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Identifying the nature of a spin-flop (SFO) transition, first- orsecond-order (FO or SO), remains a major challenge in condensed-matter physicsdue to the technically undistinguishable effect of misalignment betweenapplied-field direction and the relevant antiferromagnetic (AFM) easy axis. Aclassical SFO transition is believed to be of FO in character. Here amean-field theoretical calculation endowed with AFM exchange interaction(\emph{J}), easy axis anisotropy ($\gamma$), uniaxial single-ion exchangeanisotropy (\emph{D}), and Zeeman coupling to a magnetic field parallel to theeasy axis unambiguously reveals that a SO SFO transition indeed exists byvirtue of its relatively lower free energy. Their equilibrium phase conditionsare found to be: $D \geq 0$ (FO); $-\frac{1}{2} \gamma < D < 0$ (SO). Comparednumerically to the associated AFM and spin-flip phases, the deduced SO SFOtransition results from a negative single-ion anisotropy which is restricted toa certain range by the anisotropic exchange interaction

A second-order spin-flop transition in collinear two-sublattice antiferromagnets