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 H-z = 0 are calculated versus D and temperature T, including the ordered moment mu, the Neel temperature T-N, the magnetic entropy, internal energy, heat capacity, and the anisotropic magnetic susceptibilities chi(vertical bar vertical bar) and chi(perpendicular to) in the paramagnetic (PM) and AFM states. The high-field average magnetization per spin mu(z)(H-z, D, T) is found, and the critical field H-c(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 T-N(D) and mu(D, T). The high-field mu(z) (H-z, D, T) is determined, together with the associated spin-flop field H-SF(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 H-z - T phase diagrams are constructed. For f(J) = -1 and -0.75, where f(J) = theta(pJ) /T-NJ and theta(pJ) and T-NJ are the Weiss temperature in the Curie-Weiss law and the Neel temperature due to exchange interactions alone, respectively, phase diagrams in the H-z - T plane similar to previous results are obtained. However, for f(J) = 0 we find a topologically different phase diagram where a spin-flop bubble with PM and AFM boundaries occurs at finite H-z and T. Also calculated are properties arising from a perpendicular magnetic field, including the perpendicular susceptibility chi(perpendicular to)(D, T), the associated effective torque at low fields arising from the -DSz2 term in the Hamiltonian, the high-field perpendicular magnetization mu(perpendicular to) and the perpendicular critical field H-c perpendicular to at which the second-order AFM to PM phase transition occurs. In addition to the above results for D > 0, the T-N(D) and ordered moment mu(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.