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 −DS2z 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 Néel 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 Néel 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 −DS2z term in the Hamiltonian, the high-field perpendicular magnetization μ⊥, and the perpendicular critical field Hc⊥ 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 −DS2z uniaxial anisotropy with either sign of D, Supplemental Material is provided in which results for the thermal and magnetic properties of such no