Transition temperatures of rare-earth compounds studied with perturbation theory

The perturbation theory is employed in present Letter to study the transition temperatures of rare-earth magnets. To simplify the model, it is assumed that the ground and first excited crystal-electric-field (CEF) levels are both nonmagnetic singlets, the Heisenberg exchange interaction is only comparable to the energy gap (A) between them, and other higher levels are well separated from the first excited one, so their contributions to the bulk magnetization are negligible in low-temperature region. By treating the Heisenberg exchange as a perturbation to the CEF interaction near the critical point, explicit expressions for the Curie and Neel temperatures (T-C and T-N) are derived in terms of the Heisenberg exchange constant (J), the gap Delta and the matrix element of the total spin moment in the ordering direction between the two lowest CEF levels. For completeness and to verify the correctness of the theory, we have also derived the analytical expressions for the magnetic moments at zero temperature for both rare-earth ferromagnet and antiferromagnet, the conditions for the magnetic orderings, and calculated the spontaneous magnetizations and magnetic specific heats at finite temperatures numerically for a hexagonal ferromagnetic Pr compound with the model. This approach can be generalized to real systems to evaluate their transition temperatures and to investigate the mechanisms of magnetic ordering. (C) 2003 Elsevier B.V. All fights reserved.