Coherent control of magnon radiative damping with local photon states

Abstract

A magnon, the collective excitation of ordered spins, can spontaneously radiate a travelling photon to an open system when decaying to the ground state. However, in contrast to electric dipoles, magnetic dipoles by magnons are more isolated from the environment, limiting their radiation and coherent communication with photons. The recent progresses in strongly coupled magnon-photon system have stimulated the manipulation of magnon radiation via tailoring the photon states. Here, by loading an yttrium iron garnet sphere in a one-dimensional waveguide cavity supporting both the travelling and standing photon modes, we demonstrate a significant magnon radiative damping that is proportional to the local density of photon states (LDOS). By modulating the magnitude and/or polarization of LDOS, we can flexibly tune the photon emission and magnon radiative damping. Our findings provide a way to manipulate photon emission from magnon radiation, which could help harness angular momentum generation, transfer, and storage in magnonics.

Introduction

A magnon is an elementary excitation of magnetic structure that is used as an information carrier in magnonics and magnon spintronics1,2,3,4, because it carries polarization or “spins” since the magnetization precesses anticlockwise around the equilibrium state1,2,3,4. The interplay between a magnon and other quasiparticles enriches the functionality of spintronic devices for information transfer with low dissipation. Magnons can excite electron spins by the interfacial exchange interaction (spin pumping)5,6, phonons by magnetostriction7,8, magnons in a proximity magnet through dipolar or exchange interaction,9,10 and microwave photons by the Zeeman interaction11. The range of spin transport by the electrons and phonons is restricted by their coherence length, which could strongly depend on disorder. Photons are thereby desirable in lifting this constraint due to their long coherence time or length in high-quality optical devices, including cavities and waveguides. Very recently, pioneering works have combined the best features of cavity photons and the long-lifetime magnon in yttrium iron garnet (YIG)12,13, demonstrating the cavity-magnon-polariton dynamics14,15,16,17,18,19. Such high-cooperativity hybrid dynamics stimulate the ideas of coherent information processing with magnons. To date, these works have mainly focused on the coherent coupling between the magnon modes and the standing-wave photon modes14,15,16,17,18,19,20,21 in a confined boundary. However, the efficient delivery of coherent information requires a waveguide supporting the travelling modes22,23, in which the magnon radiation in the continuous-wave range24,25,26 remains relatively unexplored.

Due to the conservation of angular momentum, a photon emitted by magnon radiation carries a spin current. The accompanying pumping of energy causes magnon radiative damping24,25,26, which reflects the efficiency of these photon emission processes27,28,29. However, weak coupling between the magnetic dipole and the photon makes the control of magnon radiation relatively difficult27,28,29. The magnon–photon interaction is hopefully enhanced by confining the photon modes in a cavity14,15,16,17,18,19,20,21 or waveguide. This strategy raises the hope of flexibly tuning the magnon lifetime on the basis of intrinsic Gilbert damping. The damping and dephasing rates of magnon in conventional solid-state materials, which are usually difficult to control due to disorder, might result in better controllability from such magnon–photon interactions. Moreover, in information processing the high tunability of photonic environment in a microwave waveguide could improve the pumping efficiency of the photon spin current from magnon radiation22,23. We envision that if the mechanism of tuning magnon radiation by local photon states could be demonstrated, various mechanisms that are used to tune photon emission by, for instance, metamaterials, antennas, and superconducting circuits, could be implemented with magnons to add functionality in magnonic applications27,30,31,32.

In this work, we address a general way to control the photon emission from magnons and magnon radiative damping by tuning the local electromagnetic environment. The radiative damping rate is demonstrated to be proportional to the local density of states (LDOS) of photons in a coupled magnon–photon system. We place a YIG sphere into a circular waveguide cavity that resembles to a “clarinet” in shape. Similar to the acoustics of “a clarinet,” standing waves are constructed with the superposition of a continuous-wave background33,34, highlighting the crucial differences seen with a confined cavity in a normal coupling scheme. The standing-wave component causes a coherent exchange between magnons and photons and induces a splitting gap in the dispersion, while the superposed travelling-wave component plays the key role of transferring radiated spin information to an open system. By simultaneously involving both standing and continuous waves, magnon radiation is thereby effectively controlled by photon states and clearly characterized by the magnon linewidth \(\Delta H\) from photon transmission. A relative suppression of the radiative damping at the cavity resonance compared with that at the detuned frequency is observed. This phenomenon seems to be different from the conventional Purcell effect29,35,36 in the conventional confined cavity, but could be understood by considering open-system photon mode structures. These measurements are well explained as we theoretically establish the relation between macroscopic magnon radiative damping and the microscopic LDOS of microwave photons at a quantitative level. Our result opens opportunities to tune the LDOS involving magnitude and/or polarization to control the photon emission from magnons and magnon radiative damping. To the best of our knowledge, our work is the first convincing observation of LDOS-tunable magnon radiative damping in a coupled magnon–photon system, thus providing the possibility of photon-mediated spin transport with preserved coherence. Due to the linearity nature of our work, we also anticipate that our method offers a general approach to other prototype photonic systems or on-chip integrated devices for advancing the manipulation and delivery of radiated spin information.

