Several possibilities exist here. I first considered thermoelectric effects and thought there might be some differential heating causing the effect. Besides Seebeck effect, consider Thompson effect combined with Hall effect.
If the effect disappears when the remnant magnetism is lost, it could point to a combination of Hall combined with other thermoelectric effect. Normalizing the ambient across the device will rule out thermal effects.
Best way to test would be with permanently applied electrodes and the assembly placed in a styrofoam insulated container. Differential thermals must be at a minimum, this would include heating from ambient light.
I am quite familiar with low level instrumentation in the uV area having designed a lot of thermocouple preamplifiers, linearizers and electronic reference junction compensators. There are many pitfalls to be avoided.
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