Spin-polarized energy-band structure, conduction-electron polarization, spin densities, and the neutron magnetic form factor of ferromagnetic gadolinium

B. N. Harmon, A. J. Freeman

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231 Citations (Scopus)

Abstract

Conduction-electron polarization, spin densities, and neutron magnetic scattering in ferromagnetic Gd metal were studied using the spin-polarized augmented-plane-wave (APW) method in a warped-muffin-tin-potential formulation. The spin-up and spin-down bands were found to be very similar in shape to the bands from a paramagnetic calculation, with the exchange splitting proportional to the amount of d character in the bands. It was also found that the conduction-electron spin density determined from the APW wave functions is of mostly d character. This dominance of the d-like wave functions for the spin-dependent interactions is explained by (i) the much greater overlap of the 4f states with the d-like wave functions as compared to the s-p wave functions; (ii) the nearly complete d character of the bands in the region of the Fermi surface. The magnetic form factor was calculated from the conduction-electron spin density and compared with the recent neutron magnetic - form - factor measurement of Moon, Koehler, Cable, and Child. The calculated spin density was found to have the same shape as the "diffuse" density derived by Moon et al. (including a negative but much smaller in magnitude spin density at the c site in the unit cell). After the inclusion of core - polarization effects we conclude that large nonspherical contributions with Y33-Y3-3, and Y40 angular dependence are needed to explain the experimental results.

Original languageEnglish
Pages (from-to)1979-1993
Number of pages15
JournalPhysical Review B
Volume10
Issue number5
DOIs
Publication statusPublished - 1974

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Spin polarization
Gadolinium
gadolinium
Wave functions
conduction electrons
Band structure
energy bands
form factors
Neutrons
neutrons
Electrons
polarization
wave functions
Ferromagnetic materials
Fermi surface
Tin
Moon
electron spin
plane waves
Cables

ASJC Scopus subject areas

  • Condensed Matter Physics

Cite this

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title = "Spin-polarized energy-band structure, conduction-electron polarization, spin densities, and the neutron magnetic form factor of ferromagnetic gadolinium",
abstract = "Conduction-electron polarization, spin densities, and neutron magnetic scattering in ferromagnetic Gd metal were studied using the spin-polarized augmented-plane-wave (APW) method in a warped-muffin-tin-potential formulation. The spin-up and spin-down bands were found to be very similar in shape to the bands from a paramagnetic calculation, with the exchange splitting proportional to the amount of d character in the bands. It was also found that the conduction-electron spin density determined from the APW wave functions is of mostly d character. This dominance of the d-like wave functions for the spin-dependent interactions is explained by (i) the much greater overlap of the 4f states with the d-like wave functions as compared to the s-p wave functions; (ii) the nearly complete d character of the bands in the region of the Fermi surface. The magnetic form factor was calculated from the conduction-electron spin density and compared with the recent neutron magnetic - form - factor measurement of Moon, Koehler, Cable, and Child. The calculated spin density was found to have the same shape as the {"}diffuse{"} density derived by Moon et al. (including a negative but much smaller in magnitude spin density at the c site in the unit cell). After the inclusion of core - polarization effects we conclude that large nonspherical contributions with Y33-Y3-3, and Y40 angular dependence are needed to explain the experimental results.",
author = "Harmon, {B. N.} and Freeman, {A. J.}",
year = "1974",
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T1 - Spin-polarized energy-band structure, conduction-electron polarization, spin densities, and the neutron magnetic form factor of ferromagnetic gadolinium

AU - Harmon, B. N.

AU - Freeman, A. J.

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N2 - Conduction-electron polarization, spin densities, and neutron magnetic scattering in ferromagnetic Gd metal were studied using the spin-polarized augmented-plane-wave (APW) method in a warped-muffin-tin-potential formulation. The spin-up and spin-down bands were found to be very similar in shape to the bands from a paramagnetic calculation, with the exchange splitting proportional to the amount of d character in the bands. It was also found that the conduction-electron spin density determined from the APW wave functions is of mostly d character. This dominance of the d-like wave functions for the spin-dependent interactions is explained by (i) the much greater overlap of the 4f states with the d-like wave functions as compared to the s-p wave functions; (ii) the nearly complete d character of the bands in the region of the Fermi surface. The magnetic form factor was calculated from the conduction-electron spin density and compared with the recent neutron magnetic - form - factor measurement of Moon, Koehler, Cable, and Child. The calculated spin density was found to have the same shape as the "diffuse" density derived by Moon et al. (including a negative but much smaller in magnitude spin density at the c site in the unit cell). After the inclusion of core - polarization effects we conclude that large nonspherical contributions with Y33-Y3-3, and Y40 angular dependence are needed to explain the experimental results.

AB - Conduction-electron polarization, spin densities, and neutron magnetic scattering in ferromagnetic Gd metal were studied using the spin-polarized augmented-plane-wave (APW) method in a warped-muffin-tin-potential formulation. The spin-up and spin-down bands were found to be very similar in shape to the bands from a paramagnetic calculation, with the exchange splitting proportional to the amount of d character in the bands. It was also found that the conduction-electron spin density determined from the APW wave functions is of mostly d character. This dominance of the d-like wave functions for the spin-dependent interactions is explained by (i) the much greater overlap of the 4f states with the d-like wave functions as compared to the s-p wave functions; (ii) the nearly complete d character of the bands in the region of the Fermi surface. The magnetic form factor was calculated from the conduction-electron spin density and compared with the recent neutron magnetic - form - factor measurement of Moon, Koehler, Cable, and Child. The calculated spin density was found to have the same shape as the "diffuse" density derived by Moon et al. (including a negative but much smaller in magnitude spin density at the c site in the unit cell). After the inclusion of core - polarization effects we conclude that large nonspherical contributions with Y33-Y3-3, and Y40 angular dependence are needed to explain the experimental results.

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