Magnetoresistive devices can include a first and second sensor. Each of the first and second sensors can be configured to sense a first magnetic field component and a second magnetic field component. The first and second magnetic field components may be orthogonal to each other. Signals generated by the first and/or the second sensors can be used to determine local or global differentials of the magnetic field components. The first and/or the second sensors can each include four magnetoresistive sensors that can be connected in a Wheatstone bridge configuration. Further, the magnetoresistive devices can include magnets having a cavity formed therein, where the dimensions of the cavity are configured to reduce magnetic field conditions of a magnetic field in proximity to and/or within the cavity.