Hybrid magnonics: physics, circuits and applications for coherent informationprocessing

Yi Li,1 Wei Zhang,2, 1 Vasyl Tyberkevych,2 Wai-Kwong Kwok,1 Axel Hoffmann,3, a) and Valentine Novosad1, b)

1)Materials Science Division, Argonne National Laboratory, Argonne, IL 60439,USA2)Department of Physics, Oakland University, Rochester, MI 48309, USA3)Department of Materials Science and Engineering, University of Illinois at Urbana-Champaign Urbana,IL 61801

(Dated: 30 June 2020)

Hybrid dynamic systems have recently gained interests with respect to both fundamental physics and deviceapplications, particularly with their potential for coherent information processing. In this perspective, we willfocus on the recent rapid developments of magnon-based hybrid systems, which seek to combine magnonicexcitations with diverse excitations for transformative applications in devices, circuits and information pro-cessing. Key to their promising potentials is that magnons are highly tunable excitations and can be easilyengineered to couple with various dynamic media and platforms. The capability of reaching strong couplingwith many different excitations has positioned magnons well for studying solid-state coherent dynamics andexploiting unique functionality. In addition, with their gigahertz frequency bandwidth and the ease of fab-rication and miniaturization, magnonic devices and systems can be conveniently integrated into microwavecircuits for mimicking a broad range of device concepts that have been applied in microwave electronics,photonics and quantum information. We will discuss a few potential directions for advancing magnon hybridsystems, including on-chip geometry, novel coherent magnonic functionality, and coherent transduction be-tween different platforms. As future outlook, we will discuss the opportunities and challenges of magnonichybrid systems for their applications in quantum information and magnonic logic.

I. INTRODUCTION

Hybrid dynamic systems have recently attracted greatattentions due to their applications in quantum informa-tion, communications and sensing1. Thus hybrid systemsprovide a new paradigm for combining platforms and de-vices that can perform different tasks such as storing,processing and transmitting coherent states, particularlyin quantum information. In addition, coherent interac-tions that are based on those bosonic excitations are notrestricted to the quantum limit, but can be also observedin the classical regime because phase coherence can bemaintained for all the excitation quanta at the lowest en-ergy states. This significantly facilitates the research onthe fundamental physics of strong coupling between dif-ferent excitations as well as coherent manipulation andengineering of hybrid systems.

One important feature in hybrid dynamic systems isthat the coherence of information being carried in dy-namic excitations can be maintained while being trans-duced from one module to another. Coherence, whichis defined as the preservation of phase in excitationsbetween different modules, is limited by the decoher-ence rate κ, which can be determined by the frequencylinewidth. Conversely, the transduction rate is deter-mined by the coupling strength g in the frequency do-main. Therefore, in order to maintain coherence dur-ing transduction, g needs to be larger than κ. For two

a)Electronic mail: axelh@illinois.edub)Electronic mail: novosad@anl.gov

coupled systems with decoherence rate κ1 and κ2, itis convenient to define the cooperativity of the system:C = g2/κ1κ2. C > 1 and g > κ1, κ2 defines the strongcoupling regime in order to conduct any practical coher-ent information operation.

The introduction of magnons in hybrid systems startedfrom the exploration of spin ensembles coupled to mi-crowave photons2,3, where the spin-photon couplingstrength can be enhanced by increasing the total num-ber of spins N proportional to

√N4,5. Subsequently

it was quickly found that due to their orders of mag-nitude higher spin densities, magnetic materials andtheir collective spin excitations, or magnons, can providemuch stronger coupling6,7, from a few megahertz in spinensembles2,3,8 to a few hundred megahertz in yttriumiron garnet (YIG) crystals9–13, along with cooperativityup to 103 ∼ 104. This has quickly triggered broad atten-tion and activities on new hybrid platforms with differ-ent microwave cavity designs, different magnetic systemsand improved coupling14–26. Thus a research directioncalled cavity magnonics (or cavity spintronics, spin cav-itronics) has been created27–29, which focuses on the newproperties, functionality and engineering of the coherentinteractions between magnons and microwave photons.

A groundbreaking achievement came from Tabuchi,et al.30, who demonstrated coherent coupling betweena single magnon and a superconducting qubit medi-ated by a microwave cavity. The same group has sub-sequently demonstrated detection of a single magnonby continuous-wave31 and single-shot (pulse)32 inputs.These achievements open the possibility of conduct-ing quantum information operations with magnons,

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2

All-on-chip

architecture

Physic

s

Pla

o

rm

Magnon-phonon

Magnon-magnon

Magnon-optic

3D planar superconductor

dissipative coupling

nonreciprocity

Magnon-photon

S12

S21

YIG sphere

ISRR

spin pumping

Coherent transducers

Geometry

Coherent informa"on processing

FIG. 1. Growing directions and goals for magnon hybrid systems. The explorations on geometry, physics and platform lead toon-chip architecture, coherent information processing and coherent transduction, respectively.

leading to a new research field named quantummagnonics33. In addition, the capability of coupling mi-crowave excitations with optical photons via magneto-optic interactions34–37 has generated interests of usingmagnons as quantum transducers between microwavequantum information and quantum optics33,38. The po-tential of all-on-chip integration of magnon-photon hy-brid systems, particularly with high-quality-factor super-conducting resonators24,25, can further boost the applica-tions of magnon hybrid systems in quantum information.

Besides microwave photons, magnon hybrid systemshave also been extended to other excitations, such asphonons, optical photons and magnons themselves, ow-ing to the abundant coupling mechanisms associated withmagnetic materials such as magneto-elastic, magneto-optic, dipolar and exchange couplings. The coher-ent interactions of different dynamic systems have in-spired interdisciplinary explorations and provided newideas for multi-stage coherent transduction of magnonicsystems39–44.

