  We suggest coherent switching of canted antiferromagnetic (AFM) spins using
spin-orbit torque (SOT) in small magnet. The magnetic system of orthoferrite
features biaxial easy anisotropy and the Dzyaloshinskii Moriya interaction,
which is perpendicular to the easy axes and therefore creates weak
magnetization (m). A damping-like component of the SOT induces N\'eel
reorientation along one of the easy axes and then exerts torque on m, leading
to tilting of the N\'eel order l. The torque on the magnetization becomes
stronger due to coupling with the induced Oersted field or the field-like
component of the SOT, enhancing the tilting of l. Therefore, l is found to
experience deterministic switching after the SOT is turned off. Based upon both
numerical and analytical analysis of the coherent switching, XOR logic gates
are also found to be implemented in a single magnetic layer. In addition, we
investigate how magnetic parameters affect the critical reorientation angle and
current density in a simple layered structure of platinum and a canted AFM. Our
findings are expected to provide an alternative spin-switching mechanism for
ultrafast applications such as spin logic and electronic devices.