Results

Construction of photon states

To clarify the magnon radiative damping controlled by photon states, we first introduce the local electromagnetic environment inside the circular waveguide cavity as shown in Fig. 1a. This waveguide consists of a 16-mm-diameter circular waveguide and two transitions at both ends that are rotated by an angle of \(\theta\) = \(4{5}^{\circ }\). The two transitions can smoothly transform the TE10 mode of a rectangular port to the TE11 mode of a circular waveguide, and vice versa. Specifically, the microwaves polarized in the \(\hat{{\bf{x}}}\)- and \(\hat{{\bf{x}}}^{\prime}\)-directions are totally reflected at the ends of the circular waveguide, forming the standing waves around specific microwave frequencies. In contrast, the microwaves polarized in the \(\hat{{\bf{y}}}\)- and \(\hat{{\bf{y}}}^{\prime}\)-directions can travel across the transitions and therefore form a continuum of travelling waves. Therefore, in our device the standing waves can form around particular wave-vectors or frequencies that are superposed on the continuous-wave background33,34. The continuous waves help transfer the information to an open system and the standing waves provide the ingredient to form the cavity-magnon polariton. Thus, as opposed to the conventional well-confined cavity with discrete modes, our circular waveguide cavity enables us to add continuous modes to modify the photonic structure33.

Fig. 1: Magnon radiative damping controlled by LDOS (local density of photon states).
figure1

a Experimental setup of the coupled magnon–photon system in a circular waveguide cavity. b Transmission coefficient \(| {S}_{21}|\) from measurement (circles) and simulation (solid lines), with insets showing normalized LDOS distribution for standing-wave resonance at 12.14 GHz and continuous wave at 11.64 GHz. The color bar shows the scale for normalized LDOS with arbitrary unit. c By coupling the magnon mode with photon mode in a waveguide cavity, the radiative damping of a magnon can be the dominant energy dissipation channel compared to its intrinsic damping. d Measured amplitude of the transmission coefficient \(| {S}_{21}|\) as a function of the bias magnetic field. Anti-crossing dispersion can be clearly observed for coupled magnon–photon states. The squared amplitudes of the transmission coefficients (\(| {S}_{21}(H){| }^{2}\)) are shown at fixed frequencies of 11.64 GHz (e), 12.14 GHz (f), and 12.64 GHz (g), with the x-axis offset \({H}_{\mathrm{m}}\) being the biased static magnetic field at magnon resonance. The squares represent the measured \(| {S}_{21}(H){| }^{2}\) spectra, and the solid line from the lineshape fit represents the reproduced experimental results. In this figure, experimental errors are smaller than the symbol sizes.

The modes in our device can be characterized by microwave transmission using a vector network analyzer (VNA) between ports 1 and 2. A standing-wave or “cavity” resonance mode at \({\omega }_{\mathrm{c}}/2\pi\) = 12.14 GHz is clearly revealed in \({S}_{21}\) with a loaded damping factor of \(9\ \times \ 1{0}^{-3}\), as illustrated by blue circles in Fig. 1b. In the transmission spectrum, the standing waves confined in the waveguide cause a dip in transmission spectrum at the cavity resonance33. The travelling continuous waves that deliver photons from ports 1 to 2 contribute a high transmission close to 1. Because continuous waves are not negligible in our device, photon modes cannot be described by a single harmonic oscillator, as shown in previous works14,16,17,18,19. Hence, the electromagnetic fields in our waveguide cavity are described by a large number of harmonic modes37,38,39 over a wide frequency range, and each mode has a certain coupling strength with the magnon mode.

