We propose theoretically a generalized memristive system based on controlled spin polarizations in giant magnetoresistive material using a feedback loop with classical Hall Effect. The dynamics can exhibit a memristive pinched hysteretic loop while it possesses a self-crossing knot not located at the origin. Additionally, a single-looped orbit can also be observed in the system. We provide a sufficient condition for the stability based on an estimation of the Floquet exponent. The analysis shows that the non-origin-crossing dynamics is generally permitted in a class of passive memory systems that are not subject to Ohm's Law. We further develope the prevailing homogeneous definition to a broadened concept of generalized heterogeneous memristive systems, permitting the self-crossing knot not located at the origin, and ultimately to the concept of compound memory electronic systems.