  Currents can induce spin excitations in antiferromagnets, even when they are
insulating. We investigate how spin transfer can cause antiferromagnetic
resonance in bilayers and trilayers that consist of one antiferromagnetic
insulator and one or two metals. An ac voltage applied to the metal generates a
spin Hall current that drives the magnetic moments in the antiferromagnet. We
consider excitation of the macrospin mode and of transverse standing-spin-wave
modes. By solving the Landau-Lifshitz-Gilbert equation in the antiferromagnetic
insulator and the spin-diffusion equation in the normal metal, we derive
analytical expressions for the spin-Hall-magnetoresistance and spin-pumping
inverse-spin-Hall dc voltages. In bilayers, the two contributions compensate
each other and cannot easily be distinguished. We present numerical results for
a MnF$_2|$Pt bilayer. Trilayers facilitate separation of the
spin-Hall-magnetoresistance and spin-pumping voltages, thereby revealing more
information about the spin excitations. We also compute the decay of the pumped
spin current through the antiferromagnetic layer as a function of frequency and
the thickness of the antiferromagnetic layer.
