High-frequency spin-torque nano-oscillators based on bilayer antiferromagnetically coupled skyrmioniums

We propose and investigate a high-frequency spin-torque nano-oscillator (STNO) based on a bilayer structure hosting antiferromagnetically coupled skyrmioniums. Utilizing micromagnetic simulations and analytical modeling, we demonstrate that such bilayer skyrmioniums exhibit stable, field-free circular motion with enhanced frequency performance due to the suppression of the skyrmion Hall effect and improved structural robustness. We derive a modified Thiele equation incorporating effective mass and interlayer coupling effects to quantitatively describe the dynamics. Our results show that the oscillation frequency increases approximately linearly with the current density, reaching up to 8.7 GHz for a single skyrmionium pair. Furthermore, we explore multi-skyrmionium configurations and show that the oscillation frequency can be boosted to 27 GHz with five coupled pairs before destabilization occurs. These findings suggest that bilayer skyrmionium-based STNOs offer a promising platform for tunable, high-frequency spintronic applications without the need for external magnetic fields.