Strong spin-magnon coupling in a van der Waals magnet with tunable chiral symmetry

Summary

Photons have long been the dominant mediators of interactions in cavity quantum electrodynamics (QED), with recent advances in chiral cavities enabling directional light-matter coupling. Extending these capabilities to spin qubits, however, remains a major challenge, motivating the exploration of alternative solid-state platforms. Here, we report the experimental demonstration of a chiral magnonic cavity, where magnons—collective excitations of magnetically ordered solids—replace photons. We demonstrate strong spin-magnon coupling between [Gd(W₅O₁₈)₂]⁹⁻ spin qubits and antiferromagnetic magnons in the van der Waals material CrSBr, observing clear anticrossings and coherent hybridization. Crucially, we exploit the intrinsic chirality of antiferromagnetic magnons to tune the coupling strength by simply rotating an external magnetic field, dynamically controlling the magnon symmetry from linear to chiral within a single device. Our results establish magnon QED as a powerful platform for spin qubit research and introduce chirality as a control knob for information flow.

Graphical abstract

Highlights

• •Experimental demonstration of a chiral magnonic cavity, inaugurating magnon QED
• •Experimental demonstration of strong spin-magnon coupling
• •Dynamical tuning of the coupling by controlling the magnon chirality
• •Scalable solid-state platform compatible with a broad range of spin systems

Accessible overview

Photons have long been the dominant mediators of interactions in cavity quantum electrodynamics (QED), with recent advances in chiral cavities enabling directional light-matter coupling. Extending these capabilities to spin qubits, however, remains a major challenge, motivating the exploration of alternative solid-state platforms. Here, we report the experimental demonstration of a chiral magnonic cavity, where magnons—collective excitations of magnetically ordered solids—replace photons. We demonstrate strong spin-magnon coupling between [Gd(W5O18)2]⁹⁻ spin qubits and antiferromagnetic magnons in the van der Waals material CrSBr, observing clear anticrossings and coherent hybridization. Crucially, we exploit the intrinsic chirality of antiferromagnetic magnons to tune the coupling strength by simply rotating an external magnetic field, dynamically controlling the magnon symmetry from linear to chiral within a single device. Our results establish magnon-cavity QED as a powerful platform for spin qubit research and introduce chirality as a control knob for information flow. This platform could unlock the potential of spin qubits, which offer longer coherence times than superconducting qubits but have so far lagged behind. Moreover, by enabling directional information flow—a capability challenging in conventional photonic QED—magnon QED presents a compelling alternative to circuit-based approaches.

Circuit-quantum electrodynamics couples superconducting qubits to cavity photons, but extending this to spin qubits is challenging because microwave photons are too large. Magnons—collective excitations of magnetically ordered solids—offer a solution: they can be confined to much smaller volumes and naturally exhibit chirality. García-Pons et al. demonstrate a chiral magnonic cavity with strong coupling between molecular spin qubits and antiferromagnetic magnons, achieving tunable symmetry from linear to left-handed chirality.

Introduction

Confining photons in cavities amplifies their coupling to matter, allowing coherent energy exchange. This is the core idea behind cavity quantum electrodynamics (QED). A major breakthrough came in 2004 with the demonstration of strong coupling between a superconducting qubit and a photon in a superconducting resonator.¹ An analogous demonstration for single spin qubits^2,3,4 coherently coupled to bosonic modes, however, remains unrealized.

Coupling spins to cavities could enable qubit readout, the engineering of spin-spin interactions,^5,6,7,8 and the exploration of phenomena such as the superradiant phase transition^9,10 or cavity-induced correlated states of matter.^11,12 Although individual spins have been addressed electrically,^13,14 achieving strong magnetic coupling to superconducting cavities remains extremely challenging, primarily due to a scale mismatch: microwave photons are too large to be confined within the nanoscopic resonators required for efficient spin-photon coupling.¹⁵

In parallel, light-handedness is emerging as an active control knob in the field of chiral QED, where chirality is harnessed to manipulate light-matter interactions with applications including non-destructive discrimination and separation of enantiomers, symmetry-controlled engineering of quantum materials, and the development of directional quantum light sources and quantum gates.^16,17,18 Despite this potential, implementing tunable chiral cavities remains experimentally challenging.¹⁹

Overcoming these limitations may require moving beyond circuit QED to explore other solid-state excitations such as magnons, i.e., quantized collective excitations in magnetically ordered materials.²⁰ Magnons are quantum-compatible bosonic modes, as evidenced by their coherent coupling to photons,^21,22,23,24 phonons,²⁵ and superconducting qubits.^26,27 They exhibit attractive properties such as nonlinearity,²⁸ non-reciprocity,²⁹ and quantum squeezing.³⁰ In antiferromagnets (AFMs), magnons further show potential for low damping^31,32 and bands with both chiralities.^33,34 The discovery of magnetism in van der Waals (vdW) materials, including AFM order in FePS₃,³⁵ has also triggered interest in AFM magnonics down to the few-layer limit.³⁶

A natural step beyond cavity QED toward magnetic platforms is to replace photons with magnons, realizing the concept of magnon QED (Figure 1A). A key milestone in this direction is the observation of strong coherent coupling between magnons and solid-state spin qubits. Additionally, chiral magnonic effects provide a promising avenue for exploring new functionalities and applications.

