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