The Fano–Anderson Hamiltonian describes the interaction between the magnon and photon modes as given by Eq. (1)11,37:

$${\hat{H}}_{0}/\hslash ={\omega }_{\mathrm{m}}{\hat{m}}^{\dagger }\hat{m}+\mathop {\sum}\limits_{{k}_{z}}{\omega }_{{k}_{z}}{\hat{a}}_{{k}_{z}}^{\dagger }{\hat{a}}_{{k}_{z}}+\mathop {\sum}\limits_{{k}_{z}}{g}_{{k}_{z}}({\hat{m}}^{\dagger }{\hat{a}}_{{k}_{z}}+\hat{m}{\hat{a}}_{{k}_{z}}^{\dagger }),$$
(1)

where \({\hat{m}}^{\dagger }\) (\(\hat{m}\)) is the creation (annihilation) operator for the magnon in Kittel mode with frequency \({\omega }_{\mathrm{m}}\), \({\hat{a}}_{{k}_{z}}^{\dagger }\) (\({\hat{a}}_{{k}_{z}}\)) denotes the photon operator with wave vector \({k}_{z}\) and frequency \({\omega }_{{k}_{z}}\), and \({g}_{{k}_{z}}\) represents the corresponding coupling strength between the magnon and microwave photon modes. We visualize the magnon Kittel mode as a single harmonic oscillator in Eq. (1). The magnon and photon modes have intrinsic damping originating from an inherent property, but our cavity establishes coherent coupling between them24,25,26 as schematically shown in Fig. 1c.

Due to the coherent coupling between the magnon mode and photon mode, the energy of an excited magnon radiates to the photons that travel away from the magnetic sphere. This phenomenon can be pictured as the “auto-ionization” of a magnon into the propagating continuous state that induces the photon emission from the magnon, and hence, there is magnon radiative damping40,41. Such “additional” magnon dissipation induced by photon states can be rigorously calculated by the imaginary part of self-energy in the magnon Green’s function, which is expressed as \(\Delta {E}_{\mathrm{m}}={\delta }_{\mathrm{m}}+\frac{\pi }{\hslash }| \hslash g(\omega ){| }^{2}D(\omega )\). Here, \({\delta }_{\mathrm{m}}\) is the intrinsic dissipation rate of the magnon mode, and \(D(\omega )\) represents the global density of states for the whole cavity that is a count of the number of modes per frequency interval. We note that the above radiative damping is established when the on-shell approximation is valid with the energy shift of the magnon (tens to hundreds of MHz) being much smaller than its frequency (several GHz). By further defining the magnon broadening in terms of magnetic field \(\Delta E=\hslash \gamma {\mu }_{0}\Delta H\), the magnon linewidth can be expressed as Eq. 2 (Supplementary Note 1)

$${\mu }_{0}\Delta H={\mu }_{0}\Delta {H}_{0}+\frac{\alpha \omega }{\gamma }+\frac{2\pi \kappa }{\gamma }R| {\rho }_{l}(d,\omega )| ,$$
(2)

where \(\gamma\) is the modulus of the gyromagnetic ratio, and \({\mu }_{0}\) denotes the vacuum permeability. In Eq. (2), the first two terms represent the linewidth related to inherent damping of the magnon in which \({\mu }_{0}\Delta {H}_{0}\) and \(\alpha \omega /\gamma\) come from the inhomogeneous broadening at zero frequency42 and the intrinsic Gilbert damping, respectively. The last term describes the radiative damping induced by photon states in which \(| {\rho }_{l}(d,\omega )|\) represents the LDOS of magnetic fields with \(d\) and \(l\) denoting the position and photon polarization direction, respectively. Basically, the LDOS counts both the local magnetic field strength and the number of electromagnetic modes per unit frequency and per unit volume. The coefficient \(\kappa\) is expressed as \(\kappa =\frac{\gamma {M}_{\mathrm{s}}{V}_{\mathrm{s}}}{2\hslash {c}^{2}}\), with \({M}_{\mathrm{s}}\) and \({V}_{\mathrm{s}}\) being the saturated magnetization and volume, respectively, of the loaded YIG sphere. The fitting parameter \(R\) is mainly influenced by cavity design and cable loss in the measurement circuit.