Figure 1.

Magnon quantum electrodynamics

(A) One AFM magnon induces a spin transition in a nearby spin.

(B) Crystal structure of CrSBr with θ the angle between B₀ and the easy b axis.

(C) Magnetization dynamics of sublattices m₁ and m₂ for the acoustic mode.

(D) Crystal structure of GdW₁₀ with ϕ the angle between B₀ and the easy z axis.

(E) At mK temperatures, GdW₁₀ is an ideal two-level system with zero-field ground spin state ⟨S_z⟩ = ±7/2 and first excited state ⟨S_z⟩ = ±5/2 separated by Δ(B₀ = 0) = 22.3 GHz (∼1.07 K).

Spin-magnon coupling has been widely studied theoretically.^{5,6,7,8,37,38,39,40} On the experimental side, most implementations have focused on ferro- or ferrimagnetic materials but, unfortunately, have remained limited to the weak coupling regime.^28,41 AFMs, by contrast, have received less attention, since their resonances typically lie in the terahertz range,³⁴ well above the energy scales relevant for most spin qubits.^3,4 Notably, strong spin-magnon coupling has been reported in AFMs containing embedded paramagnetic ions, where exchange-mediated interactions serve as an effective coupling mechanism.^42,43 However, spins are intrinsic to such platforms, preventing independent control or readout and ruling out experiments with distant or engineered qubits.

Here, we experimentally demonstrate strong spin-magnon coupling between acoustic magnon modes in an AFM vdW insulator and a spin ensemble, establishing a platform for magnon QED. Crucially, we show that the coupling can be tuned in situ by rotating the applied magnetic field, exploiting the intrinsic chirality of AFM magnons. These results demonstrate that AFMs provide a practical realization of a magnonic chiral cavity.

Results and discussion

Experimental platform

We use CrSBr as the magnonic resonator. This layered material exhibits in-plane magnetic anisotropy, with its easy axis aligned along the crystallographic b direction (Figure 1B). Below 132 K, chromium moments order ferromagnetically within each layer and antiferromagnetically between layers.⁴⁴ When an external magnetic field B₀ is applied along the crystallographic a axis, the magnetic sublattices undergo progressive canting, aligning with the field above ∼1 T. However, all measurements in this work are performed below this critical field. In this regime, CrSBr supports two distinct spin-wave modes in the microwave range⁴⁵: acoustic modes, where the sublattices precess in phase (Figure 1C), and optical modes, where they precess out of phase. On the other hand, when B₀ is applied along the easy b axis, spin waves acquire chiral character, corresponding to left-handed (LH) and right-handed (RH) magnon modes.⁴⁵

To observe AFM resonance, we use a bulk CrSBr single crystal inductively coupled to a coplanar transmission line (TL). The transmitted signal (S₂₁ parameter) is measured from 8 mK up to 17 K using a vector network analyzer (VNA) and corrected as described in the supplemental information. As shown in Figure 2A, the acoustic mode splits into multiple resonances that can be precisely resolved up to the highest temperature available and, notably, display narrow linewidths even below 100 MHz (see supplemental information).

Figure 2.

Spin-magnon hybridization in the strong coupling regime

(A and B) Transmission pseudo-derivative spectra (see supplemental information) of a bare crystal of CrSBr and GdW₁₀, respectively, measured at 8 mK, along with theoretical fittings (solid lines).

(C) Sample assembly: GdW₁₀ is placed on top of CrSBr. The latter is placed on top of the TL with its intermediate a axis parallel to it. B₀ is the external magnetic field.

(D) Relevant coupling constants and dissipation channels. G is the collective spin-magnon coupling. κ = κ_e + κ_i, where κ_e is the magnon-photon coupling and κ_i is the intrinsic magnon loss rate. γ = γ_e + γ_i, where γ_e is the spin-photon coupling and γ_i is the intrinsic magnon loss rate.

(E) Microwave absorption spectra of sample 1 after background subtraction (see supplemental information), revealing several avoided crossings indicative of strong coupling.

(F) The right image shows the experimental S₂₁ data at B₀ = 185 mT (scatter points), showing a split resonance fitted with two Lorentzian curves (solid lines) with center frequency f_m and linewidth w_m. The left image is a zoomed-in view of the dashed rectangular region in (E), along with fitted f_m (scatter) and w_m (bars).

(G) Numerical simulations based on the theoretical model.

Spin-wave multiplicity has previously been reported in layered vdW magnets and attributed to magnetostatic surface and backward-volume modes with different in-plane k wavevectors.²² Here, we observe a substantially larger number of modes that are difficult to reconcile with different in-plane ks for two reasons. First, the most intense resonance is expected to correspond to low-k modes; however, in our experiments, the dominant mode varies from sample to sample and typically appears at intermediate order. Second, efficient excitation of intermediate-k modes is not expected when using millimeter-wide TLs, as in our experiment.

We attribute the observed mode multiplicity to a key structural feature of vdW materials: their weakly coupled layered nature. This naturally gives rise to variations in the lateral size of individual layers or small stacked groups, as directly evidenced by optical microscopy (see supplemental information). These layer-size variations are an intrinsic morphological characteristic of vdW crystals and should not be confused with crystalline defects such as stacking faults or wrinkles, which are absent in our samples.

