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Physics of Magnetism Magnetic Materials 2011 Part 4

Tham khảo tài liệu 'physics of magnetism magnetic materials 2011 part 4', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | 48 CHAPTER 5. CRYSTAL FIELDS m AE I 5 2 10 2J 1 x V I 3 2 -2 eg -------l 1 2 -8 B Figure 5.2.2. Effect of the electrostatic perturbation due to crystal fields on the 2 J l -fold degenerate groundstate level for J J. Until now we have used the 4f wave functions corresponding to the I J Jz representation to calculate the perturbing influence of the crystal field by means of the Hamiltonian given in Eq. 5.2.7 . This means that we have tacitly assumed thatthe crystal-field interaction is small compared to the spin-orbit interaction introduced via the Russell-Saunders coupling and Hund s rules and that J and m are good quantum numbers. Before applying this crystalfield Hamiltonian to 3d wave functions we will first briefly review the relative magnitude of the energies involved in the formation of the electronic states. In the survey given below we have listed the order of magnitude of the crystal-field splitting relative to the energies involved with the Coulomb interaction between electrons as measured by the energy difference between terms and the LS coupling in various groups of materials comprising materials based on rare earths R and actinides A . The numbers listed are given per centimeter. Group Shell Term energy LS coupling Crystal-field splitting Fe 3d 105 10 103 Pd Pt 4d 5d 104 102 104 R A 4f 5f 105 103 102 These energy values may be compared with the magnetic energy of a magnetic moment p in a magnetic field B Em -pa- using typical values for p lpB and B 1T one finds with PB 0.9274X 10 23 Am2 0.9274 X 10-23 J T a magnetic energy equal in absolute value to 9.274 X 10 23 J or 4.670 cm1. This then leads to the following sequences in energies For Fe-group materials crystal field LS coupling applied magnetic field For rare-earth-based materials LS coupling crystal field applied magnetic field. The physical reason for this difference in behavior is the following The 3d-electron-charge clouds reside more at the outside of the ions than the 4f-electron-charge clouds.