Photon-Magnon Synchronization Modes

• PMSMs are hybrid modes where photonic and magnonic degrees of freedom oscillate synchronously, evident through avoided crossings, level attraction, and self-oscillation phenomena.
• They are realized across various platforms—from superconducting resonators to optomagnonic networks—with tunability achieved via geometric, dissipative, and nonlinear controls.
• Advanced PMSM techniques enable enhanced magnetometer sensitivity, quantum squeezing, and entanglement, paving the way for next-generation spin–photon devices.

Photon–Magnon Synchronization Modes (PMSMs) are hybrid dynamical states in which photonic and magnonic degrees of freedom evolve at a common eigenfrequency with a fixed phase relation, or, in active cavity–magnonic systems, self-oscillation modes whose frequency and phase are jointly determined by a cavity photon mode and a magnon mode. In current literature, the term is used both explicitly and interpretively: in cavity magnonics it commonly denotes magnon–polariton normal modes generated by coherent magnon–photon coupling, whereas in nonlinear active platforms it can denote cusp-associated self-oscillation branches with unusually large magnetic responsivity (Li et al., 2023, Mi et al., 9 Jul 2025).

1. Conceptual scope and terminological usage

PMSMs are not a single universally standardized object. A practical taxonomy is that the term covers three closely related regimes. First, in linear cavity magnonics, PMSMs are the hybridized normal modes of a photon oscillator and a magnon oscillator, i.e. magnon–polaritons, whose frequency splitting and avoided crossing indicate coherent synchronization. Second, in non-Hermitian or lossy settings, PMSMs include dissipative or off-resonant synchronization configurations in which frequency splitting can disappear while linewidths, decay rates, or level attraction remain strongly modified. Third, in active cavity–magnonic systems, PMSMs can denote nonlinear self-sustained oscillation modes in which cavity gain, magnon dynamics, and coupling phase jointly determine the oscillation frequency and stability (Li et al., 2023, Joseph et al., 2 Dec 2025, Mi et al., 9 Jul 2025).

In the linear microwave setting, the basic model is the bilinear Hamiltonian

$$H = \hbar\omega_m b^\dagger b + \hbar\omega_p a^\dagger a + \hbar g(a^\dagger b + a b^\dagger),$$

with hybrid eigenfrequencies

$$\omega^{mp}_\pm = \frac{\omega_m + \omega_p}{2} \pm \sqrt{\frac{(\omega_m-\omega_p)^2}{4}+g^2}.$$

Here the synchronized state is a normal mode: photon and magnon amplitudes oscillate at a common frequency set by an eigenvector of the coupled problem (Li et al., 2023).

In several later works, this linear notion is generalized rather than abandoned. Planar cavities with multiple orthogonal photon modes support distinct synchronization configurations depending on polarization and geometry; remote cavity–magnon systems support frequency locking mediated by a lossy auxiliary mode; and optomagnonic arrays support complete synchronization, $\phi$-synchronization, and quantum phase synchronization between distant magnons through photon hopping (Maurya et al., 6 May 2026, Joseph et al., 2 Dec 2025, Xue et al., 29 Jun 2026). This suggests that PMSMs are best understood as a family of hybrid photon–magnon eigenmodes and synchronization regimes rather than a single narrowly defined excitation.

2. Coherent hybridization and normal-mode PMSMs

The canonical PMSM is the coherently hybridized photon–magnon mode identified by avoided level crossing. In the layered hybrid perovskite antiferromagnet Cu‑EA coupled to a superconducting resonator, the resonator mode lies at $\omega_p/2\pi \approx 3.5\ \text{GHz}$, and at $5.5\ \text{K}$ fitting of the anticrossing gives $g/2\pi = 45\ \text{MHz}$, $\kappa_m/2\pi \simeq 50\ \text{MHz}$, $\kappa_p/2\pi \simeq 2.7\ \text{MHz}$, and cooperativity $C \approx 15$. The system is therefore in, or very close to, strong coherent coupling, so the mixed photon–magnon modes are well defined and energy oscillates coherently between field and magnons (Li et al., 2023).

