Constructing the MIPA architecture

We design a planar cross cavity consisting of two orthogonal coplanar waveguide resonators, as sketched in Fig. 1d. The excitation of each coplanar waveguide resonator produces two degenerate D-modes³¹. The fundamental excitation of the whole structure produces the Q-mode (see supplementary Note 2 for details). Our cross cavity is a prototypical two-port device. The scattering (S-) parameters measured by Vector Network Analyzer (VNA) with an excitation power of −5 dBm from port-1 and port-2 are shown in Fig. 1e and f with two other ports shorted. The D- and Q-modes occur at ω_d/2π = 3.475 GHz and ω_q/2π = 3.675 GHz, respectively. Their radio frequency (rf) magnetic field (h) distributions are calculated by numerical simulations and presented in two insets. These two cavity modes provide two resonant channels for the input microwave. They are in phase in the reflection but out of phase in the transmission, according to Fig. 1f. The resulting opposite interference behavior in two scattering directions is the key to realizing MIPA in our device.

Although the D- and Q-modes are detuned about (ω_q − ω_d)/2π = 200 MHz, the interference between them can be mediated by a magnon mode. In the experiment, an yttrium iron garnet (YIG, Y₃Fe₅O₁₂) sphere with a diameter of 1 mm is placed at the intersection of the cross cavity. A bias magnetic field (H) with a tunable angle (θ from the y-axis shown in Fig. 1d) is applied in the x-y plane to control the excitation of the magnon mode (ω_m). This coupled cavity photon-magnon system can be modeled by the following Hamiltonian (see details in Supplementary Note 3):

Considering each mode’s damping rate and their coupling effects with external photon baths⁵⁴, the coupled dynamics derived from the Hamiltonian follow

Obviously, as long as $$ \sqrt{{\kappa }_d}{\widehat{d}}_x=\sqrt{{\kappa }_q}\widehat{q}=p_1^{in}/2$$, perfect absorption is achieved. In this condition, both reflection (S₁₁) and transmission (S₂₁) vanish, so that the input signal can be completely dissipated in the cavity, i.e., the absorption (A) is unity, A = 1 − ∣S₁₁∣² − ∣S₂₁∣² = 1. To meet this condition, one may consider adjusting both the degeneracy and intensities of the two channels by redesigning the cavity structure, similar to the idea of superscattering in metamaterials^55,56. Here we demonstrate an easier method based on a cavity magnonic approach^34,57,58, utilizing a tunable magnon mode to precisely control electromagnetic absorption by tuning either the strength or direction of the external magnetic field.

Interference-induced LA-like hybridization

To better understand the interference in our multi-channel device, we choose the transmission spectra as an example and study the magnon-mediated interference in two steps. First, we focus on the strong coupling between two D-modes and the magnon mode near ω_d (the D–M coupling). Because g_q ≪ g_d and the Q-mode is far detuned from the D-modes, the influence of the Q-mode on the D–M coupling is negligible. Three CMP modes produced by D–M coupling can be analytically solved from Eq. (2) as ω_d and $$ {\omega }_{\pm }=\mathrm{Re}\left[{\tilde{\omega }}_d+{\tilde{\omega }}_m\pm \sqrt{{\left({\tilde{\omega }}_d-{\tilde{\omega }}_m\right)}^2+4g_d^2}\right]/2$$ (as shown in Fig. 2a, more details in Supplementary Note 4). The frequencies of the three CMP modes are independent of the direction of the external magnetic field, i.e., θ, but their mode intensities are tunable by θ following the relations of $$ I_c\propto {\cos }^2\theta $$ and $$ I_{\pm }\propto {\sin }^2\theta $$, where I_c and I_± correspond to the central and side mode intensities (derivations shown in supplementary Note 4). When the external magnetic field is pointed in the y-direction (θ = 0^∘), $$ g_d\sin \theta $$ equals zero. The magnon mode is decoupled to the horizontal D-mode ($$ {\widehat{d}}_x$$). The upper- and lower-branch CMP modes (ω_±) become dark (I_± ≈ 0), while the central CMP mode at ω_d is bright, represented by black dashed lines in Fig. 2b. Then we rotate the external magnetic field to the x-direction (θ = 90^∘). $$ g_d\sin \theta $$ reaches its maximum (i.e., 2π × 65.6 MHz). The magnon mode is strongly coupled to the horizontal D-mode ($$ {\widehat{d}}_x$$), which is driven by the input signal $$ p_1^{in}$$. In this case, the central hybrid mode at ω_d vanishes, but both upper- and lower-CMP modes (ω_±) become bright (Fig. 2c), which are ready for magnon mediation in subsequent operations.

