  Antiferromagnets are robust to external electric and magnetic fields, and
hence are seemingly uncontrollable. Recent studies, however, realized the
electrical manipulations of antiferromagnets by virtue of the antiferromagnetic
Edelstein effect. We present a general symmetry analysis of electrically
switchable antiferromagnets based on group-theoretical approaches. Furthermore,
we identify a direct relation between switchable antiferromagnets and the
ferrotoroidic order. The concept of the ferrotoroidic order clarifies the
unidirectional nature of switchable antiferromagnets and provides a criterion
for the controllability of antiferromagnets. The scheme paves a way for perfect
writing and reading of switchable antiferromagnets.