Mode selectivity is often geometric. In the Cu‑EA coplanar-waveguide device, $h_{\rm rf}^y$ and $$\omega^{mp}_\pm = \frac{\omega_m + \omega_p}{2} \pm \sqrt{\frac{(\omega_m-\omega_p)^2}{4}+g^2}.$$0 couple differently to acoustic and optical antiferromagnetic modes depending on field orientation, so either only the acoustic mode or both acoustic and optical modes can enter the PMSM manifold (Li et al., 2023). In a planar electric‑LC resonator integrated with YIG, rotating the resonator selects between two orthogonal photon modes at $$\omega^{mp}_\pm = \frac{\omega_m + \omega_p}{2} \pm \sqrt{\frac{(\omega_m-\omega_p)^2}{4}+g^2}.$$1 and $$\omega^{mp}_\pm = \frac{\omega_m + \omega_p}{2} \pm \sqrt{\frac{(\omega_m-\omega_p)^2}{4}+g^2}.$$2. At $$\omega^{mp}_\pm = \frac{\omega_m + \omega_p}{2} \pm \sqrt{\frac{(\omega_m-\omega_p)^2}{4}+g^2}.$$3, only the lower-frequency photon mode is excited and the measured coupling is $$\omega^{mp}_\pm = \frac{\omega_m + \omega_p}{2} \pm \sqrt{\frac{(\omega_m-\omega_p)^2}{4}+g^2}.$$4; at intermediate angles both channels are active, with $$\omega^{mp}_\pm = \frac{\omega_m + \omega_p}{2} \pm \sqrt{\frac{(\omega_m-\omega_p)^2}{4}+g^2}.$$5 increasing from $$\omega^{mp}_\pm = \frac{\omega_m + \omega_p}{2} \pm \sqrt{\frac{(\omega_m-\omega_p)^2}{4}+g^2}.$$6 to $$\omega^{mp}_\pm = \frac{\omega_m + \omega_p}{2} \pm \sqrt{\frac{(\omega_m-\omega_p)^2}{4}+g^2}.$$7 over $$\omega^{mp}_\pm = \frac{\omega_m + \omega_p}{2} \pm \sqrt{\frac{(\omega_m-\omega_p)^2}{4}+g^2}.$$8 and $$\omega^{mp}_\pm = \frac{\omega_m + \omega_p}{2} \pm \sqrt{\frac{(\omega_m-\omega_p)^2}{4}+g^2}.$$9 decreasing from $\phi$0 to $\phi$1 over $\phi$2. The reported cooperativities are $\phi$3 and $\phi$4, so both channels lie in the strong-coupling regime, but with markedly different angular dependence (Maurya et al., 6 May 2026).

At higher frequencies and in superconducting heterostructures, coherent PMSMs extend into the ultrastrong-coupling regime. In superconductor/antiferromagnet/superconductor structures, the Swihart photon mode hybridizes with antiferromagnetic resonances at terahertz frequencies, and the coupling constant is predicted to be $\phi$5, exceeding $\phi$6 of the antiferromagnetic resonant frequency. At zero field only the lower antiferromagnetic mode couples to the photon, whereas a magnetic field activates coupling for both antiferromagnetic modes, producing a richer PMSM manifold with field-controlled mode activation (Gordeeva et al., 28 Oct 2025). Closely related superconducting ferromagnetic nanostructures also realize ultrastrong magnon–photon coupling, ultra-high cooperativity, and magnon–polariton modes with very large group velocities, providing a quantum description of PMSMs beyond the rotating-wave approximation (Silaev, 2022).

3. Dissipative, switched, and spectrally gated PMSMs

A central misconception is that PMSMs are exhausted by coherent avoided crossings. Several systems show that synchronization can be switched, suppressed, or rendered purely dissipative while the underlying photon–magnon interaction remains active. In Cu‑EA, intrinsic Dzyaloshinskii–Moriya interaction produces a coherent magnon–magnon coupling $\phi$7 between acoustic and optical branches and opens a magnon band gap $\phi$8. Broadband FMR at $\phi$9 gives $\omega_p/2\pi \approx 3.5\ \text{GHz}$0, $\omega_p/2\pi \approx 3.5\ \text{GHz}$1, and $\omega_p/2\pi \approx 3.5\ \text{GHz}$2. Because both $\omega_p/2\pi \approx 3.5\ \text{GHz}$3 and $\omega_p/2\pi \approx 3.5\ \text{GHz}$4 decrease with temperature, the band-gap center can be swept through the fixed cavity frequency, producing an on–off–on switching of coherent PMSMs: for $\omega_p/2\pi \approx 3.5\ \text{GHz}$5 the gap lies below the cavity and avoided crossings are visible; for $\omega_p/2\pi \approx 3.5\ \text{GHz}$6 the cavity lies inside the gap and the extracted $\omega_p/2\pi \approx 3.5\ \text{GHz}$7 drops to zero; for $\omega_p/2\pi \approx 3.5\ \text{GHz}$8 hybridization reappears (Li et al., 2023).

