Theory of spin-fluctuation resistivity near the critical point of binary alloys and antiferromagnets

T. G. Richard; D. J. W. Geldart

doi:10.1103/PhysRevB.15.1502

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Theory of spin-fluctuation resistivity near the critical point of binary alloys and antiferromagnets

T. G. Richard

D. J. W. Geldart

Department of Physics and Mathematics, Université de Moncton, Moncton, New Brunswick, Canada E1A 3E9

Department of Physics, Dalhousie University, Halifax, Nova Scotia, Canada B3H 3J5

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Phys. Rev. B 15, 1502 – Published 1 February, 1977

DOI: https://doi.org/10.1103/PhysRevB.15.1502

Abstract

We present a simple theory of electrical resistivity $ρ (T)$ due to critical fluctuations in the vicinity of the Néel point of antiferromagnets and the order-disorder transition temperature of binary alloys. In the disordered phase, it is shown that the singular part of $\frac{\partial ρ}{\partial T}$ varies as either plus or minus the singular part of the specific heat for $T \to T_{N}^{+}$ . The sign is determined by Fermi-surface geometry and the superlattice vector $\vec{Q}$ of the ordered state. The temperature range, somewhat above $T_{N}$ , where short-range ( $R ≪ ξ$ ) correlations are no longer dominant is also considered. Numerical results are given for both the short-range and long-range temperature regimes. In the ordered state, it is concluded that the long-range order does not enter $ρ (T)$ directly for $T \to T_{N}^{-}$ and that $\frac{\partial ρ}{\partial T}$ continues to reflect more closely the specific heat. The results are compared with experiment in the representative cases of $β$ -brass, ${Fe}_{3}$ Al, dysprosium, and holmium. Some previously unsettled questions are answered and there is good agreement with experiment.

References (40)

P. G. deGennes and J. Friedel, J. Phys. Chem. Solids 4, 71 (1958)
M. P. Kawatra and J. I. Budnick, Int. J. Magn. 1, 61 (1970) R. D. Parks, AIP Conf. Proc. 5, 630 (1972)
M. E. Fisher and J. S. Langer, Phys. Rev. Lett. 20, 665 (1968)
M. E. Fisher, Rep. Prog. Phys. 30, 615 (1967)
T. G. Richard and D. J. W. Geldart, Phys. Rev. Lett. 30, 290 (1973)
T. G. Richard, Ph.D. thesis (Dalhouie University, 1973) (unpublished)
D. J. W. Geldart and T. G. Richard, Phys. Rev. B 12, 5175 (1975)
K. Haung, Statistical Mechanics (Wiley, New York, 1963), p. 329
Y. Suezaki and H. Mori, Prog. Theor. Phys. 41, 1177 (1969)
D. J. W. Geldart and T. G. Richard, in Dynamical Aspects of Critical Phenomena, edited by J. I. Budnick and M. P. Kawatra (Gordon and Breach, New York, 1972), p. 326
R. J. Elliott and F. A. Wedgwood, Proc. Phys. Soc. Lond. 81, 846 (1963)
H. Miwa, Prog. Theor. Phys. 28, 208 (1962) ibid.29, 477 (1963)
Omitted endnote
L. P. Kadanoff et al., Rev. Mod. Phys. 39, 395 (1967)
L. P. Kadanoff, in Critical Phenomena, edited by M. S. Green (Academic, New York, 1972), p. 100
J. Als-Nielsen and O. W. Dietrich, Phys. Rev. 153, 706, 717 (1967)
W. C. Koehler, in Magnetic Properties of Rare Earth Metals, edited by R. J. Elliott (Plenum, London, 1972), p. 81
()
M. E. Fisher and A. Aharony, Phys. Rev. Lett. 31, 1238 (1973) E. Brézin, D. J. Amit, and J. Zinn-Justin, ibid. 32, 151 (1974) M. E. Fisher and A. Aharony, Phys. Rev. B 10, 2818 (1974) A. Aharony, ibid. 10, 2834 (1974)
M. E. Fisher and R. J. Burford, Phys. Rev. 156, 583 (1967)
M. Ferer, M. A. Moore, and M. Wortis, Phys. Rev. Lett. 22, 1382 (1969)
D. S. Ritchie and M. E. Fisher, Phys. Rev. B 5, 2668 (1972)
Omitted endnote
Omitted endnote
A. J. Freeman, in Magnetic Properties of Rare Earth Metals, edited by R. J. Elliott (Plenum, London, 1972), p. 245
W. J. Camp and M. E. Fisher, Phys. Rev. Lett. 26, 73 (1971)
A. Aharony, AIP Conf. Proc. 18, 863 (1974)
S. Takada, Prog. Theor. Phys. 46, 15 (1971)
T. Kasuya and A. Kondo, Solid State Commun. 14, 249 (1974)
D. S. Simons and M. B. Salamon, Phys. Rev. Lett. 26, 750 (1971)
L. Guttman and H. C. Schnyder, Phys. Rev. Lett. 22, 520 (1969)
F. J. Arlinghaus, Phys. Rev. 186, 609 (1969)
G. A. Thomas, A. B. Giray, and R. D. Parks, Phys. Rev. Lett. 31, 241 (1973)
in Intermetallic Compounds, edited by J. H. Westbrook (Wiley, New York, 1967)
K. V. Rao, Ö. Rapp, T. G. Richard, and D. J. W. Geldart, J. Phys. C 6, L231 (1973)
R. A. Craven and R. D. Parks, Phys. Rev. Lett. 31, 383 (1973)
K. V. Rao, Ö. Rapp, Ch. Johannesson, D. J. W. Geldart, and T. G. Richard, J. Phys. C 8, 2135 (1975)
R. L. Singh and D. J. W. Geldart, Solid State Commun. 20, 501 (1976)

