Numerical studies of the fundamental efficiency limit of a resonant in-plane spin-torque diode

Harvesting of the ambient electromagnetic field energy by converting the oscillating current into a direct one using a spin-torque diode is a very important topic in studies of possible methods for green energy production. In this paper we perform detailed numerical studies of such energy harvesting using an ``in-plane'' resonant spin-torque diode (STD). In order to accelerate the corresponding modeling, we first suggest two new simulation protocols which enable one to compute the frequency dependence of the rectified (dc) voltage in a single simulation run. Both methods provide a very high acceleration degree and allow one to quickly obtain the desired results in a wide range of STD parameters. In the main part of this paper we investigate the fundamental limit of STD efficiency, suggesting that the dc voltage is maximized by applying a constant external field. We demonstrate that this efficiency may be greatly enhanced when the applied field is close to the switching field of the STD free layer. Keeping in mind that the energy barrier preventing the switching of the STD magnetization to its opposite equilibrium position should still be high enough, we show that an ac current flowing through the STD affects this barrier very weakly (as opposed to the dc current). This feature allows us to predict the field values for which the output dc voltage is much larger than without an external field, still keeping the field far away from the switching point to ensure thermal stability. Our results can be employed to optimize the STD working conditions and to predict the maximal voltage that could be achieved with this relatively simple STD design (standard ``in-plane'' multilayer nanoelements).