Theory of Inelastic Neutron Scattering in the Itinerant Model Antiferromagnetic Metals. I

J. B. Sokoloff

doi:10.1103/PhysRev.185.770

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Theory of Inelastic Neutron Scattering in the Itinerant Model Antiferromagnetic Metals. I

J. B. Sokoloff

Brookhaven National Laboratory, Upton, New York 11973

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Phys. Rev. 185, 770 – Published 10 September, 1969

DOI: https://doi.org/10.1103/PhysRev.185.770

Abstract

The susceptibility functions $χ^{- +} (K, ω)$ and $χ^{zz} (K, ω)$ are calculated in the random-phase approximation at zero temperature for the Slater model of itinerant antiferromagnetism using the Hubbard Hamiltonian; from these susceptibility functions the neutron-scattering cross section is calculated. A pole is found in $χ^{- +} (K, ω)$ corresponding to a spin-wave model As in the Heisenberg model of spin waves, the residue of this pole approaches zero as the scattering vector K approaches a chemical reciprocal lattice vector $τ$ , and becomes infinite as K approaches a magnetic reciprocal-lattice vector Q. The non-spin-flip single-particle-mode scattering is found to become infinite at an energy corresponding to the magnetic splitting of the bands at the boundary of the magnetic Brillouin zone if the Fermi level lies in this gap. If the Fermi level does not lie in the gap, then there is a pole in $χ^{zz} (K, ω)$ for K near a magnetic reciprocal-lattice vector, at an energy equal to the gap energy when K = Q, corresponding to a collective excitation. Acoustic plasmon poles in $χ^{zz} (q, ω)$ are also discussed.

References (26)

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T. M. Rice, A. S. Barker, Jr., B. I. Halperin, and D. B. McWhan, J. Appl. Phys. 40, 1337 (1969)
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[c1] P. A. Fedders and P. C. Martin, Phys. Rev. 143, 245 (1966)

[c2] T. M. Rice, A. S. Barker, Jr., B. I. Halperin, and D. B. McWhan, J. Appl. Phys. 40, 1337 (1969)

[c3] L. D. Muhlestein, S. K. Sinha, Bull. Am. Phys. Soc. 13, 468 (1968) S. K. Sinha (private communication) S. Liu (private communication)

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

[c5] A. W. Overhauser, Phys. Rev. 128, 1437 (1962)

[c6] H. Yamada and M. Shimizu, J. Phys. Soc. Japan 22, 1404 (1967) ibid.25, 1001 (1968)

[c7] E. D. Thompson, Phys. Rev. Letters 19, 635 (1967)

[c8] J. B. Sokoloff, Phys. Rev. 173, 617 (1968) 180, 613 (1969)

[c9] J. Hubbard, Proc. Roy. Soc. (London) A276, 238 (1963)

[c10] J. C. Slater, Phys. Rev. 82, 538 (1951)

[c11] J. Des Cloizeaux, J. Phys. Radium 20, 606 (1959) ibid.20, 751 (1959)

[c12] C. Herring, in Magnetism, edited by George T. Rado and Harry Shul (Academic Press Inc., New York, 1966), Vol. IV, p. 312

[c13] Omitted endnote

[c14] A. B. Lidiard, Proc. Roy. Soc. (London) A224, 161 (1954)

[c15] T. Izuyama, D. J. Kim, and R. Kubo, J. Phys. Soc. Japan 18, 1025 (1963)

[c16] L. Van Hove, Phys. Rev. 95, 1374 (1954)

[c17] R. J. Elliott and R. D. Lowde, Proc. Roy. Soc. (London) A230, 46 (1955)

[c18] P. W. Anderson, Concepts in Solids (W. A. Benjamin, Inc., New York, 1964), p. 175

[c19] A. K. Rajagopol and H. Brooks, Phys. Rev. 158, 552 (1967)

[c20] J. M. Ziman, Principles of the Theory of Solids (Cambridge University Press, London, 1964), p. 320

[c21] J. E. Graebner and J. A. Marcus, Phys. Rev. 175, 659 (1968)

[c22] H. A. Mook, R. M. Nicklow, E. D. Thompson, and M. K. Wilkinson, J. Appl. Phys. 40, 1450 (1969)

[c23] D. Pines and J. R. Schrieffer, Phys. Rev. 124, 1387 (1961)

[c24] S. Asano and J. Yamashita, J. Phys. Soc. Japan 23, 714 (1967)

[c25] D. Pines and P. Nozières, The Theory of Quantum Liquids (W. A. Benjamin, Inc., New York, 1966), Vol. I, pp. 48, 319

[c26] F. Englert and M. M. Antonoff, Physica 30, 429 (1964)

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Theory of Inelastic Neutron Scattering in the Itinerant Model Antiferromagnetic Metals. I

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