Behavior of Circular Field-free Current-driven Easy-cone State Oscillator under the Presence of Thermal Noise

Second order anisotropy can create conical magnetization states which allows for field-free current driven magnetic precession in GHz ranges. In this work, we evaluate the impact of thermal noise in such oscillators. We find that while the anisotropy ratio $|\mathrm{H}_{\mathrm{K}2}/\mathrm{H}_{\mathrm{K}1}^{\mathrm{e}\mathrm{f}\mathrm{f}}|$, determines the maximum frequency - a high value of negative effective first order anisotropy is crucial for stable oscillations. Furthermore, field-free oscillations can be obtained in circular in-plane magnets where the creation of cone state is not a necessary condition.