Based on the above theoretical analysis, we find that the radiative damping is exactly proportional to the LDOS \({\rho }_{l}(d,\omega )\). To observe radiation as a dominant channel for the transfer of magnon angular momentum, both low inherent damping of the magnon and a large tunable \(| {\rho }_{l}(d,\omega )|\) are required. In the following experiment, both conditions are satisfied by introducing a YIG sphere with low Gilbert damping, and by modifying the photon mode density through tuning the LDOS magnitude, LDOS polarization, and global cavity geometry.

Magnon linewidth characterization

A highly polished YIG sphere with a 1 mm diameter is loaded into the middle plane of a waveguide cavity. Before immersing into the experimental observations, it is instructive to understand the two-dimensional (2D) spatial distribution of the LDOS in the middle plane, which is numerically simulated by CST (computer simulation technology) at the center cross-section that can well reproduce \(| {S}_{21}|\), as shown in Fig. 1b. The hot spots for the continuous waves (11.64 GHz) and standing wave (12.14 GHz) are spatially separated, providing the possibility to control LDOS magnitude by tuning the positions of the magnetic sample inside the cavity.

In our first configuration, we focus on the local position with   d = 6.5 mm, as marked in Fig. 1b. This position enables the magnon mode not only to overlap18 with the standing waves but also to couple to the continuous waves. More interestingly, as indicated by the insets in Fig. 1b, the LDOS at d = 6.5 mm is small in quantity at the cavity resonance compared with the ones in the continuous-wave range. This is opposite to the LDOS enhancement at resonance in a conventional well-confined cavity29,35,36. Therefore, according to Eq. (2), in contrast to the magnon linewidth enhancement at the cavity resonance in previous works, we expect a different linewidth evolution by varying the frequency, along with a smaller linewidth at cavity resonance \({\omega }_{\mathrm{c}}\) compared with that at the detuned frequencies.

Concretely, the magnon linewidth can be measured from the \(| {S}_{21}|\) spectra in an \(\omega\)-\(H\) dispersion map. In our measurement, a static magnetic field \({\mu }_{0}H\) is applied along the \(\hat{{\bf{x}}}\)-direction to tune the magnon mode frequency (close to or away from the cavity resonance), which follows a linear dispersion \({\omega }_{\mathrm{m}}=\gamma {\mu }_{0}(H+{H}_{\mathrm{A}})\), with \(\gamma =2\pi\,\times\,28\) GHz T−1 and \({\mu }_{0}{H}_{\mathrm{A}}=192\) Gauss as the specific anisotropy field. For our YIG sphere the saturated magnetization is \({\mu }_{0}{M}_{\mathrm{s}}\) = 0.175 T, and the Gilbert damping \(\alpha\) is measured to be \(4.3\,\times\,1{0}^{-5}\) by standard waveguide transmission with the fitted inhomogeneous broadening \({\mu }_{0}\Delta {H}_{0}\) equal to 0.19 Gauss. As the magnon resonance \({\omega }_{\mathrm{m}}\) is tuned to approach the cavity resonance \({\omega }_{\mathrm{c}}\), a hybrid state is generated with the typical anti-crossing dispersion as displayed in Fig. 1d. A coupling strength of 16 MHz can be found from the Rabi splitting at zero detuning condition, which indicates the coherent energy conversion between the magnon and the photon. This coupling strength is greater than the magnon linewidth but smaller than the cavity linewidth (~100 MHz), suggesting that our system lies in the magnetically induced transparency (MIT) regime rather than the strong coupling regime18. Dissipation of the photon mode allows the delivery of magnon radiation energy to the open environment through the waveguide cavity.

The magnon linewidth (i.e., half-width at half-maximum) is characterized by a lineshape fitting of \(| {S}_{21}(H){| }^{2}\) that is obtained from the measured transmission at a fixed frequency and different magnetic fields. Here, we focus on \(| {S}_{21}(H){| }^{2}\) at three different frequencies with one at the cavity resonance \({\omega }_{\mathrm{c}}\) and the other two chosen at continuous-wave frequencies above and below \({\omega }_{\mathrm{c}}\) (11.64 and 12.64 GHz, respectively). As the photon frequency is tuned from the continuous-wave range to the cavity resonance \({\omega }_{\mathrm{c}}/2\pi\) = 12.14 GHz, we observe that the lineshape of \(| {S}_{21}(H){| }^{2}\) varies from asymmetry to symmetry, as shown in Fig. 1e–g. These results can be well fitted (see solid lines in Fig. 1e–g), which helps us to identify an obvious linewidth suppression from the continuous-wave range (2.0/1.5 Gauss) to cavity resonance (1.0 Gauss).

