Charge conservation in spin-torque oscillators leads to a self-induced torque

Spin-torque oscillators are conventionally described by the Landau-Lifshitz-Gilbert-Slonczewski (LLGS) equation. However, at the onset of oscillations, the predictions of the conventional LLGS equation differ qualitatively from experimental results and thus appear to be incomplete. In this work we show that taking charge conservation into account leads to a previously overlooked self-induced torque, which modifies the LLGS equation. We show that the self-induced torque originates from the pumping current that a precessing magnetization drives through a magnetic tunnel junction. To illustrate the importance of the self-induced torque, we consider an in-plane magnetized nanopillar, where it gives clear qualitative corrections to the conventional LLGS description.