Electrical Switching of Tristate Antiferromagnetic Néel Order in <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mi>α</mml:mi><mml:mtext>−</mml:mtext><mml:msub><mml:mrow><mml:mi>Fe</mml:mi></mml:mrow><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msub><mml:msub><mml:mrow><mml:mi mathvariant="normal">O</mml:mi></mml:mrow><mml:mrow><mml:mn>3</mml:mn></mml:mrow></mml:msub></mml:mrow></mml:math> Epitaxial Films

We demonstrate nondecaying, steplike electrical switching of tristate N\'eel order in $\mathrm{Pt}/\ensuremath{\alpha}\text{\ensuremath{-}}{\mathrm{Fe}}_{2}{\mathrm{O}}_{3}$ bilayers detected by the spin-Hall induced anomalous Hall effect. The as-grown $\mathrm{Pt}/\ensuremath{\alpha}\text{\ensuremath{-}}{\mathrm{Fe}}_{2}{\mathrm{O}}_{3}$ bilayers exhibit sawtooth switching behavior generated by current pulses. After annealing by a high pulse current, the Hall signals reveal single-pulse saturated, nondecaying, steplike switching. Together with control experiments, we show that the sawtooth switching is due to an artifact of Pt while the actual spin-orbit torque induced antiferromagnetic switching is steplike. Our Monte Carlo simulations explain the switching behavior of $\ensuremath{\alpha}\text{\ensuremath{-}}{\mathrm{Fe}}_{2}{\mathrm{O}}_{3}$ N\'eel order among three in-plane easy axes.