When compared with the magnon linewidth \({\mu }_{0}\Delta H\) at detuned frequencies, the magnon linewidth shows a relative suppression at the cavity resonance rather than the linewidth enhancement in a conventional coupled magnon–photon system in the cavity19,43. Such suppression of the magnon linewidth qualitatively follows the LDOS magnitude, which also shows a decrease in quantity at the cavity resonance. This finding qualitatively agrees with our theoretical expectation from Eq. (2). In the following subsections, it is necessary to study the relationship between linewidth and LDOS at a quantitative level by using both theoretical calculation and experimental verification.

Magnon radiation controlled by LDOS magnitude

In this subsection we provide a quantitative control of magnon radiative damping by tuning the LDOS magnitude over a broadband frequency range. The spatial variation of the magnetic field in our waveguide cavity allows us to realize different LDOS spectra simply by choosing different positions. Similar to the experimental settings in the above section with \(d\) = 6.5 mm, we display a broadband view of the LDOS for polarization by using simulation illustrated in Fig. 2. Although \({\rho }_{x}(\omega )\) in Fig. 2a shows a typical resonance behavior, its contribution to the magnon radiation is negligible here according to the well-known fact that only photon polarization that is perpendicular to the external static magnetic field \(H\) drives the magnon linear dynamics. By following this consideration, we further simulate \({\rho }_{\perp }\) = \(\sqrt{{\rho }_{y}^{2}+{\rho }_{z}^{2}}\), which plays a dominant and important role in the magnon–photon interaction as displayed in Fig. 2b. \({\rho }_{\perp }(\omega )\) shows a dip at the cavity resonance with respect to the frequency.

Fig. 2: LDOS (local density of photon states) magnitude dependence.
figure2

a, b Simulated x-direction LDOS (\({\rho }_{x}\)) and perpendicular LDOS (\({\rho }_{\perp }\)) at  d = 6.5 mm. c Measured linewidth-frequency (\({\mu }_{0}\Delta H{\mbox{-}}\omega\)) relation (shown in squares) with calculated lines from the model (green line) at  d = 6.5 mm. d, e Simulated LDOS \({\rho }_{x}\) and \({\rho }_{\perp }\) at  d = 0 mm. f Measured linewidth-frequency \({\mu }_{0}\Delta H{\mbox{-}}\omega\) relation (squares) with calculated lines from the model (green line) at d = 0 mm. Black circles and lines indicate the measured and fitted intrinsic linewidths, respectively. g Magnon linewidth \({\mu }_{0}\Delta H\) evolution with tuning positions for different frequencies, with circles and solid lines representing the measured magnon linewidth and the linewidth computed from LDOS, respectively. Errors of linewidth fit are smaller than the size of symbols.

It is clearly seen that due to the enhancement of the global density of states at the mode cut-off of the waveguide, continuous-wave LDOS becomes increasingly significant when the frequency is decreased to approach the cut-off frequency (~9.5 GHz). This phenomenon can be viewed as a Van Hove singularity effect in the density of states for photons (see independent observation via a standard rectangular waveguide in Supplementary Note 2). Because the singularity effect is involved in the coupled magnon–photon dynamics, we can obtain a larger linewidth at the detuned frequency range, which causes a relative linewidth suppression at the cavity resonance. In contrast to the linewidth enhancement from typical Purcell effects in a confined cavity, the results shown in Fig. 2c provide a new linewidth evolution process over a broadband range. These results are obtained from lineshape fitting at each frequency, with the error of fit being smaller than the symbols. Furthermore, to compare with our theoretical model, we perform calculations using Eq. (2) with \(\kappa R=4.0\ \times \ 1{0}^{22}\,{{\mathrm{m}}}^{3}\,{{\mathrm{s}}}^{-2}\), where the fitting parameter quantity \(R \sim 0.8\). It can be observed in Fig. 2c that the measured \({\mu }_{0}\Delta H\) agrees well with the computed values from our theoretical model. This suggests that the linewidth is coherently controlled by the LDOS magnitude and shows that radiative power emission induced by continuous waves can unambiguously exceed that induced by standing waves.

