  The influence of uniaxial single-ion anisotropy -DSz^2 on the magnetic and
thermal properties of Heisenberg antiferromagnets (AFMs) is investigated. The
uniaxial anisotropy is treated exactly and the Heisenberg interactions are
treated within unified molecular field theory (MFT) [Phys. Rev. B 91, 064427
(1915)], where thermodynamic variables are expressed in terms of directly
measurable parameters. The properties of collinear AFMs with ordering along the
z axis (D > 0) in applied fields Hz = 0 are calculated versus D and temperature
T. The high-field average magnetization per spin muz(Hz,D,T) is found, and the
critical field Hc(D,T) is derived at which the second-order AFM to PM phase
transition occurs. The magnetic properties of the spin-flop (SF) phase are
calculated, including the zero-field properties TN(D) and mu(D,T). The
high-field muz(Hz,D,T) is determined, together with the associated spin-flop
field HSF(D,T) at which a second-order SF to PM phase transition occurs. The
free energies of the AFM, SF and PM phases are derived from which Hz-T phase
diagrams are constructed. For a certain combination of parameters we find a
topologically distinct phase diagram where a spin-flop bubble occurs at finite
Hz and T. Also calculated are properties arising from a perpendicular magnetic
field. In addition to the above results for D > 0, some properties with D < 0
are determined. In order to compare the properties of the above spin systems
with those of noninteracting systems with DSz^2 uniaxial anisotropy with either
sign of D, an Appendix is included in which results for the thermal and
magnetic properties of such noninteracting spin systems are provided.