In this perspective, we will discuss several emergingdirections for the development of magnon hybrid system,which are summarized in Fig. 1. First, the integrationof the magnon and microwave resonator systems, withgeometry ranging from 3D to planar, provide new oppor-tunity for device miniaturization. Second, the straight-forward engineering of the magnon hybrid systems leadsto new physics and properties which can be applied tonew device concepts and functionality in coherent infor-mation processing. Third, numerous magnon-based hy-brid systems have introduced new platforms for remoteinformation transduction with magnons. Lastly, we will

discuss how the discoveries of magnon hybrid systemscan be applied in two particular areas, i.e., quantum in-formation and magnonic logic.

II. MAGNON-PHOTON COUPLING

The interaction between magnons and microwave pho-tons has been used for decades for measuring magne-tization dynamics45–47. The microwave excitations ofmagnons are typically achieved by placing magnetic sam-ples into a microwave waveguide or cavity, and the fer-romagnetic resonance signals can be measured from thetransmission or reflection of microwave photons. The res-onance signals describe the evolution of the magnetic sus-ceptibility χm, as:

χm =ωM/2

(ωm − ω)− iαωm(1)

where ωm is the magnon resonance frequency determinedby the magnetic field, ω is the microwave frequency, αis the Gilbert damping and ωM = γµ0Ms with γ thegyromagnetic ratio and Ms the saturation magnetiza-tion. The factor 1/2 comes from the linearly polarizedmicrowave field coupled with circularly polarized magne-tization precession. The demagnetizing field is ignoredfor simplicity.

Inside a microwave cavity, the magnetic sample be-comes part of the cavity and contributes as an additionalinductance. If we consider the microwave cavity as anLCR resonator, the magnetic sample increases the totalinductance as L(χm) = L0(1 + χmVm/Vc), where L0 is

3

the intrinsic inductance of the cavity, Vc is the effectivevolume of the cavity, and Vm is the volume of the mag-netic system. The reflection of the microwave cavity canbe described as

PoutPin

=κR

i(ωp − ω) + κp(2)

where ωp = 1/√L(χm)C is the cavity resonant fre-

quency, κp = 1/(2RC) is the damping rate of the LCRresonator and κR is the coupling rate to the externalport. Eqs. (1) and (2) have a similar form because theydescribe the resonance of magnons and photons. In thelimit of linear magnetic coupling, Vm � Vc, by expandingthe χm term in Eq. (2), we have:

PoutPin

=κR

i(ωp − ω) + κp + g2

i(ωm−ω)+κm

(3)

with g =√ωpωMVM/4Vc. Eq. (3) is the fundamen-

tal equation for cavity magnonics and describes the an-ticrossing spectra in the strong coupling regime (g >κp, κm). For the coupling strength, taking MsVM =NµB , where µB = γh is the magnetic moment for a sin-gle Bohr magneton and N is the total number of spins,the expression for the coupling strength is:

g = γ

√Nµ0hωp

4Vc(4)

Eq. (4) defines one of the most important parameters incavity magnonics which determines the excitation trans-duction bandwidth or the Rabi-like oscillation betweenmagnons and photons. In addition, Eq. (4) reveals thatg goes up when 1) N becomes larger and 2) Vc becomessmaller. For 1), it is straightforward to increase the vol-ume of the magnetic sample in many cases. Howeverthe requirement for device miniaturization and integra-tion requires 2) to obtain higher sensitivity to magnonexcitations.

III. ALL-ON-CHIP PLATFORMS FOR HYBRIDMAGNONICS

All-on-chip platforms for magnon-photon hybrid sys-tems are desired for pushing towards microwave circuitapplications and device integration. However, it is adilemma that in many cases large volumes of magneticsamples are needed for strong coupling. The most com-monly studied model system consists of a yttrium irongarnet (YIG) single crystal placed inside a 3D microwavecavity10–12,14–18,21, where YIG is a ferrimagnetic materialthat has the lowest known magnetic damping coefficientdown to 10−5. Up to gigahertz coupling strength canbe reached for large enough YIG crystals11,12,18. How-ever, due to the macroscopic effective volume of the cav-ity, the coupling strength per Bohr magneton, definedas g0 = g/

√N , is usually small, much lower than 1 Hz.

nanomagnet

1 mm

superconducting

resonator

Py stripe

HBθ

Magnon

Photon

Hybrid

mode

S21

(dB)

(a) (c)

(b) (d)

FIG. 2. All-on-chip magnon-photon hybrid system with su-perconducting resonators. (a) Coplanar superconducting res-onator coupled to on-chip Py device. (b) Mode anti-crossingspectra for a 900 µm × 14 µm × 30 nm Py device, measuredfrom (a). (c) Lumped-element coplanar superconducting res-onator coupled to on-chip Py device (d) Mode anti-crossingspectra for a 40 µm × 2 µm × 10 nm Py device, measuredfrom (c). Adapted from Refs.24 and25.

This also requires a macroscopic volume of the YIG crys-tal, typically with a diameter of 1 mm, in order to ob-tain strong coupling. Planar microwave resonators suchas split-ring resonators (SRRs)13,20,48–51 and striplineresonators52–54 have been also explored for their betteron-chip integration. Because of the lower dimensions,planar resonators usually have smaller effective volumesand thus larger g0 compared with 3D cavities20. How-ever, due to much thinner conducting lines comparedwith thick 3D cavity walls, the resistive loss is overwhelm-ing and the quality factors of the planar resonators arequite low, usually less than 100, which makes it hard toextend the cooperativity.

