Direct Observation of Antimagnons with Inverted Dispersion

Problem and Context
Magnons, the bosonic quasi-particles representing spin-wave excitations, are central to low-power spintronic devices as they transfer spin information without charge transport. While conventional magnons are typically excited via microwave antennas or spin-orbit torques (SOTs) to drive auto-oscillations, their growth is often limited by dynamic instabilities and nonlinear scattering. Recent theoretical studies suggest that in magnetic systems with compensated perpendicular magnetic anisotropy (PMA), a negative damping torque can drive the magnetization into a dynamically stabilized, non-equilibrium reversed state. In this state, small-amplitude perturbations are predicted to form "antimagnons"—negative-energy spin waves characterized by an inverted dispersion relation. Despite theoretical predictions and indirect experimental signatures in confined systems, direct spectroscopic evidence of antimagnons with inverted dispersion in extended magnetic layers driven by SOT has remained elusive.

Methodology
The authors investigated an ultrathin (4 nm) bismuth-substituted yttrium iron garnet (BiYIG) film grown on a (111)-oriented yttrium scandium gallium garnet substrate. The PMA was engineered via tensile strain to nearly compensate the demagnetizing field, enabling large-angle circular precession. A 5 nm platinum (Pt) bar was deposited on the BiYIG to serve as a source of spin-orbit torque. An electrical direct current ($j_{dc}$) was applied along the Pt bar, generating a spin current via the spin Hall effect that exerts an antidamping torque on the underlying BiYIG.

To characterize the spin-wave dynamics, the researchers employed wavevector-resolved Brillouin light scattering (BLS) spectroscopy. By varying the laser incident angle, they tuned the detection wavevector ($k$) in the plane of the film. Measurements were conducted across three distinct regimes defined by the current density: (1) the quasi-equilibrium thermal magnon regime, (2) the auto-oscillation regime, and (3) the high-current regime where the magnetization is dynamically reversed. The experimental data were compared with theoretical calculations based on the Landau–Lifshitz–Gilbert (LLG) equation and micromagnetic simulations using MuMax3.

Key Results

1. Regime Transitions: As the current density increased, the system transitioned from thermal magnons to auto-oscillation at a threshold of $\sim 0.9 \times 10^7$ A/cm$^2$. Upon further increasing the current to a secondary threshold of $\sim 1.2 \times 10^7$ A/cm$^2$, the resonance frequency dropped abruptly from $\sim 2.2$ GHz to $\sim 1.7$ GHz, signaling the onset of a dynamically stabilized reversed magnetic state.
2. Inverted Dispersion: The most significant finding is the dispersion relation of the spin waves in the reversed state. While conventional magnons and auto-oscillating magnons exhibited a positive curvature (frequency increasing with wavevector), the high-current state displayed a sharp, inverted dispersion where the frequency decreased as the wavevector increased. This "downward" curvature matches the theoretical signature of antimagnons.
3. Quantitative Agreement: The experimental dispersion in the antimagnon regime was fitted using the theoretical model $f(k) = -\frac{\gamma}{2\pi} Dk^2 + \Delta$, yielding an exchange stiffness ($A = 2.8$ pJ/m) consistent with the magnon regime. The ferromagnetic resonance frequency ($\Delta \approx 1.89$ GHz) was slightly shifted due to Joule heating effects.
4. Coexistence at Threshold: Near the critical current threshold ($\sim 6.35$ mA), the BLS spectra revealed the simultaneous presence of two distinct peaks: one corresponding to conventional magnons and the other to antimagnons. This coexistence, observed experimentally and reproduced in micromagnetic simulations, suggests a chaotic regime where the magnetization texture is spatially inhomogeneous, containing domains of both aligned and reversed magnetization.
5. High-Current Behavior: At currents significantly above the threshold ($\sim 1.4 \times 10^7$ A/cm$^2$), the BLS intensity decreased, indicating that the system re-enters a quasi-linear regime with small-cone precession around the reversed field direction, consistent with the formation of a stable antimagnon state.

Significance and Claims
The paper claims to provide the first direct spectroscopic evidence of antimagnons with inverted dispersion in a magnetic insulator driven by SOT. By establishing the existence of these negative-energy excitations, the work validates theoretical predictions regarding dynamically stabilized reversed magnetic states. The authors posit that this discovery serves as a foundational step toward the emerging field of "antimagnonics." They suggest that the ability to generate and control antimagnons opens the door to exploring novel phenomena rooted in magnon-antimagnon coupling, specifically citing magnon amplification via superradiance and magnon-antimagnon entanglement. Furthermore, the observation of coexisting magnon and antimagnon phases at the critical threshold provides a unique platform for studying non-equilibrium magnetic dynamics beyond traditional spintronic systems.