Noether's theorem and conserved quantities for the crystal- and ligand-field Hamiltonians invariant under continuous rotational symmetry

Physical Review B - Condensed Matter and Materials Physics

Volumn 67, Issue 17, 2003, Pages 1744201-17442014

  Rudowicz, C ^a   Qin, J ^a  

^a CITY UNIVERSITY OF HONG KONG   (Hong Kong)

Author keywords

[No Author keywords available]

Indexed keywords

LIGAND;

ARTICLE; CALCULATION; CRYSTAL; GEOMETRY; MATHEMATICAL ANALYSIS; MATHEMATICS; PARAMETER; ROTATION; THEORY;

EID: 0037899507     PISSN: 01631829     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (82)

1. A. Zee, Fearful Symmetry - The Search for Beauty in Modern Physics (Princeton University, Princeton, NJ, 1999).
2. C. T. Hill and L. M. Lederman, Teaching Symmetry in the Introductory Physics Curriculum, website http://www.emmynoether.com/ Retrieved 22 May 2001.
3. W. J. Thompson, Angular Momentum - An Illustrated Guide to Rotational Symmetries for Physical Systems (Wiley, New York, 1994).
4. W. Greiner and G. Müller, Quantum Mechanics Symmetries (Springer, Berlin, 1994).
5. Encyclopaedia of Mathematics, edited by M. Vinogradov (Kluwer Academic, Dordrecht, 1990), Vol. 6.
6. Z. P. Li, Z. Phys. C 76, 181 (1997).
7. Z. P. Li and C. Yang, J. Phys. A 28, 5931 (1995).
8. Z. P. Li, J. Phys. A 24, 4261 (1991).
9. O. Castaños, A. Frank, and R. Lopez-Peña, J. Phys. A 23, 5141 (1990).
10. R. S. Kaushal, D. Parashar, Shalini Gupta, and S. C. Mishra, Ann. Phys. 259, 233 (1997).
11. B. G. Wybourne, Spectroscopic Properties of Rare Earth (Wiley, New York, 1965).
12. S. Altshuler and B. M. Kozyrev, Electron Paramagnetic Resonance in Compounds of Transition Elements (Wiley, New York, 1974).
13. A. Abragam and B. Bleaney, Electron Paramagnetic Resonance of Transition Ions (Clarendon, Oxford, 1970).
14. C. A. Morrison and R. P. Leavitt, Handbook on the Physics and Chemistry of Rare Earth, edited by K. A. Gschneidner, Jr. and L. Eyring (North-Holland, Amsterdam, 1982), Vol. 5.
15. C. A. Morrison, Crystal Field for Transition-Metal Ions in Laser Host Materials (Springer, Berlin, 1992).
16. Crystal Field Handbook, edited by D. J. Newman and B. Ng (Cambridge University, Cambridge, England, 2000).
17. J. Mulak and Z. Gajek, The Effective Crystal Field Potential (Elsevier, Amsterdam, 2000).
18. B. Henderson and R. H. Bartram, Crystal-Field Engineering of Solid-State Laser Materials (Cambridge University, Cambridge, England, 2000).
19. B. N. Figgis and M. A. Hitchman, Ligand Field Theory and its Applications (Wiley, New York, 2000).
20. C. Rudowicz, Chem. Phys. 97, 43 (1985).
21. C. Rudowicz, Chem. Phys. 102, 437 (1986).
22. C. Rudowicz, J. Chem. Phys. 84, 5045 (1986).
23. A. B. Roitsin, Phys. Status Solidi B 104, 11 (1981).
24. C. Rudowicz, in Crystal Field Handbook (Ref. 16), p. 259.
25. C. Rudowicz and J. Qin, Phys. Rev. B (to be published).
26. N. Karayanis, C. A. Morrison, and D. E. Wortman, J. Chem. Phys. 64, 3890 (1976).
27. F. Auzel, Mater. Res. Bull. 14, 223 (1979).
28. R. P. Leavitt, J. Chem. Phys. 77, 1661 (1982).
29. A. K. Przhevuskii, Opt. Spectrosc. 53, 414 (1982).
30. A. K. Przhevuskii, Opt. Spectrosc. 53, 499 (1982).
31. M. Kibler, Phys. Lett. A 98, 343 (1983).
32. F. Auzel and O. Malta, J. Phys. A 44, 210 (1983).
33. C. Rudowicz, Magn. Reson. Rev. 13, 1 (1987); 13, 335(E) (1988).
34. C. Rudowicz, Magn. Reson. Rev. 13, 1 (1987); 13, 335(E) (1988).
35. C. Rudowicz and S. K. Misra, Appl. Spectrosc. Rev. 36, 11 (2001).
36. G. Bacquet, J. Dugas, C. Escribe, J. M. Gaite, and J. Michoulier, J. Phys. C 7, 1551 (1974).
37. C. Rudowicz, J. Phys. C 18, 1415 (1985); 18, 3837(E) (1985).
38. C. Rudowicz, J. Phys. C 18, 1415 (1985); 18, 3837(E) (1985).
39. S. W. Ahn, S. H. Choh, and C. Rudowicz, Appl. Magn. Reson. 12, 351 (1997).
