Crystalline Stark Splitting and Microwave Resonance Absorption in Paramagnetic Salts

C. Kittel; J. M. Luttinger

doi:10.1103/PhysRev.73.162

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Crystalline Stark Splitting and Microwave Resonance Absorption in Paramagnetic Salts

C. Kittel^* and J. M. Luttinger^†

Research Laboratory of Electronics, Massachusetts Institute of Technology, Cambridge, Massachusetts

^*Now at Bell Telephone Laboratories, Murray Hill, New Jersey.
^†Now at Eidgenössische Technische Hochschule, Zürich, Switzerland.

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Phys. Rev. 73, 162 – Published 15 January, 1948

DOI: https://doi.org/10.1103/PhysRev.73.162

Abstract

A theoretical discussion is given of the application of microwave-absorption measurements to the determination of energy levels in single crystals of paramagnetic salts. Selection rules are given for magnetic-dipole transitions between sublevels in the presence of crystalline electric fields of cubic, tetragonal, trigonal, and rhombic symmetry. The Zeeman effect in the presence of crystalline electric fields is discussed in some detail for three special cases: (a) $J = \frac{5}{2}$ , cubic field; (b) $J = \frac{7}{2}$ , cubic field; (c) $J = \frac{3}{2}$ , trigonal field. These examples may correspond approximately to certain magnetically dilute salts containing ${Fe}^{+ + +}$ , ${Gd}^{+ + +}$ , and ${Cr}^{+ + +}$ ions, respectively, provided that exchange interactions do not play an important role and that the assumed symmetries are approximately correct. Numerical values are tabulated for the relative frequencies and line strengths associated with magnetic-dipole transitions in the cases discussed. The character of the spectra may change radically between the limit where the Zeeman splitting is small in comparison with the Stark splitting, and the opposite limit where the Stark splitting may be neglected.

References (18)

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C. J. Gorter, Paramagnetic Relaxation (Elsvier Publishing Company, Inc., Amsterdam, 1947)
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[c1] J. H. Van Vleck, The Theory of Electric and Magnetic Susceptibilities (Oxford University Press, London, 1932)

[c2] H. B. G. Casimir, Magnetism and Very Low Temperatures (Cambridge University Press, Teddington, England, 1940)

[c3] Université de Strasbourg, Le Magnétisme: Tome 3: Paramagnétisme (Institut International de Coopération Intellectuelle, Paris, 1940)

[c4] C. J. Gorter, Paramagnetic Relaxation (Elsvier Publishing Company, Inc., Amsterdam, 1947)

[c5] W. G. Penney and G. J. Kynch, Proc. Roy. Soc. A170, 112 (1939) J. H. Van Vleck, J. Phys. Chem. 41, 67 (1937) S. Freed, Rev. Mod. Phys. 14, 105 (1942)

[c6] E. Zavoisky, J. Phys. U.S.S.R. 9, 211, 245, 447 (1945) ibid.10, 170, 197 (1946) R. L. Cummerow and D. Halliday, Phys. Rev. 70, 433 (1946) R. L. Cummerow, D. Halliday, and G. E. Moore, 72, 173 (1947)

[c7] J. Frenkel, J. Phys. U.S.S.R. 9, 299 (1945)

[c8] D. M. S. Bagguley and J. H. E. Griffiths, Nature 160, 532 (1947) P. R. Weiss, C. A. Whitmer, H. C. Torrey, and Jen-Sen Hsiang, Phys. Rev. 72, 975 (1947)

[c9] H. C. Torrey, E. M. Purcell, and R. V. Pound, Phys. Rev. 69, 680 (1946)

[c10] H. A. Bethe, Ann. d. Physik 3, 133 (1929) E. Wigner, Göttingen Nachrichten 133 (1930)

[c11] L. Tisza, Zeits. f. Physik 82, 48 (1933)

[c12] H. Jahn, Proc. Roy. Soc. A164, 117 (1938) W. Opechowski, Physica 7, 552 (1940)

[c13] H. Bethe, Zeits. f. Physik 60, 218 (1930)

[c14] M. H. Hebb and E. M. Purcell, J. Chem. Phys. 5, 338 (1937)

[c15] J. H. Van Vleck and W. G. Penney, Phil. Mag. 17, 961 (1934)

[c16] P. Debye, Ann. d. Physik 32, 85 (1938)

[c17] R. de L. Kronig and C. J. Bouwkamp, Physica 6, 290 (1939)

[c18] G. J. Kynch, Trans. Faraday Soc. 33, 1402 (1937)

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Crystalline Stark Splitting and Microwave Resonance Absorption in Paramagnetic Salts

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