We capture this effect phenomenologically by assuming that layers of different lateral size resonate at slightly different frequencies. Since the layer sizes are random, the associated frequency shifts are also modeled as random. In the minimal model, the resonance frequency of layer l is written as ω_l = ω₀ + ϵ_l, where ω₀ is given by the Kittel formula and ϵ_l is a random variable drawn from a normal distribution with a standard deviation compatible with the experimentally observed mode splittings. The layers are coupled through the AFM vdW interaction.

This ad hoc model reproduces a distribution of modes and, crucially, allows us to compute the coupling of each mode to the TL (see methods and supplemental information). Figure 2A shows one of the resulting theoretical curves (blue line) obtained by assuming an interlayer exchange field of μ₀H_E = 0.392 T, an in-plane anisotropy field of μ₀H_a = 0.380 T along the medium a axis, and an out-of-plane anisotropy field of μ₀H_c = 1.32 T along the hard c axis. Importantly, the model correctly captures the high multiplicity of the acoustic mode, while the optical mode appears as a single broad resonance (see supplemental information).

The observed mode multiplicity is remarkable, since previous measurements on Cr-based vdW magnets typically reported a single mode with linewidths of 1–3 GHz.^{21,45,46,47,48,49} Such broad resonances are, however, consistent with many closely spaced modes, as observed in our experiments. Resolving these modes is challenging because losses to the TL (κ_e in Figure 2D) cause spectral broadening and obscure individual features. We limit losses by means of a thin layer of grease or Teflon, enabling the observation of remarkably narrow resonances. This is crucial for demonstrating spin-magnon strong coupling, as discussed in the following.

As the molecular qubit, we chose the inorganic polyoxometalate [Gd(W₅O₁₈)₂]^9–, hereafter referred to as GdW₁₀. This single-ion magnet consists of a lanthanide ion encapsulated by two ${\left[{\mathrm{W}}_5{\mathrm{O}}_{18}\right]}^{6-}$ polyanion ligands. Its sodium salt crystallizes in a triclinic unit cell, with the easy z axis in the ab plane, at ∼50° to the elongated crystal direction a (Figure 1D). We have previously shown that these lanthanoid-based molecular complexes behave as robust qubits with properties that can be tuned by an appropriate selection of the lanthanoid ion and its coordination environment^50,51,52 and coupled to photons in superconducting cavities⁵³ but still far from the strong coupling regime.⁵⁴ In the case of GdW₁₀, the ground ⟨S_z⟩ = ±7/2 and excited ±5/2 states are zero-field split by 22.3 GHz (Figure 1E), effectively forming a two-level system.⁵⁵ When an external magnetic field B₀ is applied at an angle ϕ to the z axis, the spin states become mixtures of the z projections, defining the qubit’s computational basis.

Spin transitions are characterized at 8 mK on a bare GdW₁₀ crystal, with B₀ applied along the a axis (Figure 2B). At low fields, the spectrum displays a single resonance line that splits into multiple resonances upon increasing B₀. This is attributed either to the presence of twin domains within the crystal, each with slightly different orientations of the anisotropy axis, or to local distortions in the coordination environment. The latter is likely induced by the loss of lattice water molecules during vacuum pumping used for sample cooling. In either case, the observed resonances can be well resolved at B₀ > 100 mT and exhibit narrow linewidths, down to 30 MHz (see supplemental information). Experimental data can be well accounted for by a spin Hamiltonian including zero-field anisotropy terms D = −1.23 GHz and E = 3.1 MHz and Zeeman energy with ϕ = 49°, yielding the fitted pink line in Figure 2B (see methods).

Next, we place a GdW₁₀ crystal on top of a CrSBr crystal with a minimal amount of apiezon-N grease, ensuring that the interaction between them is mediated by dipolar magnetic fields, with no contribution from exchange (Figure 2C). Both crystals are aligned along their elongated directions parallel to each other, such that the crystallographic a axis is oriented identically in both samples. For readout, the CrSBr is placed on top of a copper TL, very much like lumped-element superconducting resonators are read out via nearby TLs in circuit QED. Our setup enables a straightforward sample assembly and is readily adaptable to other families of vdW materials and spin qubits in solids. Here, we present experimental results obtained with two samples: sample 1, shown in Figure 2C, and sample 2, shown in the supplemental information.

Strong spin-magnon coupling

Figure 2E shows the transmission spectra of sample 1 after background subtraction. A series of clearly visible anticrossings appear when CrSBr modes intersect with GdW₁₀ transitions. These features are further analyzed by fitting each absorption dip to a Lorentzian function with center frequency f_m and width w_m. At the intersection, the absorption deep splits into two clear resonances, separated by the coupling energy 2G (Figure 2F, right). The fitted f_m and w_m values are superimposed on the experimental data in Figure 2F (left), with bars corresponding to w_m. Here, the main anticrossing is clearly visible at B₀ = 185 mT, with a second, smaller anticrossing at B₀ = 220 mT. The fits yield a maximum experimental collective coupling strength of G/2π = 130 MHz. This is to be compared with the experimental losses of this particular magnon mode κ/2π = w_m/2 = 62.5 MHz (see supplemental information) and γ/2π = w_m/2 = 15 MHz for the spins (see supplemental information), both measured far from the anticrossing. This yields a cooperativity of c = G²/κγ ∼ 18, placing the system within the strong coupling regime.

