Magnon contribution to the specific heat and the validity of power laws in antiferromagnetic crystals

For any crystal, the specific heat due to phonons can be written as Cph=AT3 where A is a constant and for a metal, the conduction electrons contribute a term that can be written as Cel(T)=γT. At low temperatures, however, other contributions to the specific heat may become significant. What is measured experimentally at any temperature T is the total specific heat Ctot of the solid. To separate the various contributions to Ctot, it is customary to make use of the known power-law variations of the various contributions. In the case of antiferromagnetic materials, if one uses the theory of spin-waves based on the Heisenberg Hamiltonian, one obtains a magnon contribution CM(T) to Ctot, which is of the form CM(T)=BTn, where n=3 for a 3-D (spatial) antiferromagnet, n=2 for a 2-D (layer) antiferromagnet and n=1 for 1-D (linear) antiferromagnet. The paper presents the results of calculations of CM(T) is some linear, planar and spatial antiferromagnets with a view to investigating, inter-alia, the validity of the power laws in these materials.