Fig. 2

Interference between internal photon-magnon hybrid modes.

a Schematic picture of the energy level diagram in our MIPA system. b, c shows the switching off/on of the interference between the upper-CMP mode (ω₊) and the Q-mode (ω_q) in transmission by tuning θ from 0^∘ to 90^∘. d Conventional MIT-like behavior occurs when the channel sustained by the upper-CMP mode (ω₊) is off. e LA-like hybridization occurs when the channel sustained by the ω₊ mode is on.

After characterizing the D–M coupling, we move on to the second step, i.e., the coupling between the Q- and magnon modes (the Q–M coupling) in the vicinity of ω_q. The influence of strong D–M coupling must be considered in Q–M coupling. Therefore, the Q–M coupling can be treated as the coupling between the upper-CMP mode (ω₊) and the Q-mode (Fig. 2a). Switching on/off the intensity of the upper-CMP mode (I₊) can be utilized here to manipulate the Q–M coupling. To describe this behavior, we reduce Eq. (2) to a more concise form with only the upper-CMP mode and the Q-mode (see the Supplementary Note 6 for more details).

Intuitively, LA in our device can be understood by using a coherently coupled pendulum system with two driving forces. Due to the destructive interference induced by double drives, the maximum response of the system deviates from its eigenfrequencies in the frequency domain, and thus LA-like hybridization occurs (see Supplementary Note 5). This unique hybridization behavior in cavity magnonics was previously observed in 1D Fabry-Perot cavities^37,45, cavity anti-resonance⁴⁰, planar cavities^41–43, and two-tone driven CMPs^38,44. In these works, LA was treated as a signature of the dissipative coupling effect. Although still rooted in the dissipative process, in our work, this unique hybridization behavior is achieved through destructive interference between internal channels sustained by polariton modes.

Magnon-induced nearly perfect absorption

By utilizing the interference in our device, MIPA can be realized. In addition to the suppression in the transmission, the reflection also needs to be suppressed to zero so that all input power can be absorbed and then dissipated in our device. At θ = 0^∘, the interference between the two internal channels is off. The measured squared amplitudes of the reflection and transmission at the zero detuning (Δ = ω₊ − ω_q = 0) are plotted in Fig. 3a, b. As a normal case of coherent coupling, an enhancement occurs in the reflection (a small peak in the frequency range marked in gray), accompanied by suppression in the transmission (a small dip). This opposite behavior in two scattering directions makes perfect absorption impossible. Figure 3c shows the measured absorption spectra at different bias fields, from which no evident enhancement of the absorption is observed.

Fig. 3

Absorption enhancement.

At θ = 0^∘, corresponding to conventional MIT dynamics, the squared amplitudes of the reflection (∣S₁₁∣²) enhancement and transmission (∣S₂₁∣²) suppression at zero detuning are plotted in (a) and (b). Measured absorption spectra at different bias fields are plotted in (c). By tuning θ, the measured absorption spectra at 5 different angles are plotted in (d). Typically, at θ = 90^∘, both squared amplitudes of the reflection (e) and transmission (f) are suppressed relative to the empty cavity (black solid lines). Red solid lines in (e) and (f) indicate the calculated results. Absorption spectra measured at different bias magnetic fields are plotted in (g), which shows an evident absorption enhancement (the red spot).

With θ increasing from 0^∘ to 90^∘, interference mediated by the magnon mode gradually occurs. This interference effect nearly doubles the absorption rate, as shown by the absorption spectra measured at zero detuning with increasing θ (Fig. 3d). Typically, at 90^∘, the enhanced absorption comes from the fact that both squared amplitudes of the reflection and transmission are suppressed (shown in Fig. 3e, f, respectively, with the corresponding frequency range indicated by gray color). This shows an evident difference from the aforementioned MIT behavior. Consequently, an enhancement of microwave absorption occurs, as shown by the red spot in Fig. 3g.

Generally, the demonstration of absorption enhancement embodies magnon-mediated interference between two internal channels. However, further optimization is still needed to achieve perfect absorption. Based on the aforementioned condition of $$ \sqrt{{\kappa }_d}{\widehat{d}}_x=\sqrt{{\kappa }_q}\widehat{q}=p_1^{in}/2$$ and Eq. (4), a perfect absorption condition is achieved as $$ {\kappa }_{+}{\kappa }_q\approx g_q^2+{\gamma }_{+}{\gamma }_q-\sigma \mathrm{\Delta }$$, where σ represents the small frequency difference between MIPA and ω₊. Quantitatively, for the currently used cross cavity, the left term κ₊κ_q ≈ 6 × 4π² MHz² is much smaller than the right term (40 × 4π² MHz²). To realize perfect absorption, larger κ₊ and κ_q are necessary. Considering the linear relation between κ₊ and κ_d, this problem can be solved by adjusting the coupling gaps of cavity ports.

