  In this work, IrMn$_{3}$/insulating-Y$_{3}$Fe$_{5}$O$_{12}$ exchange-biased
bilayers are studied. The behavior of the net magnetic moment $\Delta m_{AFM}$
in the antiferromagnet is directly probed by anomalous and planar Hall effects,
and anisotropic magnetoresistance. The $\Delta m_{AFM}$ is proved to come from
the interfacial uncompensated magnetic moment. We demonstrate that the exchange
bias and rotational hysteresis are induced by the irreversible switching of the
$\Delta m_{AFM}$. In the training effect, the $\Delta m_{AFM}$ changes
continuously. This work highlights the fundamental role of the $\Delta m_{AFM}$
in the exchange bias and facilitates the manipulation of antiferromagnetic
spintronic devices.