To create a different LDOS magnitude to tune the magnon radiation, the magnetic sphere is moved to the center of the cross-section with \(d\) = 0 mm. The simulated LDOS \({\rho }_{x}\) and \({\rho }_{\perp }\) are illustrated in Fig. 2d, e, respectively. The effective LDOS \({\rho }_{\perp }\) shows an enhancement at the cavity resonance but decreases at the continuous-wave range. Similar to the frequency dependence of the LDOS magnitude, the magnon linewidth is observed to be enhanced at the cavity resonance, but decreased at the continuous-wave range. This relation between the magnon linewidth and LDOS is again quantitatively verified by the good agreement between measurement and calculated results from Eq. (2), as shown in Fig. 2f. In particular, as the continuous-wave LDOS approaches zero, the radiative damping from LDOS thereby becomes negligibly small. In this case, we find that the magnon linewidth exactly returns to its intrinsic damping \({\mu }_{0}\Delta {H}_{0}+\alpha \omega /\gamma\) measured in an independent standard waveguide.

Finally, at a detailed level, to continuously tune the ratio of the standing/continuous-wave LDOS magnitude, the position of the YIG sphere is moved where \(d\) varies from 0 to 6.5 mm. Typically, for the three different frequency detunings at 0, −100, and −440 MHz, our results in Fig. 2g show that the magnon linewidth can be controlled by the enhancement, suppression, or negligible variation in the position dependence. As shown in Fig. 2g, these results show good agreement with the theoretical calculation, suggesting that the magnon linewidth can be controlled on demand by tuning the LDOS magnitude. Moreover, the photon emission efficiency from the magnon radiation can in principle be significantly enhanced with a larger magnetic sphere and a waveguide with a smaller cross-section. For example, a magnetic sphere with 2-mm diameter and a waveguide with half radius would enhance the radiation rate by 16 times (Supplementary Note 1).

Magnon radiation controlled by LDOS polarization

Having shown the relation between the magnon radiative damping in \({\mu }_{0}\Delta H\) and the LDOS magnitude, here we would like to introduce LDOS polarization as a new degree of freedom to control the magnon radiation. In our experiment, by placing the YIG sphere at \(d\) = 2.3 mm, the control of effective LDOS polarization \({\rho }_{\perp }\) around the magnetic sphere can be simply achieved by varying the direction of the external static magnetic field \(H\) with a relative angle \(\varphi\) to the \(\hat{{\bf{x}}}\)-direction as shown in Fig. 3a. Please note that compared with the complicated operation of varying the position of the YIG sphere inside a cavity, here the LDOS was controlled continuously over a large range simply by rotating the orientation of the static magnetic field. Based on the orthogonal decomposition of the LDOS for photons, \({\rho }_{\perp }\) is simulated for three typical angles, that is, \(\varphi\) = 0°, 45°, and 90°, as shown in Fig. 3b. For the relative angle \(\varphi ={0}^{\circ }\) with \(H\) being exactly in the \(\hat{{\bf{x}}}\)-direction, the LDOS is dominated by the standing-wave component, which could provide the largest coupling with the magnon mode at the cavity resonance. As the relative angle \(\varphi\) approaches 90°, continuous waves become increasingly dominant in their contribution to the LDOS, causing a peak-to-dip flip for the LDOS around the resonance frequency \({\omega }_{\mathrm{c}}\) in Fig. 3b.

Fig. 3: LDOS (local density of photon states) polarization dependence.
figure3

a Schematic of tuning orientation of external magnetic field \(H\) relative to the \(\hat{{\bf{x}}}\)-direction in the plane of waveguide cross-section. b Simulated photon LDOS perpendicular to external magnetic field \(H\) with relative angles of \(\varphi ={0}^{\circ }\), \(4{5}^{\circ }\), and \(9{0}^{\circ }\). c Measured magnon linewidth spectra, that is, \({\mu }_{0}\Delta H{\mbox{-}}\omega\) relation (squares) and calculated results (solid lines) for different angles of \(\varphi ={0}^{\circ }\), \(4{5}^{\circ }\), and \(9{0}^{\circ }\). Errors of linewidth fit are smaller than the size of symbols.