Even in that “PMSM off” regime, residual interaction survives as linewidth broadening. The cavity couples off resonantly to magnon modes at $\omega_p/2\pi \approx 3.5\ \text{GHz}$9, yielding

$5.5\ \text{K}$0

Using a CPW resonator and a lumped-element resonator, the measured $5.5\ \text{K}$1 scales linearly with $5.5\ \text{K}$2, with slope $5.5\ \text{K}$3, and gives $5.5\ \text{K}$4, consistent with broadband FMR. In other words, absence of an avoided crossing does not imply absence of magnon–photon interaction; it can instead indicate spectrally blocked coherent synchronization with residual dissipative coupling (Li et al., 2023).

A related crossover appears in the planar HRR–YIG system designed to probe the Purcell effect. There, increasing the magnon damping constant from $5.5\ \text{K}$5 to $5.5\ \text{K}$6 drives $5.5\ \text{K}$7 from $5.5\ \text{K}$8 to $5.5\ \text{K}$9, while the extracted $g/2\pi = 45\ \text{MHz}$0 changes from $g/2\pi = 45\ \text{MHz}$1 to $g/2\pi = 45\ \text{MHz}$2. For $g/2\pi = 45\ \text{MHz}$3 and $g/2\pi = 45\ \text{MHz}$4, the condition $g/2\pi = 45\ \text{MHz}$5 is satisfied and the system enters the Purcell regime: the anticrossing in transmission diminishes, the hybrid peaks merge, and the HRR linewidth is enhanced through coupling to lossy magnons (Verma et al., 8 Jan 2025).

Dissipative PMSMs can also arise from non-Hermitian coupling mechanisms rather than merely from large loss. In a remote cavity–magnon system coupled through a heavily damped transmission-line mode, elimination of the auxiliary mode yields

$g/2\pi = 45\ \text{MHz}$6

which becomes purely imaginary in the strongly damped limit: $g/2\pi = 45\ \text{MHz}$7 The resulting effective Hamiltonian has off-diagonal elements $g/2\pi = 45\ \text{MHz}$8, producing level attraction, exceptional-point physics, and time-domain ring-down signatures in which the beating frequency collapses and the cavity and magnon become frequency-locked with different decay rates (Joseph et al., 2 Dec 2025). Earlier waveguide-cavity experiments identified the same qualitative distinction between coherent and dissipative photon–magnon coupling: coherent coupling yields level repulsion, whereas cavity-Lenz-effect coupling yields level attraction with coalescence of real frequencies and splitting of linewidths (Harder et al., 2018). In planar ISRR–YIG structures, changing the split-gap orientation similarly toggles between normal and “opposite” anti-crossing by controlling the relative amplitude $g/2\pi = 45\ \text{MHz}$9 and phase $\kappa_m/2\pi \simeq 50\ \text{MHz}$0 of microwave magnetic fields, so that the effective coupling $\kappa_m/2\pi \simeq 50\ \text{MHz}$1 becomes real or purely imaginary (Bhoi et al., 2019).

4. Nonlinear PMSMs, cusp points, and instability boundaries

In active cavity–magnonic systems, PMSMs are not merely passive hybrid modes but nonlinear self-oscillation states. In a planar three-port microwave cavity with gain and a $\kappa_m/2\pi \simeq 50\ \text{MHz}$2 YIG sphere, the cavity mode at $\kappa_m/2\pi \simeq 50\ \text{MHz}$3 and the magnon mode $\kappa_m/2\pi \simeq 50\ \text{MHz}$4 form a synchronized self-oscillation with common frequency $\kappa_m/2\pi \simeq 50\ \text{MHz}$5 and fixed relative phase $\kappa_m/2\pi \simeq 50\ \text{MHz}$6. The steady-state theory is reduced to

$\kappa_m/2\pi \simeq 50\ \text{MHz}$7

$\kappa_m/2\pi \simeq 50\ \text{MHz}$8

These equations admit bistability and cusp points where two saddle-node bifurcations coalesce (Mi et al., 9 Jul 2025).

