcher R, Hoentsch J, Klunker A, Spemann D, Hochmuth H, Lorenz M and Grundmann M 2005 Phys. Rev. B 72 085214
[28] Yang Z Y, Hao Y, Rudowicz C, Yeung Y Y 2004 J. Phys.: Condens. Matter 16 3481
[29] Rudowicz C, Yang Z Y, Yeung Y Y, Qin J 2003 J. Chem. Phys. Solids 64 1419
[30] Yeung Y Y, Rudowicz C 1992 Computers Chem. 16 207
[31] Yeung Y Y, Rudowicz C 1993 J. Computational Phys. 109 150
[32] Wybourne B G 1965 Spectroscopic Properties of Rare Earths, John Wiley & Sons, Inc. New York
[33] Powell M J D, Gabriel J R, Johnston D F 1960 Phys. Rev. Lett. 5 145
[34] Fraga S, Karwowski J, Saxena K M S 1976 Handbook of Atomic Data, Elsevier, Amsterdam
[35] Yu W L and Wang J Z 1992 Chinese Science Bulletin 37 1840 (in Chinese)[余万伦、王俊忠1992 科学通报 37 1840]
[36] Zhao M G, Chin M 1995 Phys. Rev. B 52 10043
[37] Lei Y 2001 Mater. Science and Engineer. B 86 206
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