Reaction Field Approximation for Heisenberg Paramagnets and the Magnetic Specific Heat

Abstract

The concept of "reaction field" introduced by Onsager is applied to the case of a Heisenberg system in the paramagnetic phase. The procedure to obtain the static q-dependent susceptibility and pair correlation functions is reviewed and extended to calculate the magnetic specific heat. The result of this calculation is compared with experiment.Das von Onsager eingefuhrte Konzept eines ,,Reaktionsfeldes" wird auf den Fall des Heisenberg Systems in der paramagnetischen Phase angewendet. Die Prozedur, urn die statische q-abhangige Suszeptibilitat und Paarkorrelation zu erhalten, wird zusammenfassend beschrieben und auf die Berechnung der magnetischen spezifischen Wiirme erweitert. Das Resultat dieser Rechnung wird mit Experimenten verglichen.

Correlated effective field theory in transition metal compounds

“…RFA was originally proposed by Onsager [67] and was extended to the Ising system by Brout et al [68] and to an arbitrary spin system S in the entire phase space (both below and above T c ) by Scherer et al [69][70][71][72][73].…”

“…Hence this term should be subtracted from the effective field in the MF scenario. Scherer et al [69,70] assumed a linear approximation to obtain…”

“…Then they [68][69][70][71] showed, using the fluctuation-dissipation theorem in the paramagnetic phase, that the relation Z ½d 3 q=ð2pÞ 3 Â ½b À JðqÞ=JðQÞ À1 GðsÞ…”

“…For a cubic lattice with nearest neighbour interaction, the so-called lattice Green functions, GðsÞ are tabulated [74]. The transition temperature, T RFA c for s ¼ 1 would be [70] T RFA c ¼ T MF c =½Gð1Þ ð5:5:10Þ…”

“…The magnetic specific heat turned out to be [70] C H ¼ À ðsðs þ 1Þ=2Þ dlðTÞ=dT ¼ ð3=2Þk  ½1 þ ½GðsÞ 2 =½G 0 ðsÞ ð5:5:10aÞ with G 0 ðsÞ ¼ dGðsÞ=ds:…”