Superconducting coplanar resonators possess both pla-nar geometry and high quality factor. In addition, ahigh quality factor can be maintained with very small ef-fective volume, thus providing high spin sensitivity fordevice miniaturization and on-chip integrations. Re-cently, all-on-chip magnon-photon hybrid systems havebeen demonstrated55 in the strong-coupling regime by Liet al.24 and Hou et al.25. In both works, the magnonsystem consists of a Ni80Fe20 (Py) thin-film stripe fabri-cated directly on top of the signal line of the supercon-ducting resonator, which is a half-wavelength coplanarcavity with a signal line width of 20 µm [Fig. 2 (a)]. Theeffective volume of the resonator is Vm = 0.0051 mm3,much smaller than for 3D cavities. This enables a veryhigh sensitivity of g0/2π = 26.7 Hz. The choice of usinga Py device is mainly for the convenience of fabricationand thin film deposition, and Py has a higher magnetiza-tion (1 T) compared with YIG (0.2 T). Since all the spinsin the Py stripe are in good proximity to the signal lines,they all experience optimal coupling to the microwave

4

photons. A coupling strength of 152 MHz is achievedwith a 900 µm×14 µm×30 nm stripe for Li et al.24 andfor Hou et al.25 the coupling stength is 171 MHz for 2000µm×8 µm×50 nm. The coupling strength can be easilyextended by increasing the size of the Py stripe, whichhas been demonstrated in both works.

For Li et al.’s work24, the superconductor is NbN andhas a high superconducting transition temperature of 14K. The NbN films were deposited at room temperaturewith an additional ion-beam gun to assist the reactionbetween Nb and N2 during deposition56, making NbNpromising for CMOS-compatible processing. At 1.5 Kwhere the circuit is characterized, a quality factor ofQ = 7600 for the unloaded resonator and Q = 2500 forthe loaded resonator are measured, the latter correspond-ing to a photon damping rate of κp/2π = 2.0 MHz. Sim-ilar values have been also achieved by Hou et al.25. Thequality factor is much higher than non-superconductingplanar cavities. Furthermore, the loss in superconductingresonators is dominated by two-level system fluctuations,which can be suppressed at even lower temperatures57.

The achievement of strong coupling is represented bythe clear mode anticrossing between the magnon modeand the photon mode, as shown in Fig. 2 (b). A co-operativity of C = 68 from Ref.24 and 160 from Ref.25

have been reported and show that both cases are in thestrong coupling regime. The main bottleneck for increas-ing the cooperativity is the damping of Py, reportedas α = 0.017 for the Py stripe24. Although YIG canserve as an alternative for improved damping9,19,23, itstill remains a challenge to integrate YIG thin film de-vices with superconducting resonators, mainly due to theGd3Ga5O12 (GGG) substrates needed for the epitaxialgrowth of YIG films. At cryogenic temperature, the highmicrowave losses at cryogenic temperatures in GGG58–60

will reduce the quality factor of the superconducting res-onator and undermine the coherence of excitations.

Besides half-wavelength superconducting resonator asshown in Fig. 2(a), different resonator designs can yieldeven smaller effective volume for higher sensitivity ofmagnon excitation. For example, quarter-wavelength de-sign can cut the total volume of half-wavelength res-onator in half57,61. Moreover, using the design of lumped-element LC resonators which are based on planar capac-itor (C ) and inductor (L)23,25, it is possible to furtherreduce the effective volume from the L component andfurther increase g0. Shown in Fig. 2(c), Hou et al.25

also demonstrated strong magnon-photon coupling withg0/2π = 263 Hz, which is an order of magnitude largerthan the value with the CPW design.

For the future perspective, we anticipate on-chipmagnon-photon hybrid systems to become one of themain-stream platforms for studying coherent magnonicinteractions. In particular, many new device conceptsthat have been developed with YIG crystals, as will bediscussed in the next section, can be implanted into anon-chip geometry. As the majority of ferrite-based mi-crowave components are bulky and inconvenient for on-

chip integration, utilizing strong coupling and frequencytunability of magnons could lead to much more com-pacted and efficient microwave controllers or sensors aswell as for magnonic logic circuits. Moreover, coherentinteraction of on-chip magnonic devices with supercon-ducting microwave circuits can lead to applications inquantum information and sensing.

IV. NEW PROPERTIES IN COHERENT MAGNONICS

With the booming of various magnon hybrid systems,new physics are being discovered by engineering the pa-rameters and the coherence of the hybrid componentssuch as the microwave photons and magnons. In ad-dition, many device concepts can be borrowed fromthe community of photonics and quantum information,where coherent information processing has been alreadywell implemented. Below we discuss a few examples toshow the impact of coherent magnon dynamics in bothphysics and engineering.

A. Coherent spin pumping

YIG(n=1)

Py

Py

YIG(n=2)

YIG(n=0)

YIG(n=2)

Fe

FeAu

GaAs

PyPy

(a) (b)

(d) (e)

PyYIG

(c)

FIG. 3. Coherent spin pumping in magnon-magnon hy-brid systems. (a-c) Sample structures of two dynamicallycoupled magnetic layers with (a) asymmetric Fe/Au/Fe tri-layer, (b) symmetric Py/Ru/Py trilayer and (c) YIG/Py bi-layer, with mode asymmetry realized by (a) magnetocrys-talline anisotropy, (b) RKKY interaction and (c) inter-facial exchange coupling. (d) Mode anti-crossing for aYIG(100 nm)/Py(9 nm) bilayer as shown in (c). (e)Linewidth evolution for a YIG(100 nm)/Py(7.5 nm) bilayer,showing the effect of coherent spin pumping and dissipativecoupling. Adapted from Refs.62,63 and64.

