--- title: "Analytical Results for Crystalline Electric Field Eigenvalues of Trivalent Rare-Earth Ions Using Computer Algebra: Application to the Magnetism of PrX2 (X = Mg, Al, Ru, Rh, Pt) • CBPF Index" description: "CBPF INDEX is the system that tracks the scientific and technological output of CBPF. It lists the articles, books, technical reports and other publications of the whole CBPF community." canonical_url: "https://index.cbpf.br/en/publicacoes/6ad2a767639f62b11adbb5be" locale: en meta: "og:description": "CBPF INDEX is the system that tracks the scientific and technological output of CBPF. It lists the articles, books, technical reports and other publications of the whole CBPF community." "og:image": "https://index.cbpf.br/_og/d/c_Item%2Ctitulo_~QW5hbHl0aWNhbCBSZXN1bHRzIGZvciBDcnlzdGFsbGluZSBFbGVjdHJpYyBGaWVsZCBFaWdlbnZhbHVlcyBvZiBUcml2YWxlbnQgUmFyZS1FYXJ0aCBJb25zIFVzaW5nIENvbXB1dGVyIEFsZ2VicmE6IEFwcGxpY2F0aW9uIHRvIHRoZSBNYWduZXRpc20gb2YgPG1hdGg-UHJYMjwvbWF0aD4gPG1hdGg-KFggPSBNZywgQWwsIFJ1LCBSaCwgUHQpIDwvbWF0aD4%2Ctipo_Physics%2BNote%2Ccor_~I2E4MmMwMA%2Cautores_~Ui4gUi4gU29icmFsOyBBLiBQLiBHdWltYXLDo2VzOyBYLiBBLiBTaWx2YQ%2Cdetalhe_1994%2Csecao_Publications%2Cp_Ii9lbi9wdWJsaWNhY29lcy82YWQyYTc2NzYzOWY2MmIxMWFkYmI1YmUi%2Cs_IbkzXRHow_XPKuYG.png" "og:image:height": "600" "og:image:type": image/png "og:image:width": "1200" "og:title": "Analytical Results for Crystalline Electric Field Eigenvalues of Trivalent Rare-Earth Ions Using Computer Algebra: Application to the Magnetism of PrX2 (X = Mg, Al, Ru, Rh, Pt) • CBPF Index" "twitter:image": "https://index.cbpf.br/_og/d/c_Item%2Ctitulo_~QW5hbHl0aWNhbCBSZXN1bHRzIGZvciBDcnlzdGFsbGluZSBFbGVjdHJpYyBGaWVsZCBFaWdlbnZhbHVlcyBvZiBUcml2YWxlbnQgUmFyZS1FYXJ0aCBJb25zIFVzaW5nIENvbXB1dGVyIEFsZ2VicmE6IEFwcGxpY2F0aW9uIHRvIHRoZSBNYWduZXRpc20gb2YgPG1hdGg-UHJYMjwvbWF0aD4gPG1hdGg-KFggPSBNZywgQWwsIFJ1LCBSaCwgUHQpIDwvbWF0aD4%2Ctipo_Physics%2BNote%2Ccor_~I2E4MmMwMA%2Cautores_~Ui4gUi4gU29icmFsOyBBLiBQLiBHdWltYXLDo2VzOyBYLiBBLiBTaWx2YQ%2Cdetalhe_1994%2Csecao_Publications%2Cp_Ii9lbi9wdWJsaWNhY29lcy82YWQyYTc2NzYzOWY2MmIxMWFkYmI1YmUi%2Cs_IbkzXRHow_XPKuYG.png" --- > Index of every page on this site: [llms.txt](https://index.cbpf.br/llms.txt) **Physics Note****Published** # **Analytical Results for Crystalline Electric Field Eigenvalues of Trivalent Rare-Earth Ions Using Computer Algebra: Application to the Magnetism of **PrX2\PrX\_2\PrX2​** **(X=Mg,Al,Ru,Rh,Pt)\(X = Mg, Al, Ru, Rh, Pt) \(X=Mg,Al,Ru,Rh,Pt) **R. R. Sobral; A. P. Guimarães; X. A. Silva** 1994 [**Download PDF **0.1 MB](https://index.cbpf.br/files/publicacao/6ad2a767639f62b11adbb5be/pdf) [**Contact owner**]() ## **Publication details**
Authors
R. R. Sobral; A. P. Guimarães; X. A. Silva
Type
Physics Note
Status
Published
Publication date
1994
Description
The eigenvalues of the Crystalline Electric Field (CEF) Hamiltonian with cubic symmetry are analytically obtained for trivalent rare-earth ions of ground state <math>J = 5/2, 7/2, 4, 9/2, 6, 15/2\,\!</math> and <math>8\,\!</math>, via a Computer Algebra approach. In the presence of both CEF and an effective exchange field, Computer Algebra still allows a partial factorization of the characteristic polynomial equation associated to the total Hamiltonian, a result of interest to the study of the magnetic behavior of rare-earth intermetallics. An application to the <math>PrX_2\,\!</math> intermetallic compounds <math>(X = Mg, Al, Ru, Rh, Pt)\,\!</math> is reported.
Year
1994
Number
CBPF-NF-015/94
Linked to a thesis
No
Linked to a grant
No
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