  We report on the switching of the in-plane magnetization of thin yttrium iron
garnet (YIG)/Pt bilayers induced by an electrical current. The switching is
either field-induced and assisted by a dc current, or current-induced and
assisted by a static magnetic field. The reversal of the magnetization occurs
at a current density as low as $10^5$~A/cm$^{2}$ and magnetic fields of $\sim
40$~$\mu$T, two orders of magnitude smaller than in ferromagnetic metals,
consistently with the weak uniaxial anisotropy of the YIG layers. We use the
transverse component of the spin Hall magnetoresistance to sense the magnetic
orientation of YIG while sweeping the current. Our measurements and simulations
reveal that the current-induced effective field responsible for switching is
due to the Oersted field generated by the current flowing in the Pt layer
rather than by spin-orbit torques, and that the switching efficiency is
influenced by pinning of the magnetic domains.
