CRITICAL-POINT BEHAVIOR OF CLASSICAL HEISENBERG FERRIMAGNETS

This paper discusses in detail the critical properties of a class of particularly simple ferrimagnets typified by simple cubic and body-centered cubic lattices having alternate sites occupied by classical spins of different magnitudes, SA and SB. Heisenberg exchange interactions are assumed to act between nearest-neighbor sites. For such ferrimagnets, general arguments are presented which determine certain features of the dependence of the susceptibility χ and the specific heat on the variables R=SBSA and j=SASBJκT. It is easily shown that the critical point occurs at a fixed j for either sign of the exchange and arbitrary spin values. Moreover, the exponent γ of the singularity in χ has a value independent of the sign of the exchange and of the spin values. The only exception permitted occurs at the singularity of the simple antiferromagnet (R=1, j<0) which has a reduced critical exponent. The nature of the dependence of χ on R permits one to obtain its expansion in powers of j from the known expansion coefficients for the related ferromagnet. A Padé-approximant study of χ for a range of R values is described. For Ra 1, the dominant singularity for positive and negative j shows the familiar power-law behavior and is consistent with the general features of the R dependence described above. The critical points and exponents are estimated for the cases studied by a new method making use of the freedom to vary R in the ferrimagnet. A method of characterizing the weaker singularities in χ is described and investigated numerically. The implications of these results for real ferrimagnets are examined. © 1969 The American Physical Society.