Spin pumping describes the process of pumping spinangular momentum from precessing magnetization65,66.In spintronics, spin pumping is an important phe-nomenon because it is widely used for determining spin-to-charge conversion efficiency67–78, spin mixing conduc-tance and spin diffusion lengths79–82 in diverse mate-rial systems. The pumped spin angular momentum per

5

area, or spin current, can be expressed as Isp/S =(h/4π)σ↑↓m×dm/dt, where m is the macrospin unit vec-tor, σ↑↓ is the spin mixing conductance with the unit ofnumbers of channels per unit area (note that in literaturespin mixing conductance is conventionally represented byg↑↓ but here we use σ↑↓ instead to distinguish from thecoupling strength g). This definition suggests that spinpumping is a coherent process, because Isp always keepsa constant phase with m and has the same frequency asthe dynamics of magnetization. Confirming the coher-ence of spin pumping is thus a fundamental question toaddress in magnetization dynamics and also importantfor coherent interactions of magnons with other excita-tions in magnon hybrid systems.

Magnon-magnon hybrid systems provide a unique plat-form to explore the coherence of spin pumping, becausethe phase of the magnon excitations can be arbitrarilyadjusted by changing the frequency detuning of the twomagnon system. Here the pumped spin currents fromthe two magnetic layers will interfere with each other:when the magnetization precessions of the two layers arein-phase, the pumped spin currents cancel out, leadingto suppressed damping; when the precessions are out-of-phase, the pumped spin currents add up, leading to en-hanced damping. The seminal work by Heinrich et al.62

has realized the mode crossing and in-phase interferenceof mutually pumped spin current in Fe/Au/Fe trilayersby utilizing the magnetocrystalline anisotropy of the epi-taxial Fe. Then Yang et al.63 showed clear damping dif-ference between the acoustic (in-phase) and optic (out-of-phase) modes in a symmetric Py/Ru/Py structure.Owing to the Ruderman-Kittel-Kasuya-Yosida (RKKY)coupling via the Ru layer, the frequencies of the acous-tic and optic modes are well separated, which facilitatesthe damping extraction. The issue is that the frequencydetuning of the two Py layers is always zero and cannotbe modified, thus only the zero (in-phase) and π (out-of-phase) phase modes can be excited. It is worth notingthat when the two magnetic layers are not degenerate infrequency, the pumped spin current from the resonanceof one layer can drive the other layer into motion, and aphase offset of 90 degrees has been found between the twolayers83 which validates the phase relation between themagnetization dynamics and its spin pumping. However,interference between pumped spin current and magneti-zation dynamics would be a direct evidence of coherenceand is more interesting in coherent information process-ing.

Recently, Li et al.64 have shown the coherence of spinpumping in a strongly coupled magnon-magnon hybridsystem with YIG/Py thin-film bilayers. The coherentcoupling is provided by the interfacial exchange betweenYIG and Py. By exciting the perpendicular standing spinwave (PSSW) modes in YIG, mode intersection can berealized and engineered84–86. In addition, the frequencydetuning can be controlled by the external biasing field,leading to the observation of mode anticrossing. In thestrong coupling regime, the two hybrid modes are well

separated and their linewidths can be individually ex-tracted. From the linewidth plot, it is clear that whenthe frequency detuning is zero at ωc/2π = 9.4 GHz, onehybrid mode has a significantly larger linewidth than theother, similar to the observation of linewidth differencein Py/Ru/Py structure63. This is due to the effect ofspin pumping from the YIG/Py interface. The full evo-lution of the spin pumping linewidth enhancement, withthe precession phase difference decided by the frequencydetuning, can be nicely fitted to the theory, showing thecoherence of the spin pumping. Moreover, the coherentnature of the dissipative spin pumping process leads to adissipative coupling, or an imaginary component of g inEq. (3), as compared to the real component of g from in-terfacial exchange. The dissipative coupling is importantfor engineering the hybrid dynamics, with examples oflevel attraction which has in fact been observed alreadyin the work from Heinrich et al.62.

B. Exceptional points

In a two-level system, exceptional points are mathe-matically defined as the singularities where the two eigen-values, and their corresponding eigenvectors, simultane-ously coalesce87,88. In a magnon-photon hybrid system,the two eigenvalues of Eq. (1) are:

ω± =ωm + ωp

2− κm + κp

2± 1

2

√(∆ω − i∆κ)2 + 4g2

(5)

where ∆ω = ωm − ωp and ∆κ = κm − κp. The excep-tional point happens when ∆ω = 0 and ∆κ = 2g. Atthis condition, the square root term becomes zero andtwo eigenvalues become one. Expressed differently, at theexceptional points the Hamiltonian cannot be fully diag-onized and only one eigen-solution remains. This pecu-liar property has prompt many studies of non-Hermitiansystems and applications in enhanced sensing89,90.

The advantage of magnon-photon hybrid systems isthat ∆ω, ∆κ and g can be all tuned in-situ in orderto realize the exceptional point, which has been shownin two recent works91,92. In each case, the magnon sys-tem is based on a single-crystal YIG sphere and the mi-crowave cavity is defined by a 3D rectangles [4(a-b)]. TheYIG sphere is mounted on a movable rod and the posi-tion of the YIG sphere in the cavity can be modifiedin order to change g. Fig. 4(c) shows the measuredmicrowave reflection of the cavity as a function of theYIG insertion depth x at ∆ω = 0, with g tuned by xas g/2π = 1.3|x| MHz/mm. When |x| is large, the sys-tem is in the strong coupling regime and two dips in thespectrum represent the two split modes at the anticross-ing gap minimum. As |x| is decreased to 1.2 mm, thetwo dips merge into a single dip, which indicates the ex-ceptional point. Further decreasing |x| (and g) will leadto the intrinsic resonant absorption of the cavity withthe magnon mode decoupled. The exceptional point also

6

(a) (b)

(c) (d)EPEP1 EP2

FIG. 4. Realizing exceptional points with tunable magnon-photon coupling. (a-b) Two different microwave cavity struc-tures for tunable magnon-photon coupling strength. (c)Demonstration of exceptional points by tuning the insertiondepth of the YIG sphere for the geometry in (a). (d) En-hanced dω/dH slope and sensitivity at one exceptional pointfor the geometry in (b). Adapted from Refs.91 and92.

marks the transition from the weak-coupling regime tothe magnetically induced transparancy (MIT) regime11.Furthermore, in Ref.92 the value of g can be tuned by x,y and the field angle θ, thus allowing the determinationof an exceptional surface in the variable space and ex-ploration for high-dimension non-Hermitian physics93,94.We also note that recently exceptional points betweentwo coupled YIG spheres have been demonstrated medi-ated by a microwave cavity95. Here the two magnonicresonators are dissipatively coupled (g is imaginary) sothe exceptional points take place at a finite frequencydetuning.

