  Phenomenology similar to the nonreciprocal charge transport violating
Onsagers reciprocity relations can develop in directionally inhomogeneous
conducting films with nonuniform Hall coefficient along the current trajectory.
The effect is demonstrated in ferromagnetic CoPd films and analyzed in
comparison with the unidirectional magnetoresistance phenomena. We suggest to
use an engineered inhomogeneity for spintronics applications and present the
concept of mixed symmetry Hall devices in which transverse to current Hall
signal is measured in a longitudinal contacts arrangement. Magnetization
reversal and memory detection is demonstrated in the three terminal and the
partitioned normal metal-ferromagnet (NM - FM) device designs. Multi-bit memory
is realized in the partitioned FM-NM-FM structure. The relative amplitude of
the antisymmetric signal in the engineered ferromagnetic devices is few percent
which is 10 to 1000 times higher than in their unidirectional magnetoresistance
analogues.
