Generalized Susceptibilities and Magnetic Properties of Some bcc Transition Metals

W. E. EVENSON; G. S. FLEMING; S. H. LIU

doi:10.1103/PhysRev.178.930

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Generalized Susceptibilities and Magnetic Properties of Some bcc Transition Metals

W. E. EVENSON^*, G. S. FLEMING, and S. H. LIU

Institute for Atomic Research and Department of Physics, Iowa State University, Ames, Iowa 50010

^*Danforth Foundation Fellow. Present address: Department of Physics, University of Pennsylvania, Philadelphia, Penna.

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Phys. Rev. 178, 930 – Published 15 February, 1969

DOI: https://doi.org/10.1103/PhysRev.178.930

Abstract

Using the energy bands for tungsten calculated by Mattheiss, we have calculated the generalized susceptibilities $χ (q)$ along $Γ H$ for several bcc transition metals by appropriately adjusting the Fermi energies. The Fermi energies were chosen using Mattheiss's integrated density of states to have the proper number of electrons per atom to correspond to (a) the chromium series, (b) the vanadium series, and (c) europium. We have used procedures developed in our calculation of $χ (q)$ for the heavy rare earths. The generalized susceptibility that corresponds to the chromium group has several small peaks and a prominent, narrow peak very near to $H$ . The position of this prominent peak corresponds to the magnetic periodicity of chromium and to a Kohn anomaly observed in the Cr and Mo phonon spectra. The susceptibility for the vanadium group has a peak near the broad dip in the $[00 q] L$ branch of the phonon spectrum of niobium. The susceptibility for europium has a peak near the magnetic wave vector for europium. The Fermi surface for Eu derived from this set of bands is quite similar to that calculated by Andersen and Loucks, and the susceptibility shows the important nesting across the tetracube and the superegg pieces of the Fermi surface.

References (16)

W. E. Evenson and S. H. Liu, Phys. Rev. Letters 21, 432 (1968)
W. E. Evenson and S. H. Liu, Phys. Rev. 178, 783 (1969)
L. F. Mattheiss, Phys. Rev. 139, A236 (1965)
W. M. Lomer, Proc. Phys. Soc. (London) 80, 489 (1962)
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D. C. Rorer, D. G. Onn, and H. Meyer, Phys. Rev. 138, A1661 (1965)
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H. B. Møller and A. R. Mackintosh, in Inelastic Scattering of Neutrons (International Atomic Energy Agency, Vienna, 1965), Vol. 1, p. 95
A. D. B. Woods and S. H. Chen, Solid State Commun. 2, 233 (1964)
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G. P. Arnold, C. E. Olsen, and N. G. Nereson, J. Appl. Phys. Suppl. 33, 1135 (1962) C. E. Olsen, N. G. Nereson, and G. P. Arnold, 35, 1031 (1964) N. G. Nereson, C. E. Olsen, and G. P. Arnold, Phys. Rev. 135, A176 (1964)
O. K. Andersen and T. L. Loucks, Phys. Rev. 167, 551 (1968)

[c1] W. E. Evenson and S. H. Liu, Phys. Rev. Letters 21, 432 (1968)

[c2] W. E. Evenson and S. H. Liu, Phys. Rev. 178, 783 (1969)

[c3] L. F. Mattheiss, Phys. Rev. 139, A236 (1965)

[c4] W. M. Lomer, Proc. Phys. Soc. (London) 80, 489 (1962)

[c5] P. A. Fedders and P. C. Martin, Phys. Rev. 143, 245 (1966)

[c6] S. H. Liu, Phys. Letters 27, 493 (1968)

[c7] D. C. Rorer, D. G. Onn, and H. Meyer, Phys. Rev. 138, A1661 (1965)

[c8] J. W. Gibson and R. A. Hein, Phys. Rev. Letters 12, 688 (1964) R. T. Johnson, O. E. Vilches, J. C. Wheatley, and S. Gygax, ibid. 16, 101 (1966)

[c9] H. B. Møller and A. R. Mackintosh, in Inelastic Scattering of Neutrons (International Atomic Energy Agency, Vienna, 1965), Vol. 1, p. 95

[c10] A. D. B. Woods and S. H. Chen, Solid State Commun. 2, 233 (1964)

[c11] S. H. Chen and B. M. Brockhouse, Solid State Commun. 2, 73 (1964)

[c12] Y. Nakagawa and A. D. B. Woods, Phys. Rev. Letters 11, 271 (1963)

[c13] A. D. B. Woods, in Inelastic Scattering of Neutrons (International Atomic Energy Agency, Vienna, 1965), Vol. 1, p. 87

[c14] A. D. B. Woods and B. M. Powell, Phys. Rev. Letters 15, 778 (1965)

[c15] G. P. Arnold, C. E. Olsen, and N. G. Nereson, J. Appl. Phys. Suppl. 33, 1135 (1962) C. E. Olsen, N. G. Nereson, and G. P. Arnold, 35, 1031 (1964) N. G. Nereson, C. E. Olsen, and G. P. Arnold, Phys. Rev. 135, A176 (1964)

[c16] O. K. Andersen and T. L. Loucks, Phys. Rev. 167, 551 (1968)

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Generalized Susceptibilities and Magnetic Properties of Some bcc Transition Metals

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