The main technical interest of exceptional points isthat the sensitivity can be significantly enhanced93,94,96.This can be demonstrated in Fig. 4(d), where the fielddependence of the two hybrid modes shows a square-rootbehavior and with enhanced slope near the exceptionalpoint92. This is because in Eq. (5) when ∆κ = 2g andwith small frequency perturbation ∆ω � ∆κ, the square-root term becomes ±

√i∆κ∆ω/2, which exhibit a ∆ω1/2

dependence and can generate a much larger change ofω± for a given ∆ω compared with the uncoupled regime(g = 0, δω± = ±∆ω/2). We also note the explo-ration of exceptional points in RKKY coupled magnon-magnon hybrid systems, where the coupling strength gcan be tuned by the thickness of the barrier of the syn-thetic antiferrimagnet97,98. This provides the all-thin-film based platform for exploring non-Hermitian physicsand advanced sensing.

C. Nonreciprocity

Nonreciprocity is an important concept that hasfound many applications in microwave and opticalcommunications101–103, with examples of circulators andisolators. It is important to implement noise-free, phasepreserving information processing and amplification es-pecially in the quantum regime. To realize nonreciprocalsignal transmission, one needs to break the time-reversalsymmetry of the system. The traditional examples aremicrowave ferrite circulators and optical Faraday isola-tors, where the symmetry is broken by the magnetizationvector of ferrites in the devices. Symmetry-breaking canbe also artificially introduced by engineering the propa-gation paths of the electromagnetic waves for asymmetricphase accumulation, with recent progress in photonics102,optomechanics104–106 and microwave circuits107–109.

Incorporating magnon-photon hybrid systems opensup new features in controlling nonreciprocity for coher-ent information processing with magnonics. Recently,two groups have demonstrated nonreciprocal microwavetransmission by coherently coupling a circuit-board mi-crowave cavity to a YIG sphere99,100. In particular,nearly 100% isolation can be achieved from the engi-neered cooperative dynamics of magnon and photon res-onance. Compared with other schematics to create non-reciprocity, magnon hybrid systems are highly tunablein frequency, phase and coupling strengths, allowing forconvenient engineering and implementation of desirednonreciprocal characteristics.

In the first work by Wang, et al.99, the microwavecavity is a half-wavelength microstrip resonator form-ing a cross line with the feeding microtrip transmissionline, as shown in Fig. 5(a). A YIG sphere is placedadjacent to both the cavity and the microstrip line sothat the magnon mode is coupled to both the standing-wave photons (cavity) and the propagating photons (mi-crostrip). It has been shown that dissipative couplingbetween magnons and photons can be achieved when thetwo harmonic resonator systems are both coupled to thesame traveling photons54,110,111. This is also known asreservoir engineering112–114. With proper adjustment ofthe YIG sphere location, the coherent (real) and dissi-pative (imaginary) couplings can be tuned to be equaland in balance. In this situation, when the magnonand photon resonators have a certain frequency detun-ing, the damping of the magnon-dominating hybrid modewill be completely compensated with the energy pumpingfrom the dissipative coupling. From the viewpoint of mi-crowave circuits, a zero-dissipation resonator will absorball the energy and completely block microwave transmis-sion. This is reflected as a second inverse resonance peakwith infinite depth [ω− in Fig. 5(b), where ω+ corre-sponds to the cavity-dominating peak near ∆c/2π = 0].However, when the microwave propagating direction isreversed, the sign of the dissipative coupling will also bereversed. This will in turn reverse the sign of the fre-quency detuning between magnons and photons in order

7

(a) (f )

(b) (c)

(d) (e)

(g)

FIG. 5. Realizing microwave nonreciprocity with engineered magnon-photon hybrid systems. (a) Microwave resonator designincorporating both traveling and standing waves, with the position of the YIG sphere adjusted by a 3D positioner. (b-c)Nonreciprocal |S21| and |S12| measured from the circuit when the magnetic field is tuned to ωm = ωc − 2JΓ/α. Completeisolation valley is observe at ω− for |S21|, while no valley is observed for |S12|. (d-e) Same for (b-c) except that the magneticfield is tuned to ωm = ωc + 2JΓ/α. No isolation valley is observe at ω− for |S21|, while complete isolation is observed for|S12|. (f) Microwave resonator design with two circularly polarized degenerate modes. (g) Nonreciprocal S21 and S12 measuredfor different magnon-photon coupling strengths (YIG locations). At z = 0.9 mm complete isolate valley is observed for S21,corresponding to the destructive interference between the cavity mode and the crosstalk transmission mode. Adapted fromRefs.99 and100.

to reach the zero-damping condition, with the infinite-depth resonance peak ending up on the other side of thebroad cavity peak [ω+ in Fig. 5(e)]. Thus nonreciprocalmicrowave transmission with perfect isolation is realized.