Near such cusp points, the PMSM frequency becomes extraordinarily sensitive to magnetic field. The effective gyromagnetic ratio is $\kappa_m/2\pi \simeq 50\ \text{MHz}$9, and the reported enhancement reaches $\kappa_p/2\pi \simeq 2.7\ \text{MHz}$0 at the cusp point and $\kappa_p/2\pi \simeq 2.7\ \text{MHz}$1 for the sixth-order oscillating mode. The same platform supports emission linewidth narrowing to $\kappa_p/2\pi \simeq 2.7\ \text{MHz}$2, and the quoted magnetometer sensitivity is $\kappa_p/2\pi \simeq 2.7\ \text{MHz}$3. In this usage, PMSMs are nonlinear synchronized oscillator branches rather than merely normal-mode splittings, and their cusp singularity is the central metrological resource (Mi et al., 9 Jul 2025).

Nonlinearity can also destroy PMSMs. In a room-temperature YIG-sphere/split-ring-resonator hybrid, low microwave power gives pronounced level repulsion with fitted parameters $\kappa_p/2\pi \simeq 2.7\ \text{MHz}$4, $\kappa_p/2\pi \simeq 2.7\ \text{MHz}$5, $\kappa_p/2\pi \simeq 2.7\ \text{MHz}$6, and $\kappa_p/2\pi \simeq 2.7\ \text{MHz}$7, together with Rabi-like oscillations in time-domain transmission. As the power rises, however, nonlinear spin-wave interactions broaden the magnon linewidth and suppress the coupling. The mechanism is Suhl’s first-order instability: a resonantly excited magnetostatic mode parametrically excites two counter-propagating magnons at half its frequency. Below the threshold field $\kappa_p/2\pi \simeq 2.7\ \text{MHz}$8, the three-magnon condition is satisfied and the coupled modes vanish at high power; above that threshold, for example near the $\kappa_p/2\pi \simeq 2.7\ \text{MHz}$9 mode around $C \approx 15$0, the instability criterion is not satisfied and hybridization remains robust (Wagle et al., 29 Jan 2026).

These two nonlinear directions—cusp enhancement and Suhl-induced suppression—show that PMSMs are bounded not only by linear detuning and damping but also by nonlinear stability. A plausible implication is that practical PMSM devices require simultaneous optimization of coupling, damping, and nonlinear thresholds rather than only maximization of $C \approx 15$1.

5. Quantum synchronization, squeezing, blockade, and entanglement

The quantum generalization of PMSMs appears most explicitly in optomagnonic and cavity-QED settings. In coupled WGM optomagnonic resonators, each site contains an optical WGM mode and a YIG magnon mode, and the two cavities are coupled by phase-dependent photon hopping

$C \approx 15$2

Using a covariance-matrix formalism, the dynamics of the two distant magnon modes are quantified by complete synchronization $C \approx 15$3, $C \approx 15$4-synchronization $C \approx 15$5, and quantum phase synchronization $C \approx 15$6. When the hopping phase is varied from $C \approx 15$7 to $C \approx 15$8, the magnon trajectories evolve from weakly correlated motion to a highly synchronized state, and stronger photon hopping enhances all synchronization measures while thermal noise suppresses them (Xue et al., 29 Jun 2026).

Magnon–cavity QED with squeezed driving provides a different quantum PMSM regime. In a system with two microwave cavity modes and a single magnon mode, cavity 1 is driven coherently and parametrically by a term $C \approx 15$9. The resulting drift matrix defines three hybrid fluctuation modes, and the paper shows that without squeezed driving the system exhibits zero entanglement and squeezing, whereas with squeezed driving the entanglement between the squeezed cavity mode and the magnon mode can be transferred to the second cavity mode, yielding two cavity–magnon entanglements, photon–photon entanglement, and a genuinely tripartite entangled state. The magnon mode can also be prepared in a squeezed state through the magnon–cavity beam-splitter interaction (Zhou et al., 2022).

Ultrastrong coupling makes the quantum structure of PMSMs more pronounced. In ferromagnetic and antiferromagnetic cavity–magnon systems beyond the rotating-wave approximation, exact integral solutions for the second-order photon correlation function show that counter-rotating magnon–photon interactions induce quadrature squeezing in the cavity mode. In ferromagnetic cavities, squeezing increases with coupling-strength asymmetry, whereas in antiferromagnetic cavities the two opposite-chirality magnon modes suppress quantum effects and impose a lower bound on the equal-time correlation, with the minimal possible $h_{\rm rf}^y$0 in the AFM cavity approximately $h_{\rm rf}^y$1 (Falch et al., 2024).