Accordingly, in our experiment, we obtain a magnon linewidth enhancement at \(\varphi ={0}^{\circ }\) as shown in Fig. 3c with red squares. As the relative angle \(\varphi\) is tuned towards 90°, we thereby anticipate and indeed obtain a linewidth suppression at the cavity resonance shown with blue squares, showing good agreement with the linewidth scaling of \({\rho }_{\perp }\) in Eq. (2). The theoretically calculated linewidth \({\mu }_{0}\Delta H\) is plotted for each \(\varphi\) in Fig. 3c with \(\kappa R\) consistent with the previous subsection. The good agreement between experimental and theoretical findings suggests flexible control of magnon radiation via LDOS polarization. Moreover, by not restricting the tuning of the relative angle between \(H\) and LDOS polarization in the 2D plane, there may be an increased possibility of realizing magnon radiation engineering by pointing \(H\) to an arbitrary direction in the whole 3D space.

Magnon radiation controlled by cavity geometry

Our device allows us to tune the LDOS magnitude and polarization together simply by rotating the relative angle \(\theta\) between the two transitions33, that is, the global geometry of our circular waveguide cavity. This approach can validate and enrich our observations that the same magnon harmonic mode radiates a different amount of power depending on the surrounding photon environment. In this subsection, we insert a rotating part in the middle plane of the cavity, so that the relative angle \(\theta\) between two transitions can be smoothly adjusted. By tuning the angle \(\theta\) from 45° to 5°, our system shows a significant change in photon transmission as illustrated in Fig. 4a, accompanied by significant enhancements in the cavity quality factor and global density of states44,45. In addition the cavity resonance shows a redshift to 11.79 GHz due to the increase in cavity length. The YIG sphere is placed at the center of the cavity cross- section with  d = 6 mm, and the external magnetic field is applied in the \(\hat{{\bf{x}}}\)-direction. These experimental conditions provide stable magnon–photon coupling strength when \(\theta\) is tuned, as shown by the nearly unchanged mode splitting in Fig. 4b.

Fig. 4: Cavity geometry dependence.
figure4

a Cavity mode transmission profile when rotating the relative angle \(\theta\). b Rabi splitting spectra for different angles \(\theta\). c Simulated LDOS (local density of photon states) \({\rho }_{\perp }\) for different \(\theta\). d Measured magnon linewidth spectra (\({\mu }_{0}\Delta H{\mbox{-}}\omega\) relation) when tuning the relative angle \(\theta\). e, f shows comparison between theoretical results and measurement at 11.79 GHz cavity resonance (e) and 11.45 GHz continuous-wave frequency (f). The dashed lines are intrinsic linewidths of the YIG (Yttrium iron garnet) sphere. Errors of linewidth fit are smaller than the size of symbols.

Our hybrid system now readily allows us to investigate the magnon radiation controlled by cavity geometry. In particular, tuning the relative angle \(\theta\) from 45° to 5° leads to a redistribution of photon states in the cavity, greatly enhancing the LDOS near the cavity resonance and allowing the continuous-wave LDOS to be controlled in the opposite way, as illustrated by the simulated LDOS \({\rho }_{\perp }\) in Fig. 4c. Based on the theoretical model, we expect that the magnon linewidth can quantitatively follow the geometry-controlled LDOS \({\rho }_{\perp }\). The results from measurements under different \(\theta\) are shown in Fig. 4d, and we indeed obtain linewidth \({\mu }_{0}\Delta H\) with similar behavior to that of the simulated LDOS \({\rho }_{\perp }\). As is evident in Fig. 4e, f, we find that the linewidth is well reproduced by our theoretical model with \(\kappa R\) adjusted to \(4.3\,\times\,1{0}^{22}\,{{\mathrm{m}}}^{3}{{\mathrm{s}}}^{-2}\). By tuning LDOS via the relative angle \(\theta\), the experimental linewidth is enhanced 20-fold at the cavity resonance in comparison with the intrinsic damping of the magnon, as illustrated by the dashed lines.

Discussion

Understanding and controlling magnon radiative damping is essential in tuning the magnon lifetime and transporting spin information by travelling photons in magnonic or spintronic applications27,28,29,46,47. By revealing the quantitative relation between magnon radiative damping and photon LDOS for the first time, to the best of our knowledge, our work introduces three perspectives for better exploring and using magnon radiation in future research.

Flexible control of magnon lifetime

Photon LDOS construction can flexibly tune the magnon lifetime on the basis of intrinsic Gilbert damping. Magnon with a long lifetime is useful for information storage and memory, while magnon with a suppressed lifetime would bring an advantageous impact for realizing a fast repetition rate in the device29. Our work explores some techniques including LDOS magnitude, polarization and global environment to control magnon radiative damping, which could open paths for various methods for controlling the LDOS to tune the magnon lifetime in a flexible and precise fashion and provides a new ingredient to advanced communication processing48.