In the second work by Zhang, et al.100, the microwavecavity is a substrate integrated waveguide (SIW) cavity[Fig. 5(f)], which is a rectangular waveguide built into acircuit board with the sidewall defined by plated throughhole vias. Compared with transmission line based mi-crowave resonators, SIW cavities are more convenientfor engineering the microwave profiles. In this case, thecavity can host circularly polarized eigenmodes, whichare the combination of two linearly polarized eigenmodeswith degenerate energy level by design. Furthermore,the two microwave ports are designed to excite only onecircularly polarized modes. When the YIG sphere is sat-urated along the z direction, the magnon excitations onlycouple to one helicity of the microwave mode, thus break-ing the symmetry and creating the nonreciprocity. Inthe practical circuit, there is a finite crosstalk betweenthe two port (meaning the transmission is nonzero evenwhen the SIW cavity is not on resonance). The magnon-photon coupling mediated microwave transmission thusinterfere with the crosstalk transmission constructivelyor destructively, leading to the complete isolation as theposition of the YIG sphere is set to z = 0.9 mm [Fig.5(g)]. A similar effect based on a ring resonator has alsobeen proposed115.

In magnonics, nonreciprocity has also been extensivelyexplored. The main mechanism is to create a differ-ence in effective field for different magnon propagat-ing directions, with examples of surface anisotropy116,Dzyaloshinskii-Moriya interaction117,118 and dipolarfield119,120. On the other hand, nonreciprocity based onmagnon hybrid systems takes advantage of the phase andcoupling engineering. In the above two examples, themagnon-photon coupling is employed to tune the ampli-tude and phase of the resonator photons, which inter-fere with the traveling microwave photons and create fullisolation. This approach sacrifices bandwidth and gainsisolation depth. For coherent information processing, cir-cuits are usually running in narrow band, thus the tun-ability of magnons makes life much easier to match thebandwidth. Compared with conventional ferrite-basedcirculators, strong coupling between magnons and pho-tons will significantly reduce the volume of magneticmaterials needed for reaching isolation. We also notethe development of surface acoustic wave (SAW) isola-tors based on magnon-phonon coupling121–123, where thenonreciprocal effects in magnonics are utilized to cre-ate nonreciprocity in SAWs when coupled to magnons.Similar to magnon-photon coupling, strong magnon-phonon coupling have also been proposed to producedeep isolation123. This will benefit from the low damp-ing and high-efficiency energy excitation of SAWs for mi-crowave applications. However, one of the challenges re-

8

mains to engineer strong coupling between magnons andSAW, which depends sensitively on the sample processingand microstructure124.

V. NEW HYBRID MAGNONIC PLATFORMS FORREMOTE INFORMATION TRANSDUCTION

Magnons can couple to many excitations that haveplayed important roles in quantum information, such asmicrowave photons, optical photons, phonons, supercon-ducting qubits and NV centers, making magnons highlyrelevant for quantum information transduction33,38. Astransducers, magnons have been employed to mediate thecoupling between microwave photons and phonons41,43,as well as microwave and optical photons34–37. Forthe application in magnonics, dynamic coupling be-tween distant magnetic elements has become anemerging topic for magnon-based coherent informationprocessing39,42,44,85,125. While the role of transducer hasbeen extensively reviewed elsewhere33,38, here we brieflydiscuss the aspect of magnonics and take a few schemat-ics as examples, especially for the purpose of coherenttransduction between remote systems which is essentialfor scalable integration [Fig. 6(a)].

Cavity mediated remote transduction. Strongcoupling between microwave cavity and magnons canbe used to coherently couple multiple magnetic systemswith the information exchanged via microwave photons.One example is the coherent coupling between two YIGspheres in a 3D cavity39, as shown in Fig. 6(b). Thekey ingredient is that a pair of coils are placed beside thetwo YIG sphere, which can be used to control their field(frequency) detuning. Fig. 6(d) shows two characteristicmode anticrossing for a field detuning of -14 Oe and 0 Oe.For a detuning of -14 Oe, two clear avoided crosses withthe gap 2(g/2π) = 13.4 MHz are observed correspond-ing to the strong coupling between the microwave cavityand each YIG sphere. When the detuning is set to zero,only one avoided cross is observed and the anticrossinggap is larger than the case of individual YIG spheres.What happens is that the degenerate magnon modes ofthe two YIG spheres have formed new collective modes asin-phase and out-of-phase dynamics. The locations of theYIG spheres are selected such that the microwave fieldsof the cavity photons are identical and in-phase. Thusthe microwave photons only couple to the in-phase modeand are decoupled from the out-of-phase mode. The in-phase mode shows an gap of 2

√2(g/2π) = 18.9 MHz,

√2

times larger than the gap for a single YIG sphere. Thisis because the total volume of two YIG spheres is twicethe value of a single sphere, thus the number of spins alsodoubles.

Let’s imagine how the two YIG spheres communi-cate in the triple-zero-detuning case (ωYIG1 = ωYIG2 =ωcavity). If initially the excitation resides in YIG 1 withan amplitude of A for the transverse magnetization mo-tion, the total excitations of the two YIG spheres can

magnon magnoncarrier

resonator

strong

coupling

strong

coupling(a)

(b) (c)

(d) (e)

FIG. 6. (a) Remote transduction of coherent magnon exci-tations in magnon hybrid systems. (b) Cavity photon medi-ated remote coupling between two YIG spheres. Two coilsare used to introduce frequency detuning between the twoYIG spheres. (c) Cavity reflection spectra for a field detuningof -14 Oe and 0 Oe. (d) Phonon mediated remote couplingbetween two YIG films by the GGG substrate. (e) Ferro-magnetic resonance spectra of the YIG/GGG/YIG trilayer.Adapted from Refs.39 and44.

be viewed as the superposition of < A/2,A/2 > and< A/2,-A/2 >, which correspond to the in-phase andout-of-phase modes, respectively. The in-phase mode willstart its Rabi-like oscillation with cavity photon modewith a bandwidth of

√2g. The out-of-phase mode, which

does not interact with either the in-phase or the cavitymode, will remain as the eigenmode. Thus we will ob-serve that the excitation in YIG 1 oscillates between Aand A/2, and the excitation in YIG 2 oscillations be-

tween 0 and −A/2, with a period of 2π/√

2g. Similarcavity-mediated remote magnon-magnon coupling havealso been shown with different efforts40,42,95,126–128, in-cluding utilizing spin pumping42 and in the dispersiveregime40,127.

