Phenomenology similar to the non-reciprocal charge transport violating Onsager's reciprocity relations can develop in directionally inhomogeneous conducting films with non-uniform 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 are 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 10-103 times higher than in their unidirectional magnetoresistance analogues.