The Effect of Interactions in a Paramagnetic on the Entropy and Susceptibility

Abstract

Van Vleck's theory of magnetic dipole interaction is extended to take into account magnetic anisotropy of the individual ions, and hyperfine splitting. The entropy and susceptibility are expressed as power series in 1/T as far as the term in 1/T4. Explicit formulae are found for the term in 1/T2 in the entropy, the important term at high temperatures, and for the Curie-Weiss Δ's; for paramagnetics with one ion in the unit cell and axial symmetry, and for the Tutton salts. This is done both in the case of a general interaction and also for pure magnetic dipole-dipole interaction. It is shown that the contributions of interactions and of hyperfine splitting to both the entropy and the susceptibility are additive as far as the term in 1/T3, and that hyperfine splitting introduces into the susceptibility shape-dependent terms which cannot be included in the Curie-Weiss Δ. This is followed by a review of the properties of cerium magnesium nitrate, the rare earth ethylsulphates, and the Tutton salts in relation to this theory.