Deeply nonlinear magnon-photon hybrid excitation

We investigate the microwave-power dependence of magnon-photon coupling in a yttrium iron garnet-sphere/split-ring-resonator hybrid system at room temperature and demonstrate that nonlinear spin-wave interactions suppress the coupling through power-induced dissipation of magnetostatic modes. At low microwave power, the modes exhibit pronounced level repulsion, evidencing strong coupling to the microwave field. As the power increases, however, magnon linewidth broadening progressively weakens the coupling and ultimately suppresses it entirely below a threshold external magnetic field. We show that this behavior originates from Suhl’s first-order instability: magnetostatic modes, which couple to the resonator, parametrically excites two counter-propagating magnons at half its frequency, causing modes below the threshold external magnetic field to vanish. In contrast, magnon modes above the threshold field remain robust even at high power, as the instability criterion is not satisfied in that regime. These results reveal a well-defined nonlinear boundary for magnon-photon coupled systems and highlight a favorable regime for exploiting nonlinear magnonics for frequency conversion, switching, and other functional magnonic devices.

💡 Research Summary

In this work the authors investigate how strong microwave driving influences the coupling between magnons in a yttrium‑iron‑garnet (YIG) sphere and photons in a split‑ring resonator (SRR) at room temperature. The hybrid device consists of a 0.75 mm YIG sphere placed at the centre of a copper‑lined SRR fabricated on a high‑dielectric substrate. A static magnetic field is applied perpendicular to the feed line, and the microwave power supplied by a vector network analyzer is varied from –20 dBm to +13 dBm while recording the S21 transmission as a function of frequency and field.

At low power (–20 dBm) the transmission spectra display clear avoided‑crossing features between the SRR mode (~2.5 GHz) and the uniform (1,1) magnon mode of the sphere. By fitting these anticrossings with a coupled‑harmonic‑oscillator model the authors extract a coupling strength g≈70 MHz, which exceeds both the resonator loss rate (κp≈38 MHz) and the magnon loss rate (κm≈6 MHz). Consequently the cooperativity C=g²/(κpκm) is greater than one, confirming that the system operates in the strong‑coupling regime.

When the microwave power is increased, the magnon linewidth broadens dramatically. At –5 dBm the avoided‑crossing gap narrows, at 0 dBm the two branches essentially merge, and at +10 dBm the magnon resonances disappear entirely, leaving only the bare SRR response. Time‑domain analysis (inverse Fourier transform of the S21 data) shows pronounced Rabi‑like oscillations at low power, which are progressively damped and finally vanish at high power, indicating loss of coherent energy exchange.

The authors attribute this power‑dependent suppression to the first‑order Suhl instability (three‑magnon splitting). In this process the driven uniform magnon mode parametrically decays into a pair of counter‑propagating magnons at half its frequency. The instability threshold field h_thr is given by Eq. (1) and the condition ωp < ωcr (Eq. 2) must be satisfied. For a spherical YIG sample the critical frequency ωcr≈2ωM/3≈3.27 GHz (μ0Ms≈178 mT). Because the SRR resonance is at 2.5 GHz, the condition ωp/2 lies above the minimum of the spin‑wave dispersion only for external fields around 87 mT. In this regime the uniform mode can undergo three‑magnon splitting, leading to strong nonlinear damping and eventual disappearance of the magnon resonance once the drive exceeds the threshold power.

Conversely, at higher fields (e.g., 130 mT) the uniform mode frequency lies within the spin‑wave continuum and ωp/2 falls below the dispersion minimum, so the Suhl instability criterion is not met. Consequently the magnon linewidth remains essentially unchanged with power and the magnon‑photon coupling persists even at the highest drive levels.

Additional observations include a “fold‑over” shift of the magnon resonance toward higher fields and an asymmetric lineshape at large powers, both hallmarks of nonlinear magnetization dynamics when the precession angle becomes large. The authors also note a smaller avoided crossing near 114 mT that is insensitive to power, further confirming the role of the instability condition.

Overall, the paper establishes a clear nonlinear boundary for magnon‑photon hybrid systems: below a critical external field and above a critical microwave power, the first‑order Suhl instability destroys the magnon mode and suppresses coupling; above the critical field the instability is absent and strong coupling survives. This delineation provides a practical guideline for designing magnon‑based nonlinear devices such as power‑controlled switches, frequency converters, or memory elements that exploit the abrupt transition between coupled and decoupled regimes.