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Upon femtosecond-laser stimulation, generally materials are expected torecover back to their thermal-equilibrium conditions, with only a fewexceptions reported. Here we demonstrate that deviation from thethermal-equilibrium pathway can be induced in canonical 3Dantiferromagnetically (AFM) ordered Sr$_2$IrO$_4$ by a single 100-fs-laserpulse, appearing as losing long-range magnetic correlation along one directioninto a glassy condition. We further discover a `critical-threshold ordering'behavior for fluence above approximately 12 mJ/cm$^2$ which we show correspondsto the smallest thermodynamically stable $c$-axis correlation length needed tomaintain long-range quasi-two-dimensional AFM order. We suggest that thisbehavior arises from the crystalline anisotropy of the magnetic-exchangeparameters in Sr$_2$IrO$_4$, whose strengths are associated with distinctlydifferent timescales. As a result, they play out very differently in theultrafast recovery processes, compared with the thermal equilibrium evolution.Thus, our observations are expected to be relevant to a wide range of problemsin the nonequilibrium behavior of low-dimensional magnets and other relatedordering phenomena.

Single laser pulse driven thermal limit of the quasi-two dimensional magnetic ordering in Sr$_2$IrO$_4$