Delivering coherent information of cavity-magnon polariton to open systems

Although the weak interaction between the magnetic dipole and photons can be enhanced by confining the photon mode in a cavity, the confinement restricts the information of the closed system to be efficiently transferred to the open system and vice versa. Our constructed magnon–photon system can combine both the standing and travelling photon modes to couple the magnon mode. The traveling channel allows us to deliver the coherent information out, thus advancing the efficient tuning of the dynamics of the cavity-magnon polariton. Manipulation of magnon radiation to an open system, as we demonstrated, is very attractive for exploring new physics related to magnon dissipative procession49, such as dissipative coupling in a magnon-based hybrid system50.

Stimulating the advancement of hybrid magnonics

Controllable magnon radiation could stimulate hybrid magnonic systems to access new frontiers. Recent studies show that coherent information at a single magnon level can be coherently transferred to a photon or superconducting qubit through radiation at millikelvin temperatures14,51, revealing the quantum nature to the hybridized magnonic system. At room temperature, the magnon–photon mode coupling is generally restricted in linear harmonic dynamics, while recent research breaks this harmonic restriction by using a feedback mechanism, exhibiting nonlinear triplet spectra similar to quantum dots21. Controlling magnon radiation in these new regimes could stimulate the advancement of hybrid magnonics.

In conclusion, we observe and show the ability to control the photon emission from magnon and magnon radiative damping in the hybrid magnon–photon system, bridging their relation to the tunable photon LDOS. One quantitative method to design and tune the radiation efficiency of the magnon is provided based on tailoring the photon LDOS including LDOS magnitude and/or polarization, thereby possibly leading to a general technique of tuning magnon relaxation on demand. Our measurements are mainly performed in the MIT regime with large photon damping, which causes radiative damping by photon dissipation, while travelling-wave photons can directly transfer the magnon energy to an open system. Overall, our study introduces a mechanism to coherently manipulate magnon dynamics by local photon states and suggests a promising potential toward the development of magnon-based hybrid devices and related coherent information processing.

Methods

Device description

Our waveguide cavity is made up of a cylindrical waveguide and two circular rectangular transitions coaxially connected at both ends. Through the transition, a smooth change between TE10 mode of rectangular waveguide port and TE11 one of cylindrical waveguide can be established. Via coaxial cables, the cavity is connected to the input/output ports of a VNA. With an input power of 0 dBm, the transmission signals can be precisely picked up by VNA. YIG sphere is fixed firmly inside the cavity with scotch tape, with its location tunable on demand to couple with different microwave magnetic fields. YIG and the scotch tape, as dielectric materials, can slightly influence the microwave fields distribution in our experiment. We neglect the small dielectric influence in our theoretical treatment.

Theoretical description

In Supplementary Note 1, the theory of magnon spontaneous radiation in the waveguide including the derivation of the magnon linewidth induced by the LDOS is provided.

Data availability

The data that support the findings of this study are available from the corresponding authors upon reasonable request.

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Acknowledgements

T.Y. was supported by the Netherland Organization for Scientific Research (NWO). This work was funded by the National Natural Science Foundation of China under Grant Nos. 11974369 and 11804352, the Shanghai Pujiang Program No. 18PJ1410600, SITP Innovation Foundation (CX-245), and Independent Research Project of State Key Laboratory of Infrared Physics (No. Z201920). We would like to thank Y. Zhao, J. Sirker, L.H. Bai, P. Hyde, Y.M. Blanter, and G.E.W. Bauer for useful discussions.

Author information

B.Y. and Y.S.G. set up the hybrid system and conducted the experiment, as well as analyzed the data. T.Y., in discussions with B.Y. and C.-M.H., developed the theory part. J.W.R. and Y.T.Z. contributed to the design of the cavity parts. B.Y. and T.Y. prepared all the figures as well as the Supplementary Information. T.Y., W.L. and C.-M.H. together supervised the work. All authors contributed to writing the paper.

Correspondence to Tao Yu or W. Lu or C.-M. Hu.

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Yao, B., Yu, T., Gui, Y.S. et al. Coherent control of magnon radiative damping with local photon states. Commun Phys 2, 161 (2019). https://doi.org/10.1038/s42005-019-0264-z

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