To confirm the interpretation of the experimental data, we employ a simplified theoretical model in which the ensemble of GdW₁₀ qubits collectively couples to CrSBr magnons via a coupling strength G. In addition, photons through the TL couple to the CrSBr at a rate κ_e, which, together with the intrinsic loss rate κ_i, defines the total energy decay rate of CrSBr κ = κ_e + κ_i. Similarly, the TL couples to GdW₁₀ spins with rate γ_e and intrinsic loss γ_i, yielding a total decay rate γ = γ_e + γ_i (Figure 2D). We develop the corresponding input-output formalism to calculate the transmission spectrum S₂₁ (see supplemental information). Using experimentally determined exchange and anisotropy parameters for CrSBr and GdW₁₀, as well as the experimentally measured collective coupling rate G/2π = 130 MHz, we fit the model with a single free parameter, ϕ, which represents the angle between the external magnetic field B₀ and the quantization axis of GdW₁₀. Setting ϕ = 46°, a value consistent with possible tilting of the GdW₁₀ crystal during mounting, we successfully reproduce the experimental results, as shown in Figure 2G.

We highlight that the observed multiplicity of magnon modes in CrSBr does not affect the observed spin-magnon coupling effect. Split modes are simply the new eigenmodes of the antiferromagnetic Hamiltonian of layered CrSBr, and some of them couple strongly to Gd-spin transitions as we demonstrate here.

Magnon QED physical implementation

The observation of an anticrossing confirms the coupling between CrSBr and GdW₁₀ resonances. In the following, we demonstrate that while GdW₁₀ exhibits the nonlinear behavior characteristic of a collection of paramagnetic spins (qubits), the magnon modes in CrSBr retain their linear and harmonic character, even when the Gd ensemble is saturated by increasing the driving power. This establishes the CrSBr-GdW₁₀ system as an ideal platform for magnon QED, where the magnons act as a linear cavity field and GdW₁₀ as a saturable quantum matter component. In this regime, the dynamics can be effectively captured by a Tavis-Cummings model:

$$\frac{H}{\mathrm{\hslash }}={\omega }_M{a}^{†}a+\frac{\Delta \left(B_0\right)}{2}\sum _j{\sigma }_j^z+\sum _j{g}_j{\sigma }_j^{+}a+\mathrm{h}.\mathrm{c}.,$$

where ω_M is the magnon frequency, a^† (a) is the magnon creation (annihilation) operator, Δ(B₀) denotes the GdW₁₀ transition shown in Figure 2B, σ^z and σ⁺ are Pauli matrices describing this transition, g_j is the single spin-single magnon coupling, and ℏ is the reduced Planck constant. Here, we emphasize that the collective coupling G introduced above is related to the single spin-magnon couplings via $G=\sqrt{{\sum }_j{\left|g_j\right|}^2}$. Note that this Hamiltonian includes only a single magnon mode—the one that couples most strongly to the spins—although additional magnon modes could in principle be included.

To demonstrate nonlinearity in the behavior of GdW₁₀, we examine the effect of increasing input power P_in. Measurements are performed at B₀ > 300 mT to ensure that the GdW₁₀ spins are decoupled from CrSBr modes. For P_in ≤ −10 dBm, the delivered power is sufficiently low to keep the sample temperature close to 8 mK, with at most a ∼20 mK increase (see supplemental information). At higher powers, the sample heats up, reaching 150 ± 20 mK at P_in = 10 dBm. Even at these temperatures, the thermal population of Gd spins in the ground state remains extremely high: tanh (Δ/T) × 100 = 99.999, where Δ = 1.07 K is the energy gap between the ground and first excited spin states expressed in Kelvin.

Figure 3A shows the transmission through a bare GdW₁₀ crystal at different P_in, evidencing a progressive decrease of the absorption dip for P_in ≥ 0 dBm. A similar trend is observed in sample 1 (data not shown). In Figure 3B, we plot the power dependence of the visibility Υ, defined as the amplitude of the absorption dip on a linear scale (see Figure 3A). At very low input powers, Υ tends to γ_e/γ. The latter quantifies the fraction of photons absorbed by the spin ensemble relative to the total number of photons. As power increases, Υ sharply decreases to zero.

Figure 3.

Power control over the spin qubit population

(A) Transmission S₂₁ parameter of a bare GdW₁₀ crystal at different input powers given in the legend.

(B) Amplitude of the absorption dip Υ vs. power (scatter) for sample 1 at B₀ = 320 mT on a linear scale. The solid line shows the theoretical model. The dashed vertical line highlights the strong coupling condition $\sqrt{N_{\text{eq}}/N}=\gamma /G,\kappa /G$.

(C) The top images show the transmission pseudo-derivative spectra of sample 1 at three representative input powers, as indicated. The bottom images show the results of fitting the main magnonic resonance in transmission data (top) with Lorentzian curves centered at f_m (dots) and with linewidths w_m (bars).