In the same work39, it has been pointed out that theout-of-phase mode acts as the dark mode and may havelong coherence time because it is isolated from the hybridsystem. To be able to read the excitation informationfrom the dark mode, the system can be engineered suchthat a small frequency detuning ∆ω is set between thetwo YIG sphere. In the absence of the microwave cavity,the in-phase and out-of-phase modes are no longer degen-erate and will hop from one to the other. In the presence

9

of the microwave cavity, only the in-phase mode couplesto the cavity photons. Thus the cavity output signal willexhibit a periodic oscillation with time, and the periodis determined by ∆ω, as the information is repeatedlystored into and retrieved from the dark mode. Zhang etal. has demonstrated this process with up to eight YIGspheres39.

Phonon-mediated remote transduction. Co-herent interactions betweens magnons and phononsresult in their hybrid excitations known as magnonpolarons129–135. They are different from incoherentmagnon-phonon interactions as studied in spin Seebeckeffect. In particular, phonons have been extensively ex-plored in coherent information processing such as in op-tomechanics and quantum information; coupling withmagnons can incorporate the great tunability of magnonsinto the phonon systems. Recently, An, et al.44 haveexplore phonon-mediated remote magnon interaction ina YIG(200 nm)/GGG(500 µm)/YIG(200 nm) structure[Fig. 6(c)]. The two YIG layers are grown by liquidphase epitaxy on a two-side-polished GGG substrate. Fora one-side YIG sample, multiple mode anticrossings areobserved between the YIG Kittel mode and the perpen-dicular standing acoustic waves (n ∼ 1400) of the GGGsubstrate. Note that the acoustic wave has 1-cm half-decay length and a coherence time of 2 µs at 5 GHz,much better than what magnons can achieve. For thetwo sided YIG sample, the mode anticrossing spectra isshown in Fig. 6(e). A small frequency detuning betweenthe two YIG layers comes from the variation of mag-netization. Similar to the previous example, there arein-phase and out-of-phase hybrid modes for the two YIGlayers. The difference is that the phonon-mediated cou-pling favors the two hybrid modes alternatively for theexcitation of the odd or even phonon modes. When theFMR of one YIG layer is excited, phonon-mediated cou-pling will drive the other YIG layer to precess in-phaseor out-of-phase with respect to the excited YIG layer.Thus the total microwave absorption will be increased ordecreased, respectively, as a result of constructive or de-structive interference between the two YIG layers. Thisinterference is measured as alternating FMR amplitudesalong the Kittel dispersion line [labeled as FMR 1 andFMR 2 in Fig. 6(e)].

VI. FUTURE OUTLOOKS

The development of magnon hybrid systems, includingtheir advantages of on-chip integration, exploiting newproperties in coherent magnonics and remote informa-tion transduction, will bring about new interdisciplinaryopportunities in coherent information processing. Belowwe discuss the role of magnons in two emerging opportu-nities: quantum information and magnonics.

A. Quantum information

Magnonic

components

microwave

op!c photon

phonon

qubit 1

qubit 2

qubit 3

......

FIG. 7. Diagram of magnonic components acting as on-chipquantum transducers and controllers for different qubits.

With the demonstration of single-magnon interactionwith a qubit30–32, quantum magnonics has become a re-alistic topic. The main potential of magnons in quan-tum information is to act as an intermediate informationtransfer station for quantum transduction, coherent in-formation control and entanglement generation (Fig. 7).In particular, the convenience of tunability and on-chipintegration are keys for applications in quantum informa-tion.

We anticipate two future platforms for addressingqubits with on-chip geometry and scalability. The firstplatform is the hybrid system between magnonic devicesand superconducting microwave circuits. With planar su-perconducting microwave resonators, the novel function-ality from cavity spintronics such as nonreciprocal trans-mission, isolation and enhanced sensitivity should beachievable in an all-on-chip architecture. The dampingrate of single-crystal YIG can be as low as 1 MHz at a fre-quency of 5 GHz10,60,136 along with a sub-GHz magnon-photon coupling strength, which ensures hundreds of co-herent Rabi-like oscillation cycles. However, integratingYIG devices on planar superconducting circuits wouldbe a challenge. This is because that the ideal magneticmaterial, YIG thin films, needs to be grown on GGGsubstrate in order to maintain its low damping prop-erty, but at cryogenic temperature GGG has complexmicrowave property and exhibits large losses, which willundermine the coherence of all microwave excitations.To realize GGG-free YIG thin film devices, one way isto fabricate free-standing YIG thin-film devices137,138 orcut YIG crystals into small pieces and transfer themonto superconducting microwave circuits. GGG-free YIGgrowth such as on silicon139 may provide an alterna-tive solution. New low-damping magnetic materials suchas CoFe140–142, complex magnetic insulators143 and or-ganic ferrimagnets144 could provide new ideas for de-vice implementation at cryogenic temperature. Besidesmicrowave photons, magnon-mediated coherent trans-ductions of optical photons and phonons provide newquantum interfaces and research topics such as cavityoptomagnonics38 and cavity magnetomechanics41. Wealso note the efforts of optical waveguides fabricated frommagnonic materials, compared with bulk magnetic crys-tals, for on-chip microwave-to-optics conversion145,146.