40. C. Rudowicz, in Proceedings of the International Conference Spectroscopy, X-Ray, and Crystal Chemistry of Minerals, Kazan, Russia, edited by A. I. Bahtin (Kazan University, Kazan, 1998), p. 31-41.
41. C. Rudowicz, S. B. Madhu, and I. Akhmadoulline, Appl. Magn. Reson. 16, 447 (1999).
42. Y.Y. Yeung and D. J. Newman, J. Chem. Phys. 82, 3747 (1985).
43. Y.Y. Yeung and D. J. Newman, J. Chem. Phys. 84, 4470 (1986).
44. M. C. F. Cunha, H. F. Brito, L. B. Zinner, and G. Vicentini, Coord. Chem. Rev. 119, 1 (1992).
45. J. B. Gruber, M. D. Seltzer, V. J. Pugh, and F. S. Richardson, J. Appl. Phys. 77, 5882 (1995).
46. D. E. Wortman and C. A. Morrison, Opt. Mater. 4, 487 (1995).
47. O. L. Malta, E. Antic-Fidancev, M. Lemaitre-Blaise, A. Milicic-Tang, and M. Taibi, J. Alloys Compd. 228, 41 (1995).
48. C. Görller-Walrand and K. Binnemans, in Handbook on the Physics and Chemistry of Rare Earths, edited by K. A. Gschneidner, Jr. and L. R. Eyring (Elsevier, New York, 1996), Vol. 23, p. 155.
49. A. L. Videira and L. D. Carlos, J. Chem. Phys. 105, 8878 (1996).
50. T. A. Hopkins, J. P. Bolender, D. H. Metcalf, and F. S. Richardson, Inorg. Chem. 35, 5347 (1996).
51. J. R. Quagliano, N. J. Cockroft, K. E. Gunde, and F. S. Richardson, J. Chem. Phys. 105, 9812 (1996).
52. T. A. Hopkins, D. H. Metcalf, and F. S. Richardson, Inorg. Chem. 37, 140 (1998).
53. Z. Gajek, J. Phys.: Condens. Matter 12, 415 (2000).
54. Y. Y. Yeung, in Crystal Field Handbook (Ref. 16), p. 160.
55. J. Karwowski, M. Bancewicz, O. N. Ventura, and G. F. H. Diercksen, J. Phys. A 26, 5581 (1993).
56. F. Rajadll, J. Planelles, and J. Karwowski, J. Phys. A 26, 3883 (1993).
57. J. Karwowski, F. Rajadll, J. Planelles, and V. Mas, At. Data Nucl. Data Tables 61, 177 (1995).
58. M. G. Clark, J. Chem. Phys. 54, 697 (1971).
59. C. Rudowicz and R. Bramley, J. Chem. Phys. 83, 5192 (1985).
60. B. Bihari, K. K. Sharma, and L. E. Erickson, J. Phys.: Condens. Matter 2, 5703 (1990).
61. J. Mulak and Z. Gajek, Pol. J. Chem. 67, 1489 (1993).
62. Y. M. Chang, T. H. Yeom, Y. Y. Yeung, and C. Rudowicz, J. Phys.: Condens. Matter 5, 6221 (1993).
63. J. Mulak, Pol. J. Chem. 67, 2053 (1993).
64. Z. Gajek, J. Mulak, and J. C. Krupa, J. Solid State Chem. 107, 413 (1993).
65. D. Bravo and F. J. Lopez, J. Chem. Phys. 99, 4952 (1993).
66. T. H. Yeom, S. H. Choh, Y. M. Chang, and C. Rudowicz, Phys. Status Solidi B 185, 417 (1994).
67. J. Qin, C. Rudowicz, Y. M. Chang, and Y. Y. Yeung, Phys. Chem. Miner. 21, 532 (1994).
68. J. Mulak, J. Solid State Chem. 115, 92 (1995).
69. D. Bravo, K. Polgar, and F. J. Lopez, Phys. Status Solidi B 103, 65 (1997).
70. J. E. Munoz-Santiuste, A. Lorenzo, L. E. Bausa, and J. García Solé, J. Phys.: Condens. Matter 10, 7653 (1998).
71. K. Das, D. Ghosh, and B. M. Wanklyn, J. Phys.: Condens. Matter 11, 1745 (1999).
72. C. Rudowicz, M. Chua, and F. Reid, Physica B 291, 327 (2000).
73. M. F. Reid, L. van Pieterson, R. T. Wegh, and A. Meijerink, Phys. Rev. B 62, 14 744 (2000).
74. V. Lavin, P. Babu, C. K. Jayasankar, I. R. Marti, and V. D. Rodriguez, J. Chem. Phys. 115, 10 935 (2001).
75. B. M. Flanagan, P. V. Bernhardt, E. R. Krausz, S. R. Lüthi, and M. J. Riley, Inorg. Chem. 41, 5024 (2002).
76. D. Åberg and S. Edvardsson, Phys. Rev. B 65, 045111 (2002).
77. C. Rudowicz and H. W. F. Sung, Physica B 300, 1 (2001).
78. R. Bramley and S. J. Strach, Chem. Rev. 83, 49 (1983).
79. R. Bramley, Int. Rev. Phys. Chem. 5, 211 (1986).
80. C. Rudowicz, I. Akhmadoulline, and S. B. Madhu, Manual for the Computer Package CST for Conversions, Standardization, and Transformations of the Spin Hamiltonian and the Crystal-field Hamiltonian, Research Report AP-97-12, Department of Physics and Materials Science, City University of Hong Kong, 1997.
81. C. Rudowicz and J. Qin, Comput. Chem. (Oxford) 26, 149 (2002).
82. C. Rudowicz and Y. Y. Zhou, J. Phys. Chem. Solids 60, 17 (1999).