Related AFM-cavity work emphasizes bright and dark PMSMs and their blockade physics. For a linearly polarized cavity mode coupled to two chiral antiferromagnetic magnons, the symmetric bright mode couples to photons while the antisymmetric dark mode does not. The bright mode exhibits both magnon and photon blockade due to a weak effective nonlinearity, whereas the dark mode exhibits only magnon blockade for a detuned cavity photon. Applying a DC magnetic field lifts the degeneracy of the antiferromagnetic chiral magnon modes, destroys the dark mode, and leads to an unconventional photon blockade (Falch et al., 11 Apr 2025). Superconducting ferromagnetic nanostructures provide a complementary ultrastrong-coupling picture: the magnon–polariton quantum vacuum consists of squeezed magnon and photon states with squeezing controlled by external magnetic field, and excited magnon–polariton states contain bipartite entanglement between magnons and photons (Silaev, 2022).

6. Platforms, observables, misconceptions, and outlook

PMSMs now span a broad hardware landscape. Representative microwave platforms include superconducting coplanar-waveguide and lumped-element resonators coupled to Cu‑EA flakes, planar electric‑LC resonators integrated with YIG films, hexagonal ring resonators with YIG thin films, split-ring resonators loaded with YIG spheres, and remote 3D cavity–magnon systems linked by a programmable transmission line (Li et al., 2023, Maurya et al., 6 May 2026, Verma et al., 8 Jan 2025, Wagle et al., 29 Jan 2026, Joseph et al., 2 Dec 2025). High-frequency and superconducting implementations include S/FI/S and S/FM/I/S nanostructures, as well as predicted S/AFM/S heterostructures at terahertz frequencies (Silaev, 2022, Gordeeva et al., 28 Oct 2025). Optomagnonic realizations extend the PMSM concept to distant magnons mediated by photon hopping in coupled WGM resonators (Xue et al., 29 Jun 2026).

The principal observables are spectroscopic and dynamical. Frequency–field maps of $h_{\rm rf}^y$2 or reflection spectra reveal avoided crossings, level attraction, mode switching, and dark states. Linewidth analysis extracts damping renormalization, cooperativity, and Purcell broadening. Time-domain ring-down resolves coherent beat notes, disappearance of beating at dissipative locking, and enhanced decay in the Purcell regime. In nonlinear systems, emission spectra, hysteresis, and bifurcation diagrams reveal cusp points, mode disappearance, and higher-order oscillation branches (Li et al., 2023, Verma et al., 8 Jan 2025, Joseph et al., 2 Dec 2025, Mi et al., 9 Jul 2025).

Several misconceptions recur. One is that PMSMs require visible anticrossing; the Cu‑EA band-gap regime, the Purcell HRR–YIG regime, and dissipative cavity-Lenz-effect systems all show that hybrid interaction can persist without resolvable splitting (Li et al., 2023, Verma et al., 8 Jan 2025, Harder et al., 2018). Another is that stronger coupling alone guarantees useful PMSMs; the Suhl-instability study shows that nonlinear dissipation can entirely suppress hybridization below a field threshold, while the blockade studies show that effective anharmonicity rather than bare $h_{\rm rf}^y$3 controls single-excitation behavior (Wagle et al., 29 Jan 2026, Falch et al., 11 Apr 2025). A third is that PMSMs are intrinsically microwave and ferromagnetic; recent work places them in optomagnonic WGM networks, superconducting nanostructures, and terahertz antiferromagnetic heterostructures (Xue et al., 29 Jun 2026, Silaev, 2022, Gordeeva et al., 28 Oct 2025).

Current directions point toward material and architectural control of synchronization itself. Intrinsic magnon band engineering via Dzyaloshinskii–Moriya interaction can switch PMSMs on and off spectrally; resonator orientation can redistribute coupling between competing photon channels; phase shifters can tune dissipative coupling remotely; photon-hopping phase can control synchronization of distant magnons; and DC field, strain, or electric field are plausible routes to faster reconfiguration where temperature tuning is presently slow (Li et al., 2023, Maurya et al., 6 May 2026, Joseph et al., 2 Dec 2025, Xue et al., 29 Jun 2026). Taken together, these developments position PMSMs as a unifying language for coherent hybridization, dissipative mode locking, nonlinear self-oscillation, and quantum-correlated photon–magnon dynamics across cavity magnonics, optomagnonics, and superconducting spin–photon platforms.