Figure 4a shows a theoretical calculation of the absorption rate at zero detuning (Δ = 0) by varying κ_d and κ_q. We notice that the absorption rate can be enhanced to 100% with a slight increase in κ_d and κ_q. The white dashed line in Fig. 4a indicates the region in which the absorption rate is over 90%. Nearly perfect absorption can be achieved throughout a wide range of these two parameters, which offers a large fabrication tolerance for cavity fabrication. Accordingly, we make another cross cavity, keeping the same design but slightly increasing κ_d and κ_q. At the condition of θ = 90^∘, as the upper-CMP mode ω₊ approaches the Q-mode, drastic suppression of both the squared amplitudes of the reflection and transmission occurs, as shown in Fig. 4b. Therefore, an optimized absorption up to 96% is achieved (Fig. 4c), which unambiguously exhibits the possibility of realizing MIPA. Based on our theoretical model, all spectra can be well reproduced, shown as solid lines in Fig. 4b, c (see details in Supplementary Note 7). We note that, since our model takes advantage of the linear harmonic dynamics, this theory is promising to be generalized to other harmonic systems, or scaled down to the quantum regime.

Fig. 4

Near-perfect absorption.

a Theoretical calculation of the maximal absorption of our cavity magnonic device as a function of κ_d and κ_q. The white dashed line indicates the region in which the maximal absorption rate is over 90%. Green and yellow sparks indicate the parameters of the currently used and modified cross cavities, respectively. b Measured square of reflection (∣S₁₁∣² in blue circles) and transmission (∣S₂₁∣² in orange circles) of the modified cavity magnonic device, shown in dB scale. MIPA occurs when two dips coalesce. Correspondingly, the measured absorption spectrum is plotted in c in red circles, which shows enhancement compared with empty cavity absorption (black solid line). The measured maximal absorption rate is 96%. Solid orange and blue lines in b and red lines in c are results calculated by using Eq. (2).

In conclusion, we realize near-perfect absorption by utilizing magnon-mediated two-channel interference in a cavity magnonic device, i.e., MIPA. Unlike conventional CPA techniques that manipulate the interference of multiple coherent input signals, MIPA in our device needs only a single input signal. Due to the high tunability of the magnon mode, our method exhibits flexibility in controlling the absorption by using an external magnetic field. By simultaneously suppressing our device’s reflection and transmission, nearly perfect absorption (96%, close to the predicted value of 100%) is achieved. By implementing the spin pumping effect²⁶ in the magnetic material, MIPA could allow the incoming microwave to be maximally utilized for the generation and manipulation of spin currents which can be further electrically detected for the magnon-based energy harvesting and sensing. The extrinsic damping rates of the upper-branch polariton mode κ₊ and the Q-mode κ_q, may also be used as effective gains to construct a parity-time-symmetric system³⁴. This idea will be useful for designing tunable modulators and switches with knowledge enriched by pseudo-Hermiticity and exceptional-point physics. Additionally, because of the destructive interference in transmission, an LA-like hybridization between a CMP mode and a cavity photon mode is observed, which offers a versatile method for the realization of LA in coherent information processing.

Device description

The cross cavity used in our experiment is fabricated on a 0.762 mm thick RO4350B substrate, consisting of two half-wavelength coplanar waveguide resonators with a length of 25 mm and a central conductor width of 1.14 mm. Input/output ports are coupled to the cross cavity via coupling gaps. For the first cross cavity, the coupling gaps’ width is 0.2 mm. κ_d and κ_q are designed to be small to maintain high quality (Q-) factors of the D- and Q-modes. Using this device, both the mode hybridization and interference behaviors can be clearly presented. For the modified cross cavity, the width of coupling gaps is designed as 50 μm to enhance the κ_d and κ_q. This cavity is designed to demonstrate MIPA, so that Q-factors of cavity modes are not the main concern. The magnon mode used in our experiment is the Kittel mode supported by a 1 mm diameter YIG sphere. It follows the linear dispersion ω_m = γ(H + H_A), where γ, H_A, and H represent the gyromagnetic ratio, anisotropy field, and static bias magnetic field, respectively. During the experiment, our cavity magnonic device is placed on a rotatable platform, so that the direction of the bias magnetic field relative to our device can be precisely controlled.

Theory

Details of theoretical derivations of MIPA are provided in Supplementary Notes 1–4.