Influence of uniaxial single-ion anisotropy on the magnetic and thermal properties of Heisenberg antiferromagnets within unified molecular field theory

The influence of uniaxial single-ion anisotropy -DSz² 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 (2015)], 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 field Hz=0 are calculated versus D and temperature T, including the ordered moment μ, the N\'eel temperature TN, the magnetic entropy, internal energy, heat capacity, and the anisotropic magnetic susceptibilities χ_∥ and χ_⊥ in the paramagnetic (PM) and AFM states. The high-field average magnetization per spin μz(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 μ(D,T). The high-field μz(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 fJ=-1 and -0.75, where fJ=θpJ/TNJ and θpJ and TNJ are the Weiss temperature in the Curie-Weiss law and the N\'eel temperature due to exchange interactions alone, respectively, phase diagrams in the Hz-T plane similar to previous results are obtained. However, for fJ=0 we find a topologically different phase diagram where a spin-flop bubble with PM and AFM boundaries occurs at finite Hz and T. Also calculated are properties arising from a perpendicular magnetic field, including the perpendicular susceptibility χ_⊥(D,T), the associated effective torque at low fields arising from the -DSz² term in the Hamiltonian, the high-field perpendicular magnetization μ_⊥, and the perpendicular critical field H_c⊥ at which the second-order AFM to PM phase transition occurs. In addition to the above results for $D>0$, the TN(D) and ordered moment μ(T,D) for collinear AFM ordering along the x axis with $D<0$ are determined. In order to compare the properties of the above spin systems with those of noninteracting systems with -DSz² uniaxial anisotropy with either sign of D, Supplemental Material is provided in which results for the thermal and magnetic properties of such noninteracting spin systems are given.