To describe this behavior, we solve the dynamical equations beyond the weak-driving limit, abandoning the linear-response regime. The visibility follows $\mathrm{{\rm Y}}=\frac{{\gamma }_e/\gamma }{1+4{\mathrm{\Lambda }}^2/\left({\gamma }_i{\gamma }_{\Vert }\right)}$. Here, Λ² = αP_in, with α accounting for attenuation at the sample position and absorption efficiency (see supplemental information) and γ_‖ being the spin relaxation rate. This model fits the data reasonably well, offering a clear physical interpretation. As the number of photons (proportional to Λ²) approaches γ_iγ_‖, the system enters a saturated regime where spins can no longer efficiently relax to equilibrium, marking the onset of nonlinear transmission. Thus, Υ directly reflects the ratio N_eq/N, i.e., the ratio of spins remaining in the ground state to total spins coupled to the TL.

On the other hand, transmission measurements of CrSBr performed at varying input powers (Figure 3C; supplemental information) do not exhibit saturation effects: the transmission response remains unchanged across the entire power range. This confirms that the magnon dynamics in CrSBr stay within the linear-response regime, remaining a linear harmonic oscillator throughout the explored conditions.

Figure 3C displays the transmission spectra of sample 1 at three P_in (top). The coupling strength is better resolved by fitting the experimental transmission data to Lorentzian curves and plotting the resulting center frequency f_m and linewidth w_m (Figure 3C, bottom). At low power (−30 dBm), the primary avoided crossing is clearly visible, along with several smaller anticrossings at the intersections between CrSBr acoustic modes and GdW₁₀ spin transitions. These features are reflected in the two resolved anticrossings in the bottom image of Figure 3C. As the drive power increases, most of the smaller anticrossings disappear, though the main one remains visible at 0 dBm. This is also captured in the bottom image: the main avoided crossing closes, but the linewidths remain broadened, indicating weak coupling. For higher powers, all signatures of coupling vanish, leaving only the resonance lines associated with the CrSBr modes with no visible linewidth broadening.

This can be easily understood in view of the above-discussed theory. Reducing the effective number of equilibrium spins leads to a renormalized coupling strength, $G_{\text{eff}}=G\sqrt{N_{\text{eq}}/N}$. The strong coupling condition is then G_eff > γ,κ, allowing us to calculate the threshold power for strong coupling. As shown in Figure 3B, this occurs at P_in = 0 dBm. Therefore, the disappearance of anticrossings results from the saturation of the GdW₁₀ ensemble, while nonlinearities in the spin-wave spectrum are negligible.

Next, we present additional evidence demonstrating that spin-magnon coupling in GdW₁₀-CrSBr is coherent. For this, we focus on the results obtained with sample 2. Figure 4A shows the low-power transmission at 8 mK, where a single anticrossing can be observed. The resulting coupling is slightly smaller than that of sample 1, yielding G/2π = 80 MHz. The differences relative to the collective spin-magnon coupling observed in sample 1 arise primarily from the smaller size of the GdW₁₀ crystal in sample 2, which is roughly half that of sample 1. More importantly, these measurements evidence the presence of bright and dark states below and above the avoided crossing, respectively. A similar effect is observed in sample 1, although it is obscured by the many anticrossings. Notice the significant reduction of the upper polaritonic dip in the right image of Figure 2F, indicating the formation of a dark state getting decoupled from the readout TL.

Figure 4.

Tunable magnonic chiral cavity

(A) Transmission pseudo-derivative spectra for sample 2 with B₀ along the a axis (acoustic mode). An avoided crossing is visible with a bright state below the anticrossing (white arrow) and a dark state above it (black arrow).

(B) Theoretical model evidencing the formation of an anticrossing and bright/dark states.

(C) Experimental configuration for the coplanar waveguide excitation of the acoustic mode, with B₀ along the a axis.

(D) Dynamics of the effective magnetization m_eff resulting from the coherent addition of both sublattice magnetizations.

(E) Same as in (A) but for B₀ along the b axis (LH mode). No signatures of coupling are visible.

(F) Theoretical model corresponding to the experimental data in (E).

(G) Experimental configuration to excite the LH mode with B₀ along the b axis.

(H) Resulting m_eff precessing within the ac plane, LH with respect to B₀.

This demonstrates coherent coupling. Consider the single-excitation polaritons, superpositions of the magnon mode and spin transitions, |ψ⟩ = P^†|0⟩⊗|S_z = −7/2⟩ with $P^{†}=\cos \xi /2a_q^{†}+\sin \xi /2\frac{1}{\sqrt{7/2}G}{\sum }_j{g}_j{S}_j^{+}\text{,}$ where |0⟩⊗|S_z = −7/2⟩ is the ground state of the CrSBr-GdW₁₀ system and the mixing angle ξ = tan⁻¹(G/|Δ(B₀) − ω|) quantifies the relative spin/magnon character of the polariton.

Because both GdW₁₀ and CrSBr couple to the TL, at a specific magnetic field, the relative amplitudes and phases render the coupling operator P^† orthogonal to the polariton creation operator, decoupling the state from the TL and producing a dark state. Conversely, the other polariton branch forms a bright state with enhanced visibility (Figures 2F and 4A).

Realization of a magnonic chiral cavity

Magnetic materials host generally elliptically polarized magnons. In ferromagnets, a single magnon mode exhibits a fixed RH chirality, whereas AFMs, due to their two-sublattice structure, support two modes of opposite chirality, with polarization governed by the crystal anisotropy.

