Unrestricted Dirac-Fock theory: Relativistic determination of core polarization hyperfine interactions

J. P. Desclaux; A. J. Freeman; J. V. Mallow

doi:10.1016/0304-8853(77)90138-X

Unrestricted Dirac-Fock theory: Relativistic determination of core polarization hyperfine interactions

J. P. Desclaux^*, A. J. Freeman, J. V. Mallow

^*Corresponding author for this work

Physics and Astronomy

Research output: Contribution to journal › Article › peer-review

15 Scopus citations

Abstract

The unrestricted Dirac-Fock (UDF) method is developed for determining relativistic contributions to the hyperfine interaction, notably that due to core polarization. Radial core-polarization of the one-electron (jj-coupled) spin orbitals is obtained by relaxing the restraint in restricted Dirac-Fock (RDF) theory that the radial part be independent of the magnetic quantum number, the projection m_j of j. Relativistic effects on the core polarization are obtained by comparison with results obtained from the non-relativistic spin polarized Hartree-Fock (m_s unrestricted) and spin plus orbital polarized Hartree- Fock (m_s plus m_j unrestricted) calculations. For the 5d transition series ions, the relativistic core polarization enhancement factor, S_s(z), is determined to be about a factor of two and so is much smaller than the isomer shift charge density enhancement factor (≈6) found earlier for these same ions. Comparison is made with limited experimental data available to date; for the case of atomic Re, excellent agreement is obtained with experiment.

Original language	English (US)
Pages (from-to)	265-276
Number of pages	12
Journal	Journal of Magnetism and Magnetic Materials
Volume	5
Issue number	4
DOIs	https://doi.org/10.1016/0304-8853(77)90138-X
State	Published - 1977

Funding

We are grateful to B.D. Dunlap, D.E. Ellis, J.A. McMillan, and G. Shenoy for discussions. One of us (AJF) is grateful to his scientific collaborators at the Hebrew University, Israel (E.R. Bauminger, S.G. Cohen, I. No~,ik, and S. Ofer) for their close cooperation, which was supported by the U.S.-lsrael Binational Science Foundation. One of us (AIF) is grateful to L.J. Vamerin for handling the editorial aspects of this manuscript, including the anonymous refereeing~ provide important information about magnetic interactions in a wide variety of magnetic and other materials,O n the theoreticals ide, the unrestricted Hartree-Fock method \I[ \],i n its various formulations, has had a great number of significant successes in explaining the origin of a large hyperfine field observed at the n.-clei of magnetic materials, by NMR, MOssbauer, electron paramagnetic resonance (EPR) and other methods. In particular, the spin polarized Hartree-Fock (SPHF) Supported by the National Science Foundation and the U.S. Energy Research and Development Administration.

ASJC Scopus subject areas

Electronic, Optical and Magnetic Materials
Condensed Matter Physics

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10.1016/0304-8853(77)90138-X

Cite this

@article{ed8f56669e904977b00b8985c39dee82,

title = "Unrestricted Dirac-Fock theory: Relativistic determination of core polarization hyperfine interactions",

abstract = "The unrestricted Dirac-Fock (UDF) method is developed for determining relativistic contributions to the hyperfine interaction, notably that due to core polarization. Radial core-polarization of the one-electron (jj-coupled) spin orbitals is obtained by relaxing the restraint in restricted Dirac-Fock (RDF) theory that the radial part be independent of the magnetic quantum number, the projection mj of j. Relativistic effects on the core polarization are obtained by comparison with results obtained from the non-relativistic spin polarized Hartree-Fock (ms unrestricted) and spin plus orbital polarized Hartree- Fock (ms plus mj unrestricted) calculations. For the 5d transition series ions, the relativistic core polarization enhancement factor, Ss(z), is determined to be about a factor of two and so is much smaller than the isomer shift charge density enhancement factor (≈6) found earlier for these same ions. Comparison is made with limited experimental data available to date; for the case of atomic Re, excellent agreement is obtained with experiment.",

