We study field-induced phase transitions of the minimal exchange model proposed earlier for ${\mathrm{BaCo}}_2{\left({\mathrm{AsO}}_4\right)}_2$, a candidate for the Kitaev honeycomb model, using numerical minimization of classical spin clusters. We show that an experimentally observed sequence of steplike transitions in magnetic field is realized in the phase diagram of the minimal model. Surprisingly, an intermediate up-up-down plateau phase is stabilized only in the proximity of a double-zigzag–zigzag phase boundary. We systematically map out the region of stability of an experimentally observed cascade of transitions and argue that ${\mathrm{BaCo}}_2{\left({\mathrm{AsO}}_4\right)}_2$ exchange parameters are close to a region of strong phase competition, which can explain the suppressed saturation field.

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• Magnetic phase transitions
• Quantum fluctuations & noise
• Spin valves
• Kitaev-Heisenberg model