The behavior of AFMs can be better understood in terms of the effective net magnetization, defined as the sum of contributions from both sublattices, with handedness defined relative to the externally applied field. In CrSBr, applying B₀ along the a axis excites the acoustic mode (Figure 4C), for which the effective net magnetization oscillates predominantly along the hard c axis and is nearly linearly polarized (Figure 4D). Rotating B₀ within the ab plane progressively imprints a chiral character on the acoustic mode, which evolves into an LH mode. For B₀ along the b axis (Figure 4G), the effective magnetization precesses almost circularly within the ac plane, exhibiting LH chirality relative to B₀ (Figure 4H). The same field configuration similarly tunes the optical magnon mode into an RH-polarized mode, although these modes occur at frequencies above 30 GHz, well beyond our experimentally accessible range.

This phenomenon enables the realization of a tunable magnonic chiral cavity, in which the magnon polarization can be continuously controlled. By varying the orientation of B₀, the mode can evolve from nearly linear polarization to circular polarization, with either LH or RH chirality.

Here, we exploit this property to achieve dynamic control of the spin-magnon coupling, which relies on a fundamental property of electron spins: the electron g-factor, which relates the magnetic moment to angular momentum, is positive for electron spin transitions. As a result, spin transitions in GdW₁₀ can be efficiently driven by either linearly polarized excitations (such as the acoustic mode) or circularly polarized excitations with RH character (with respect to the local easy z axis), whereas LH-polarized excitations couple only weakly to electronic spin transitions.

According to our theory, driving the LH magnon mode in CrSBr reduces the spin-magnon coupling to approximately half of its maximum value (see supplemental information). This residual coupling originates from two effects: (1) the easy z axis of GdW₁₀ is not collinear with B₀ and (2) the magnon mode is not perfectly circularly polarized but retains some ellipticity, particularly near the crystal edges (see supplemental information).

Figures 4A and 4E show experimental measurements obtained when exciting the acoustic (Figure 4A) and LH magnon (Figure 4E) modes in sample 2. Data in Figure 4A clearly show an anticrossing, indicative of strong coupling. In contrast, Figure 4E reveals no coupling signatures, evidencing the selective suppression of spin-magnon interactions. Experimental results are compared to the theoretically calculated spectra of sample 2. We use the same material parameters as for sample 1, setting ϕ as the only fitting parameter. Figure 4B shows the calculated absorption for the acoustic mode (θ = 0 and ϕ = 54°) using G/2π = 80 MHz, as determined experimentally. The model accurately reproduces the observed anticrossing. In contrast, Figure 4F presents the results obtained when exciting the LH mode (θ = 90° and ϕ = 144°), assuming half the coupling, i.e., G = 40 MHz, which is compatible with experimental measurements.

We have observed the same effect in sample 1, where excitation of LH magnons produces no measurable anticrossing, only a slight linewidth broadening consistent with the weak spin-magnon coupling regime (see supplemental information).

This mechanism enables dynamically tuning the spin-magnon coupling. This highlights a distinct advantage of exploiting AFMs for magnon QED, demonstrating that the coherent interaction can be switched on or off in situ, not by redesigning the device but simply by changing the direction of an external magnetic field.

Conclusions

To conclude, we have experimentally demonstrated that the CrSBr-GdW₁₀ system is accurately described by linear magnon modes and spin transitions analogous to light-matter interactions. These results establish AFM vdW materials coupled to spin qubits as a practical and tunable platform for magnon QED, an emerging paradigm where cavity photons are replaced by discrete, externally controllable magnon modes. Moreover, AFM materials naturally host more than two magnetic sublattices, giving rise to several magnon branches with distinct polarization properties, including linear and chiral modes. These modes can be dynamically selected and controlled. We exploit this feature to realize a tunable magnonic chiral cavity that allows us to dynamically tune the spin-magnon coupling strength within a single device—an essential capability for isolating the spin system from the magnonic resonator and thereby enhancing qubit coherence.

Our experimental results are a starting point for the systematic envelopment of magnon QED. Future studies may focus on other vdW magnets with distinct spin anisotropies, as well as compatible solid-state spin systems, such as diamond color centers or silicon dopants. This might, for the first time, enable the achievement of magnon-mediated long-range spin-spin interactions.^5,6,7,8 This approach offers a solution to the long-standing challenge of implementing high-fidelity two-qubit gates with spin qubits, such as nitrogen-vacancy centers. Layered vdW magnets might also enable on-demand magnon engineering exploitation, e.g., layer twisting,^56,57 and optimum miniaturization of magnonic resonators down to the 2D (bilayer) limit,^21,22 offering a route to ultrastrong spin-magnon coupling and access to superradiant regimes^9,10 and cavity material engineering.^11,12 Additionally, AFMs uniquely allow dynamic control of magnon polarization between linear and circular modes, opening opportunities for chiral QED.^16,17,18