author = "Desclaux, \{J. P.\} and Freeman, \{A. J.\} and Mallow, \{J. V.\}",

note = "Funding Information: We are grateful to B.D. Dunlap, D.E. Ellis, J.A. McMillan, and G. Shenoy for discussions. One of us (AJF) is grateful to his scientific collaborators at the Hebrew University, Israel (E.R. Bauminger, S.G. Cohen, I. No\textasciitilde{},ik, and S. Ofer) for their close cooperation, which was supported by the U.S.-lsrael Binational Science Foundation. One of us (AIF) is grateful to L.J. Vamerin for handling the editorial aspects of this manuscript, including the anonymous refereeing\textasciitilde{} Funding Information: provide important information about magnetic interactions in a wide variety of magnetic and other materials,O n the theoreticals ide, the unrestricted Hartree-Fock method \textbackslash{}I[ \textbackslash{}],i n its various formulations, has had a great number of significant successes in explaining the origin of a large hyperfine field observed at the n.-clei of magnetic materials, by NMR, MOssbauer, electron paramagnetic resonance (EPR) and other methods. In particular, the spin polarized Hartree-Fock (SPHF) Supported by the National Science Foundation and the U.S. Energy Research and Development Administration. Copyright: Copyright 2018 Elsevier B.V., All rights reserved.",

year = "1977",

doi = "10.1016/0304-8853(77)90138-X",

language = "English (US)",

volume = "5",

pages = "265--276",

journal = "Journal of Magnetism and Magnetic Materials",

issn = "0304-8853",

publisher = "Elsevier B.V.",

number = "4",

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T1 - Unrestricted Dirac-Fock theory

T2 - Relativistic determination of core polarization hyperfine interactions

AU - Desclaux, J. P.

AU - Freeman, A. J.

AU - Mallow, J. V.

N1 - Funding Information: We are grateful to B.D. Dunlap, D.E. Ellis, J.A. McMillan, and G. Shenoy for discussions. One of us (AJF) is grateful to his scientific collaborators at the Hebrew University, Israel (E.R. Bauminger, S.G. Cohen, I. No~,ik, and S. Ofer) for their close cooperation, which was supported by the U.S.-lsrael Binational Science Foundation. One of us (AIF) is grateful to L.J. Vamerin for handling the editorial aspects of this manuscript, including the anonymous refereeing~ Funding Information: provide important information about magnetic interactions in a wide variety of magnetic and other materials,O n the theoreticals ide, the unrestricted Hartree-Fock method \I[ \],i n its various formulations, has had a great number of significant successes in explaining the origin of a large hyperfine field observed at the n.-clei of magnetic materials, by NMR, MOssbauer, electron paramagnetic resonance (EPR) and other methods. In particular, the spin polarized Hartree-Fock (SPHF) Supported by the National Science Foundation and the U.S. Energy Research and Development Administration. Copyright: Copyright 2018 Elsevier B.V., All rights reserved.

PY - 1977

Y1 - 1977

N2 - The unrestricted Dirac-Fock (UDF) method is developed for determining relativistic contributions to the hyperfine interaction, notably that due to core polarization. Radial core-polarization of the one-electron (jj-coupled) spin orbitals is obtained by relaxing the restraint in restricted Dirac-Fock (RDF) theory that the radial part be independent of the magnetic quantum number, the projection mj of j. Relativistic effects on the core polarization are obtained by comparison with results obtained from the non-relativistic spin polarized Hartree-Fock (ms unrestricted) and spin plus orbital polarized Hartree- Fock (ms plus mj unrestricted) calculations. For the 5d transition series ions, the relativistic core polarization enhancement factor, Ss(z), is determined to be about a factor of two and so is much smaller than the isomer shift charge density enhancement factor (≈6) found earlier for these same ions. Comparison is made with limited experimental data available to date; for the case of atomic Re, excellent agreement is obtained with experiment.

AB - The unrestricted Dirac-Fock (UDF) method is developed for determining relativistic contributions to the hyperfine interaction, notably that due to core polarization. Radial core-polarization of the one-electron (jj-coupled) spin orbitals is obtained by relaxing the restraint in restricted Dirac-Fock (RDF) theory that the radial part be independent of the magnetic quantum number, the projection mj of j. Relativistic effects on the core polarization are obtained by comparison with results obtained from the non-relativistic spin polarized Hartree-Fock (ms unrestricted) and spin plus orbital polarized Hartree- Fock (ms plus mj unrestricted) calculations. For the 5d transition series ions, the relativistic core polarization enhancement factor, Ss(z), is determined to be about a factor of two and so is much smaller than the isomer shift charge density enhancement factor (≈6) found earlier for these same ions. Comparison is made with limited experimental data available to date; for the case of atomic Re, excellent agreement is obtained with experiment.

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DO - 10.1016/0304-8853(77)90138-X

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VL - 5

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JO - Journal of Magnetism and Magnetic Materials

JF - Journal of Magnetism and Magnetic Materials

IS - 4

ER -

Unrestricted Dirac-Fock theory: Relativistic determination of core polarization hyperfine interactions

Abstract

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