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We study field-induced phase transitions of the minimal exchange modelproposed earlier for BaCo$_2$(AsO$_4$)$_2$, a candidate for Kitaev honeycombmodel, using numerical minimization of classical spin clusters. We show thatexperimentally observed sequence of step-like transitions in magnetic field isrealized in the phase diagram of the minimal model. Surprisingly, intermediateup-up-down plateau phase is stabilized only in the proximity of adouble-zigzag$-$zigzag phase boundary. We systematically map out the region ofstability of experimentally observed cascade of transitions and argue thatBaCo$_2$(AsO$_4$)$_2$ exchange parameters are close to a region of strong phasecompetition, which can explain suppressed saturation field.

Proximity-induced sequence of field transitions in Kitaev candidate BaCo$_2$(AsO$_4$)$_2$