We consider the current-induced dynamics of insulating antiferromagnets in a
spin Hall geometry. Sufficiently large in-plane currents perpendicular to the
N\'{e}el order trigger spontaneous oscillations at frequencies between the
acoustic and the optical eigenmodes. The direction of the driving current
determines the chirality of the excitation. When the current exceeds a
threshold, the combined effect of spin pumping and current-induced torques
introduces a dynamic feedback that sustains steady-state oscillations with
amplitudes controllable via the applied current. The ac voltage output is
calculated numerically as a function of the dc current input for different
feedback strengths. Our findings open a route towards terahertz
antiferromagnetic spin-torque oscillators.Comment: 5+ pages, 4 figure