Methods

Spin-wave theory in CrSBr

To model the spin dynamics in CrSBr, we start from the bilinear spin Hamiltonian

$$\begin{array}{cc}H& =-J\sum _n\sum _{⟨i,j⟩}{\mathbf{S}}_{i,n}·{\mathbf{S}}_{j,n}+J_L\sum _n\sum _j{\mathbf{S}}_{j,n}·{\mathbf{S}}_{j,n+1}\\ & +\frac{D_a}{2}\sum _n\sum _j{\left({\mathbf{S}}_{j,n}·\mathbf{a}\right)}^2+\frac{D_c}{2}\sum _n\sum _j{\left({\mathbf{S}}_{j,n}·\mathbf{c}\right)}^2\\ & -g_{\alpha }{\mu }_B{\mathbf{B}}_0·\sum _n\sum _j{\mathbf{S}}_{j,n}\end{array}\text{,}$$ (Equation 1)

where S_i are spin-3/2 operators at Cr sites, J_ij denotes the exchange couplings between nearest-neighbor Cr atoms (including in-plane ferromagnetic and interlayer antiferromagnetic terms), D_b,c are single-ion anisotropies along the b and a crystallographic directions, g is the g-factor, μ_B is the Bohr magneton, and B₀ is the external magnetic field. The spin positions and stacking geometry—accounting for the monoclinic structure of CrSBr—are fully specified in the supplemental information.

We analyze the low-energy excitations of the above spin Hamiltonian (Equation 1) using a bosonic Bogoliubov-de Gennes formalism. After performing a Holstein-Primakoff transformation around the classical ground state, we expand the spin operators to quadratic order and Fourier transform to momentum space. This yields a bosonic Hamiltonian of the form

$$H_{\mathrm{M}}=\sum _{\mathbf{k}}{\varphi }_{\mathbf{k}}^t{\hat{h}}_{\mathbf{k}}{\varphi }_{\mathbf{k}}\text{,}$$ (Equation 2)

where ${\varphi }_{\mathbf{k}}={\left(a_{\mathbf{k},1},\dots ,a_{\mathbf{k},N},a_{-\mathbf{k},1}^{†},\dots ,a_{-\mathbf{k},N}^{†}\right)}^T$ is a 2N-component Nambu spinor describing N magnon bands arising from the magnetic unit cell.

Diagonalization of ${\hat{h}}_{\mathbf{k}}$ gives the magnon dispersions shown in Figure 2. When the external magnetic field is applied along the crystallographic a axis, the system supports linearly polarized acoustic and optical spin-wave modes. In contrast, for fields applied along the b axis, the eigenmodes acquire circular polarization: the magnon eigenvectors diagonalizing the Hamiltonian can be written in terms of the circular components of the magnetization, as discussed in detail in the supplemental methods section “nature of the magnon modes.” This field-dependent polarization is central to understanding the emergence of chiral spin-wave dynamics in CrSBr.

This bosonic approach is complemented with micromagnetic simulations, as described in the supplemental methods section “numerical simulations.” These simulations solve the Landau-Lifshitz-Gilbert equations on a discretized lattice, using parameters consistent with the spin model. They provide a real-space picture of the magnetization dynamics and confirm the mode structure and polarization predicted by the analytical theory.

Modeling stacking disorder in CrSBr

To account for the multiple magnonic resonances observed in CrSBr, we construct a random stacking model that treats the bulk material as a disordered assembly of magnetic bilayers of varying sizes. The system is described by an effective bosonic Hamiltonian of the form

$$H_{\text{stack}}=\sum _l{\varphi }_l^{†}{\hat{h}}_{ll}{\varphi }_l+{\varphi }_l^{†}{\hat{h}}_{l,l+1}{\varphi }_{l+1}+\mathrm{h}.\mathrm{c}.,$$ (Equation 3)

where ${\hat{h}}_{ll}$ captures the spin-wave dynamics within the l-th bilayer and ${\hat{h}}_{l,l+1}$ encodes the antiferromagnetic coupling between adjacent layers. Stacking disorder is introduced by assigning different diagonal energies to each

$$\text{diag}\left({\hat{h}}_{ll}\right)\to \text{diag}\left({\hat{h}}_{ll}\right)+{ϵ}_l\text{,}$$ (Equation 4)

drawn from a normal distribution whose width reflects the structural randomness. The distribution variance of ϵ_l is tuned to match the number and spectral spread of resolved peaks observed in the experiment. The model captures the key features of the experimental transmission spectrum reasonably well. Naturally, we do not aim to fit each line exactly, as the model is random and the spectral lines vary between realizations, as seen in measurements on different samples. More information can be found in the supplemental information.

Spin transitions in GdW₁₀

The microwave absorption spectrum of GdW₁₀ can be described by a spin Hamiltonian that includes zero-field splitting and Zeeman interactions:

$$H=-3\mathrm{\hslash }D{S}_z^2+\mathrm{\hslash }\frac{E}{2}\left(S_{+}^4+S_{-}^4\right)+g{\mu }_B{\mathbf{B}}_0·\mathbf{S}\text{,}$$ (Equation 5)

where D and E are the zero-field anisotropy parameters.

Spin-magnon coupling

Since we focus on a specific magnon mode and spin transition, we project the full spin Hamiltonian of GdW₁₀ onto an effective two-level subspace. At zero field, this is well approximated by the S_z transition 7/2↔5/2. When an external field B₀ is applied at an angle ϕ with respect to the GdW₁₀ easy axis (z axis), the eigenstates become mixtures of S_z projections. This leads to the effective Hamiltonian

$$H_{\text{eff},\text{Gd}}=-\frac{\Delta \left(B_0\right)}{2}{\sigma }^z-g{\mu }_B\hat{\mathbf{B}}·\mathbf{\sigma }\text{,}$$ (Equation 6)

where σ^z = |1⟩ ⟨1| − |0⟩ ⟨0| and σ are Pauli matrices acting on the two-level subspace.

