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

## TL;DR

This paper introduces Voltage Controlled Spin Oscillators (VCSOs) utilizing VCMA effect, enabling frequency modulation and voltage locking, with potential for enhanced synchronization using negative capacitance materials, supported by theoretical analysis and simulations.

## Contribution

It proposes a novel VCSO design with voltage-controlled frequency modulation and locking mechanisms, expanding the control capabilities of spin oscillators.

## Key findings

- VCSOs can be modulated by VCMA voltage and DC current.
- A new voltage locking mechanism via AC VCMA voltage is demonstrated.
- Negative capacitance materials can expand locking range for synchronization.

## Abstract

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.