Abstract
The magnetizationM of bismuth is calculated as a function of the magnetic fieldH atT=0 for binary, bisectrix, and trigonal orientations in the range of highH, from beyond the last de Haas-van Alphen oscillation up to 400 kG. The method of calculation is to sum the energies of the occupied energy levels and then to differentiate with respect toH; the energy levels are based on the ellipsoidal but nonparaboloidal model of the band structure. In qualitative and almost quantitative agreement with experiment, considerable departures ΔM are found from the proportionality betweenM andH which holds in the limit of lowH, and the results are presented in the form of tables and graphs of ΔM as a function ofH; the field dependence of the Fermi energy is also presented. An important contribution to the nonproportionality ΔM at highH proves to come from the electrons in the filled band and this contribution is calculated by a special method involving a cutoff parameter; the value chosen for this cutoff parameter affects only the proportional part ofM, but not ΔM.
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References
W. J. de Haas and P. M. van Alphen,Leiden Comm. 220 d. (1932).
N. L. Brignall and D. Shoenberg,J. Phys. C. 7, 1499 (1974) and unpublished data; see also N. L. Brignall, Ph.D. Thesis, Cambridge University (1972).
D. Shoenberg, inProc. Conference on Semi-metals, Cardiff, September 1973 (to be published).
M. H. Cohen and E. I. Blount,Phil. Mag. 5, 115 (1960).
M. H. Cohen,Phys. Rev. 121, 387 (1961).
R. N. Brown, J. G. Mavroides, and B. Lax,Phys. Rev. 129, 2055 (1963).
L. W. Roeland, G. J. Cock, F. A. Muller, and D. Shoenberg,Physica 793, 95 (1975).
G. E. Smith, G. A. Baraff, and J. M. Rowell,Phys. Rev. 135, A118 (1964).
V. S. Edelman,Zh. Eksp. Teor. Fiz. 64, 1735 (1973);Zh. Eksp. Teor. Fiz. Pisma,18, 236 (1973).
F. A. Buot,The Physics of Semi-metals and Natrow Gap Semiconductors (Pergamon Press, Oxford, 1971, p. 99.
M. P. Vecchi and M. S. Dresselhaus,Phys. Rev. B 9, 3257 (1974).
G. A. Baraff,Phys. Rev. 137, A842 (1965).
A. A. Abrikosov,J. Low Temp. Phys. 8, 315 (1972).
R. N. Bhargava,Phys. Rev. 156, 785 (1967).
C. M. Hurd and P. Coodin,J. Phys. Chem. Solids 28, 523 (1967).
D. Shoenberg and M. Zaki Uddin,Proc. Roy. Soc. A 156, 687 (1936).
R. C. Barklie, unpublished work.
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Supported in part by the U.S. National Science Foundation.
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McClure, J.W., Shoenberg, D. Magnetic properties of bismuth at high fields. J Low Temp Phys 22, 233–255 (1976). https://doi.org/10.1007/BF00654705
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DOI: https://doi.org/10.1007/BF00654705