The coupling operator depends on the local orientation of the magnetic field and can be written as

$$\mathbf{\sigma }={\sigma }^{+}\left(\mathbf{c}+i\sin \varphi \mathbf{a}\right)+\mathrm{h}.\mathrm{c}.,$$ (Equation 7)

where ϕ is the angle between B₀ and the easy z axis of the GdW₁₀ ion.

The quantized magnetic field generated by the CrSBr magnons, evaluated at the Gd position and approximated from magnetostatics, is

$$\hat{\mathbf{B}}\left(r,\phi =\pi /2\right)=\frac{{\mu }_0\mathcal{A}{R}^2}{2r^2}\left[\lambda \mathbf{a}+i\mathbf{c}\right]{\hat{a}}_{\lambda }+\mathrm{h}.\mathrm{c}.,$$ (Equation 8)

where

$$\mathcal{A}=\sqrt{\frac{2\mathrm{\hslash }\gamma M_s}{V}}\text{,}$$ (Equation 9)

γ is the gyromagnetic ratio, M_s is the saturation magnetization, and V is the mode volume of the CrSBr resonator. The integer λ = 0, ±1 labels the case for the acoustic, RH, and LH modes, respectively. Here, R is the effective radius used to model the spatial localization of the magnetization at the CrSBr edges, and r is the spin-magnon separation.

The resulting collective spin-magnon Hamiltonian takes the form

$$H=-\frac{\Delta \left(B_0\right)}{2}{\mathrm{\Sigma }}^z+{\omega }_M{a}^{†}a-iG\left(\lambda \sin \varphi +1\right){\mathrm{\Sigma }}^{+}a+\mathrm{h}.\mathrm{c}.,$$ (Equation 10)

with collective operators defined as ${\mathrm{\Sigma }}^z={\sum }_j{\sigma }_j^z$ and ${\mathrm{\Sigma }}^{+}=G^{-1}{\sum }_j{g}_j{\sigma }_j^{+}$.

The collective coupling strength is

$$G=C_M\sqrt{\frac{M_s}{V}}{\left(\frac{R}{r}\right)}^2\sqrt{N_{\text{Gd}}}\text{,}$$ (Equation 11)

where

$$C_M=g{\mu }_B{\mu }_0\sqrt{\frac{\gamma }{2\mathrm{\hslash }}}\approx 2\times {10}^{-7}{\mathrm{m}}^2/\mathrm{s}·\sqrt{\mathrm{A}}$$

and N_Gd is the number of Gd ions that interact coherently with the magnon mode. The volume scales as V ∼ R²L, where L is the lateral dimension of the CrSBr resonator.

Resource availability

Lead contact

Requests for further information and resources should be directed to and will be fulfilled by the lead contact, Maria Jose Martínez-Pérez (pemar@unizar.es).

Materials availability

This study did not generate new materials.

Data and code availability

• •All original code has been deposited at GitHub under https://github.com/dzueco/spin-magnon and is publicly available as of the date of publication.
• •Any additional information required to reanalyze the data reported in this paper is available from the lead contact upon request.

Acknowledgments

This work is funded and supported by the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (948986 QFaST); the European Union – NextGenerationEU (Regulation EU 2020/2094), through CSIC’s Quantum Technologies Platform (QTEP); the Aragón Regional Government through project QMAD (E09_23R); MCIN for the Advanced Materials and the Quantum Communication programs with funding from European Union NextGenerationEU (PRTR-C17.I1), the Generlitat Valenciana and the Government of Aragon; the Spanish MCIN/AEI/10.13039/501100011033 through grants CEX2023-001286-S and CEX2024-001467-M; and the MCIN/AEI/10.13039/501100011033 and CEX2023-001286-S funded by MICIU/AEI /10.13039/501100011033 and the European Union FEDER through projects PID2022-140923NB-C21 and PID2023-149309OB-I00. The authors acknowledge the use of facilities and technical support from the National Facility ELECMI ICTS, node “Laboratorio de Microscopias Avanzadas (LMA)” at Universidad de Zaragoza. E.C. acknowledges Generalitat Valenciana (PROMETEO Program CIPROM/2024/51) and the European Union NextGenerationEU (Cátedras Chip Program TSI-069100-2023-0012) for financial support. D.G.-P. acknowledges a JAE-PRE grant from CSIC. J.P.-B. acknowledges Spanish MICIU/AEI/10.13039/501100011033 and NextGeneration EU/PRTR through grant JDC2022-049096-I.

Author contributions

M.J.M.-P. and D.Z. conceived the idea and, together with E.C., supervised the project; E.C., S.M.-V., C.B.-C., and I.G.-M. chose, designed, and synthesized the magnetic materials; M.J.M.-P., D.G.-P., and J.P.-B. built the setup, performed the measurements, and analyzed the data; D.Z., M.J.M.-P., and X.d.A. performed the numerical simulations; D.Z. developed the theory; and M.J.M.-P. and D.Z. wrote the paper with input from all authors.

Declaration of interests

The authors declare no competing interests.

Published: May 8, 2026