The susceptibilities and molecular-field constants of rare-earth compounds from mean-field theory

Abstract

The mean-field theory is employed in present work to study the validity conditions for a popular formula which is widely used to calculate the susceptibilities of rare-earth compounds and their molecular-field constants from known transition temperatures [Proc. R. Soc. Lond. 276A (1963) 19; Phys. Rev. 163 (1967) 444]. To facilitate the theoretical analysis, we consider a special system, CeTe 2, whose magnetic behavior below T N is mainly governed by the lowest crystal-field (CF) Kramers doublet according to our recent theoretical studies. We find that, when the external field and the localized moment are both considerably weak, the formula can be safely used, but, when their magnitudes are appreciable with respect to temperature, one has to include the both terms in the Hamiltonian and perform the calculations self-consistently in order to calculate the susceptibility accurately; and to reflect the intrinsic magnetic properties of a system, the external field must be very weak in experimental measurements or theoretical calculations. Finally, we propose an alternative approach to determine the exchange constant from the known transition temperature, or vice versa.