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.

10 pages, 5 figures