[c1] P. G. deGennes and J. Friedel, J. Phys. Chem. Solids 4, 71 (1958)

[c2] M. P. Kawatra and J. I. Budnick, Int. J. Magn. 1, 61 (1970) R. D. Parks, AIP Conf. Proc. 5, 630 (1972)

[c3] M. E. Fisher and J. S. Langer, Phys. Rev. Lett. 20, 665 (1968)

[c4] M. E. Fisher, Rep. Prog. Phys. 30, 615 (1967)

[c5] T. G. Richard and D. J. W. Geldart, Phys. Rev. Lett. 30, 290 (1973)

[c6] T. G. Richard, Ph.D. thesis (Dalhouie University, 1973) (unpublished)

[c7] D. J. W. Geldart and T. G. Richard, Phys. Rev. B 12, 5175 (1975)

[c8] K. Haung, Statistical Mechanics (Wiley, New York, 1963), p. 329

[c9] Y. Suezaki and H. Mori, Prog. Theor. Phys. 41, 1177 (1969)

[c10] D. J. W. Geldart and T. G. Richard, in Dynamical Aspects of Critical Phenomena, edited by J. I. Budnick and M. P. Kawatra (Gordon and Breach, New York, 1972), p. 326

[c11] R. J. Elliott and F. A. Wedgwood, Proc. Phys. Soc. Lond. 81, 846 (1963)

[c12] H. Miwa, Prog. Theor. Phys. 28, 208 (1962) ibid.29, 477 (1963)

[c13] Omitted endnote

[c15] L. P. Kadanoff et al., Rev. Mod. Phys. 39, 395 (1967)

[c16] L. P. Kadanoff, in Critical Phenomena, edited by M. S. Green (Academic, New York, 1972), p. 100

[c17] J. Als-Nielsen and O. W. Dietrich, Phys. Rev. 153, 706, 717 (1967)

[c18] W. C. Koehler, in Magnetic Properties of Rare Earth Metals, edited by R. J. Elliott (Plenum, London, 1972), p. 81

[c19] ()

[c20] M. E. Fisher and A. Aharony, Phys. Rev. Lett. 31, 1238 (1973) E. Brézin, D. J. Amit, and J. Zinn-Justin, ibid. 32, 151 (1974) M. E. Fisher and A. Aharony, Phys. Rev. B 10, 2818 (1974) A. Aharony, ibid. 10, 2834 (1974)

[c21] M. E. Fisher and R. J. Burford, Phys. Rev. 156, 583 (1967)

[c22] M. Ferer, M. A. Moore, and M. Wortis, Phys. Rev. Lett. 22, 1382 (1969)

[c23] D. S. Ritchie and M. E. Fisher, Phys. Rev. B 5, 2668 (1972)

[c24] Omitted endnote

[c26] Omitted endnote

[c27] A. J. Freeman, in Magnetic Properties of Rare Earth Metals, edited by R. J. Elliott (Plenum, London, 1972), p. 245

[c28] W. J. Camp and M. E. Fisher, Phys. Rev. Lett. 26, 73 (1971)

[c29] A. Aharony, AIP Conf. Proc. 18, 863 (1974)

[c30] S. Takada, Prog. Theor. Phys. 46, 15 (1971)

[c31] T. Kasuya and A. Kondo, Solid State Commun. 14, 249 (1974)

[c32] D. S. Simons and M. B. Salamon, Phys. Rev. Lett. 26, 750 (1971)

[c33] L. Guttman and H. C. Schnyder, Phys. Rev. Lett. 22, 520 (1969)

[c34] F. J. Arlinghaus, Phys. Rev. 186, 609 (1969)

[c35] G. A. Thomas, A. B. Giray, and R. D. Parks, Phys. Rev. Lett. 31, 241 (1973)

[c36] in Intermetallic Compounds, edited by J. H. Westbrook (Wiley, New York, 1967)

[c37] K. V. Rao, Ö. Rapp, T. G. Richard, and D. J. W. Geldart, J. Phys. C 6, L231 (1973)

[c38] R. A. Craven and R. D. Parks, Phys. Rev. Lett. 31, 383 (1973)

[c39] K. V. Rao, Ö. Rapp, Ch. Johannesson, D. J. W. Geldart, and T. G. Richard, J. Phys. C 8, 2135 (1975)

[c40] R. L. Singh and D. J. W. Geldart, Solid State Commun. 20, 501 (1976)

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Theory of spin-fluctuation resistivity near the critical point of binary alloys and antiferromagnets

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