A sensor for sensing an external magnetic field along a sensing direction comprises a sensor bridge. The sensor bridge has a first sensor leg that includes a first magnetoresistive sense element and a second sensor leg that includes a second magnetoresistive sense element. The first and second sense elements have respective first and second pinned layers having the same reference magnetization. The first and second sense elements have respective first and second sense layers, each self-biased to have a first sense magnetization. A permanent magnet layer is proximate the second sense element. In the absence of an external magnetic field, the permanent magnet layer magnetically biases the first sense magnetization of the second sense layer produce a second sense magnetization of the second sense layer that differs from the first sense magnetization, and the first sense layer of the first sense element retains the first sense magnetization.