  The ability to manipulate antiferromagnetic (AF) moments is a key requirement
for the emerging field of antiferromagnetic spintronics. Electrical switching
of bi-state AF moments has been demonstrated in metallic AFs, CuMnAs and
Mn$_2$Au. Recently, current-induced "saw-tooth" shaped Hall resistance was
reported in Pt/NiO bilayers, while its mechanism is under debate. Here, we
report the first demonstration of convincing, non-decaying, step-like
electrical switching of tri-state N\'eel order in Pt/$\alpha$-Fe$_2$O$_3$
bilayers. Our experimental data, together with Monte-Carlo simulations, reveal
the clear mechanism of the switching behavior of $\alpha$-Fe$_2$O$_3$ N\'eel
order among three stable states. We also show that the observed "saw-tooth"
Hall resistance is due to an artifact of Pt, not AF switching, while the
signature of AF switching is step-like Hall signals. This demonstration of
electrical control of magnetic moments in AF insulator (AFI) films will greatly
expand the scope of AF spintronics by leveraging the large family of AFIs.
