Frequency Modulation and Voltage Locking of the Voltage Controlled Spin Oscillators (VCSOs)

The oscillating frequency of typical Spin Torque Nano Oscillators (STNOs) can be modulated by injected DC current or bias magnetic field. And phase locking of STNOs to an external Radio Frequency (RF) signal can be imposed by AC current or RF bias magnetic field. However, in this study, we have proposed a Voltage Controlled Spin Oscillators (VCSOs) by introducing Voltage Controlled Magnetic Anisotropy (VCMA) effect. The oscillating frequency of VCSOs can be modulated by VCMA voltage as well as injected DC current. Furthermore, we have shown a novel locking mechanism caused by AC VCMA voltage. Both the frequency modulation and voltage locking mechanism are analyzed theoretically by Nonlinear Auto-oscillator theory and verified by numerical simulation. At last, we proposed that by utilizing negative capacitance material to enhance VCMA effect, the locking range for voltage locking can be expanded thus may lead to easy mutual synchronization of multiple VCSOs.