Nota de FísicaPublicado
Analytical Expressions for Crystal Fields of Hexagonal Symmetry: High Temperature Magnetic Susceptibility Applications
R. R. Sobral; A. P. Guimarães; X. A. Silva
1996
Datos de la publicación
- Autores
- R. R. Sobral; A. P. Guimarães; X. A. Silva
- Tipo
- Nota de Física
- Estado
- Publicado
- Fecha de publicación
- 1996
- Descripción
- Crystal Field (CF) Theory is a standard tool for analyzing thermal, spectroscopic, magnetic and related properties in solids containing transition ions. In the case of rare earth ions, the CF eigenvalues were the object of a systematic study for cubic and hexagonal symmetry; the results were computed numerically and displayed in table or graphic form. This paper discusses the use of Computer Algebra (CA) to obtain analytical results of interest for the studies of magnetic behavior of rare-earth intermetallic compounds, where the CF has hexagonal symmetry. In the first part, CA techniques are applied to obtain the characteristic polynomials of the CF hamiltonian. A remarkable result is that for most J's the characteristic polynomials are entirely factored, allowing the analytical derivation of the eigenvalues as a function of the CF parameters. A comparison with the values obtained numerically is made for two cases, showing, as expected, excellent agreement. In the second part, a model hamiltonian containing the CF term and exchange is used, and an expression for the high temperature susceptibility (HTS), suitable for algebraic computation is derived. We compute the HTS expressions using results of the first part plus the partially factored polynomials of the model hamiltonian. In the molecular field approximation, we re-obtain results of the literature for HTS in the parallel and perpendicular directions. This treatment may be extended to other high anisotropy systems, both hexagonal and rhombohedral, as the nitrided <math>R_{2}Fe_{17}\,\!</math> intermetallic compounds.
- Año
- 1996
- Número
- CBPF-NF-054/96
- Vínculo con tesis
- No
- Vínculo con beca
- No