Antiferromagnetism in Chromium Alloys. I. Neutron Diffraction

W. C. Koehler; R. M. Moon; A. L. Trego; A. R. Mackintosh

doi:10.1103/PhysRev.151.405

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Antiferromagnetism in Chromium Alloys. I. Neutron Diffraction

W. C. Koehler and R. M. Moon

A. L. Trego^* and A. R. Mackintosh^†

Solid State Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee

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

^*Present address: Los Alamos Scientific Laboratory, Mercury, Nevada.
^†Alfred P. Sloan Research Fellow. Present address: Technical University, Copenhagen, Denmark.

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Phys. Rev. 151, 405 – Published 11 November, 1966

DOI: https://doi.org/10.1103/PhysRev.151.405

Abstract

The magnetic properties of Cr alloys containing small amounts of the transition metals V, Mn, Nb, Mo, Tc, Ru, Rh, Ta, W, and Re have been studied by powder and, in some cases, single-crystal neutron-diffraction techniques. Mn, Tc, Ru, Rh and Re, which increase the electron-to-atom ratio, also increase the Néel temperature and magnetic moment, which reach maximum values of about 700°K and $0.75 μ_{B}$ , compared with 311°K and $0.40 μ_{B}$ for pure Cr. The wave vector of the magnetic structure also increases until, at a concentration of about 1%, it changes abruptly to $\frac{2 π}{a}$ and the structure becomes commensurable with the lattice. The addition of V, Nb or Ta, which reduces the electron-to-atom ratio, or of Mo or W, for which it remains constant, diminishes the Néel temperature and moment and reduces the wave vector. Ta is the most effective in modifying the properties of pure Cr, followed by Nb and V, W, and Mo in that order. In all cases studied the transition temperature from a transverse- to a longitudinal-wave magnetic structure is reduced by alloying. These observations can be explained by the two-band model of Lomer, which has been studied in detail by Fedders and Martin. The wave vector of the magnetic periodicity connects electron and hole sheets of the Fermi surface and its magnitude and rate of change with electron concentration are in semiquantitative agreement with the energy-band calculations of Loucks. The Néel temperature is proportional to the ordered moment, and varies very rapidly with electron concentration in a way which can be qualitatively explained by the form of the Fermi surface. The variation of the ordered moment with temperature follows the BCS superconducting energy-gap function, as predicted by the theory.

References (29)

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Omitted endnote
Omitted endnote
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[c1] C. G. Shull and M. K. Wilkinson, Rev. Mod. Phys. 25, 100 (1953)

[c2] L. Corliss, J. Hastings, and R. Weiss, Phys. Rev. Letters 3, 211 (1959)

[c3] V. N. Bykov, V. S. Golovkin, N. V. Ageev, V. A. Levdik, and S. I. Vinogradov, Dokl. Akad. Nauk SSSR 128, 1153 (1959) [English transl.: Soviet Phys.—Doklady 4, 1070 (1959)]

[c4] G. E. Bacon, Acta Cryst. 14, 823 (1961)

[c5] G. Shirane and W. J. Takei, J. Phys. Soc. Japan 17, Suppl. B-III, 35 (1962)

[c6] P. J. Brown, C. Wilkinson, J. B. Forsythe, and R. Nathans, Proc. Phys. Soc. (London) 85, 1185 (1965)

[c7] J. Graebner and J. A. Marcus, J. Appl. Phys. 37, 1262 (1966)

[c8] H. B. Møller, K. Blinowski, A. R. Mackintosh, and T. Brun, Solid State Commun. 2, 109 (1964)

[c9] A. Arrott, S. A. Werner, and H. Kendrik, Phys. Rev. Letters 14, 1022 (1965)

[c10] T. J. Bastow and R. Street, Phys. Rev. 141, 510 (1966)

[c11] M. K. Wilkinson, E. O. Wollan, W. C. Koehler, and J. W. Cable, Phys. Rev. 127, 2080 (1962)

[c12] A. L. Trego, Ph.D. thesis, Iowa State University, 1965 (unpublished) J. G. Booth, Battelle Memorial Institute Annual Topical Report to the U. S. Office of Naval Research, 1964 (unpublished)

[c13] A. L. Trego and A. R. Mackintosh (to be published)

[c14] Y. Hamaguchi, E. O. Wollan, and W. C. Koehler, Phys. Rev. 138, A737 (1965)

[c15] H. B. Møller, A. L. Trego, and A. R. Mackintosh, Solid State Commun. 3, 137 (1965)

[c16] O. N. Carlson, F. A. Schmidt, and W. M. Paulson, Trans. Am. Soc. Metals 57, 356 (1964)

[c17] R. M. Moon, W. C. Koehler, and A. L. Trego, J. Appl. Phys. 37, 1036 (1966)

[c18] Omitted endnote

[c19] Omitted endnote

[c20] A. B. Lidiard, Proc. Phys. Soc. (London) A66, 1188 (1953)

[c21] A. W. Overhauser, Phys. Rev. 128, 1437 (1962)

[c22] T. Nagamiya, K. Motizuki, and K. Yamasaki, in Proceedings of the International Conference on Magnetism, Nottingham, 1964 (The Institute of Physics and The Physical Society, London, 1965)

[c23] D. Penn, Phys. Rev. 142, 350 (1966)

[c24] W. M. Lomer, Proc. Phys. Soc. (London) 80, 489 (1962)

[c25] P. A. Fedders and P. C. Martin, Phys. Rev. 143, 245 (1966)

[c26] D. R. Hamann and A. W. Overhauser, Phys. Rev. 143, 183 (1966)

[c27] T. L. Loucks, Phys. Rev. 139, A1181 (1965) private communication

[c28] L. F. Mattheiss, Phys. Rev. 134, A970 (1964)

[c29] J. Bardeen, L. N. Cooper, and J. R. Schrieffer, Phys. Rev. 108, 1175 (1957)

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Antiferromagnetism in Chromium Alloys. I. Neutron Diffraction

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Antiferromagnetism in Chromium Alloys. II. Transport Properties

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