  Electrical detection of the 180 deg spin reversal, which is the basis of the
operation of ferromagnetic memories, is among the outstanding challenges in the
research of antiferromagnetic spintronics. Analogous effects to the
ferromagnetic giant or tunneling magnetoresistance have not yet been realized
in antiferromagnetic multilayers. Anomalous Hall effect (AHE), which has been
recently employed for spin reversal detection in non-collinear
antiferromagnets, is limited to materials that crystalize in ferromagnetic
symmetry groups. Here we demonstrate electrical detection of the 180 deg N\'eel
vector reversal in CuMnAs which comprises two collinear spin sublattices and
belongs to an antiferromagnetic symmetry group with no net magnetic moment. We
detect the spin reversal by measuring a second-order magnetotransport
coefficient whose presence is allowed in systems with broken space inversion
symmetry. The phenomenology of the non-linear transport effect we observe in
CuMnAs is consistent with a microscopic scenario combining anisotropic
magneto-resistance (AMR) with a transient tilt of the N\'eel vector due to a
current-induced, staggered spin-orbit field. We use the same staggered
spin-orbit field, but of a higher amplitude, for the electrical switching
between reversed antiferromagnetic states which are stable and show no sign of
decay over 25 hour probing times.