10

Furthermore, we point out the electrical excitationsof SAWs have been recently incorporated in quantuminformation147–150. Studying magnon-photon interac-tions with SAWs124,151–153 will benefit from convenientbandwidth engineering154 compared with exciting thebulk mechanical resonance modes.

The second emerging platform is the coherent interac-tion with spin qubits such as NV centers155. The un-derlying physics is that propagating spin waves exert aneffective rf field to a proximal NV center at the surfaceof the magnonic waveguide (5-10 nm away), which ex-cites the NV center and triggers the optically detectedmagnetic resonance (ODMR). Because of the excitationconfinement in magnetic media, magnon excitations canpropagate for long distance, by a range of ∼ 100 µm inlow-damping YIG, and are shown to provide a few hun-dreds times stronger rf field than then radiation fromthe microwave antenna155. This capability can be ap-plied to selectively addressing remote spin qubits by uti-lizing the controllability of magnons, acting as a pro-grammable microwave control bus. The interaction be-tween magnons and NV centers has been also appliedto NV center magnetometry owing to the ultrahigh sen-sitivity and spatial resolution156–160. Furthermore, allthe experiments can be realized at room temperature,making YIG an ideal low-damping material for carryingmagnon excitations. Another proposal is to implementlong-distance entanglement of spin qubits mediated bypropagating magnons161. The operation time of the two-qubit gate, when the spin qubits are 25 nm away fromthe thin-film ferromagnetic transducer, is estimated tobe a few tens of nanoseconds, which is much faster thanthe decoherence time of tens of µs for NV centers. Onechallenge will be the on-chip integration of high-qualityYIG and diamond systems, which requires material en-gineering for compatible magnon-NV hybrid platforms.

Figs. 8(a) and (b) show the illustrations for two pro-posed functionality, quantum transduction and entan-glement generation, respectively, with on-chip magnon-ics and superconducting circuits. In Fig. 8(a), a mag-netic element overlaps and couples with two circuit quan-tum electrodynamics (cQED) systems (each cQED sys-tem contains a superconducting microwave cavity and aqubit which are strongly coupled). This leads to strongmagnon-photon coupling on both side, whilst cQED sys-tems do not interact with each other directly. Quantumexcitation from one side of cQED can be transferred tothe other side mediated by magnons. Due to the fre-quency tunability of magnons, the quantum transductioncan be turned on or off by setting the magnon frequencyas degenerate with or far away from the frequency of thetwo cQED systems. This magnon frequency tuning pro-cess can be realized with high bandwidth by using anadjacent current-carrying line as shown in Fig. 8(a).

Quasi-classically, the process of magnon-mediated co-herent information transfer in such non-stationary sys-tem can be described by a system of coupled equations

cQED 1 cQED 2

(a) Quantum transduction

(b) Entanglement generation

cQED 1

cQED 2

FIG. 8. Proposed functionality in quantum information withmagnon hybrid system. (a) Quantum transduction withmagnons between two cQED systems. (b) Magnonic hybridsplitter for entanglement generation. Blue lines denote copla-nar microwave waveguide. Yellow blocks denote magneticdevices and circuits. Black circuits denote superconductingqubits. The broad black stripe in (a) denotes controlling mi-crowave electrodes for tuning the magnon frequency.

for the complex amplitudes c1,2(t) and cm(t) of the ex-citations in the superconducting microwave cavities andmagnonic resonator, respectively162:

dc1dt

= −iω1c1 − κ1c1 − ig1mcm , (6a)

dc2dt

= −iω2c2 − κ2c2 − ig2mcm , (6b)

dcmdt

= −iωm(t)cm − κmcm − ig1mc1 − ig2mc2 (6c)

Here ω1,2 are the eigen-frequencies of the cavities,ωm(t) is the time-dependent magnon frequency, κ1,2 arethe decoherence rates for the two cavities, and gim are thecoupling rates between cavity i and magnonic resonator.

Fig. 9 shows the results of numerical simulations ofEqs. (6) for the case of linear sweep of the magnonfrequency (ωm(t) = ω0 + ρt) with the rate ρ/2π = 2.5MHz/ns. In the simulations, two cavities have a frequen-cies difference of (ω2−ω1)/2π = 40 MHz, the decoherencerates of the two cavity modes and magnon mode are setas κ1/2π = κ2/2π = 0 and κm/2π = 1 MHz, respec-tively, and the coupling rates are g1m/2π = g2m/2π = 20MHz. Initially, at t = −200 ns, only the first cavitymode was populated (c1 = 1, c2,m = 0). The top panelin Fig. 9 shows the time dependence of the populationsP1,2 = |c1,2|2 of the cavity modes, while the bottompanel demonstrates the behavior of the magnon modePm = |cm|2. As one can see from Fig. 9, the sweep ofthe magnon frequency ωm(t) across the resonance region

11

ωm ≈ ω1,2 results in almost complete coherent transferof information state from the first microwave cavity tothe second one. Note, that the simulations were donefor rather conservative estimation of the coupling fre-quencies g1,2/2π = 20 MHz, which are about one orderof magnitude lower than experimentally observed cou-pling rates in hybrid systems of similar geometry. It alsoobvious from Fig. 9 that the relative magnon popula-tion Pm stays rather low during whole transfer process(Pm < 0.2), which means that this type of the coherentinformation transfer is almost insensitive to the decoher-ence processes in the magnonic subsystem. Finally, wenote that the process shown in Fig. 9 achieves coherenttransfer of information between cavity modes of differentfrequencies. All this illustrates versatility and practicalpotential of coherent information manipulation in non-stationary hybrid magnon-cQED systems.

FIG. 9. Coherent excitation transduction for the schematicin Fig. 8(a). Temporal profiles of the populations P1,2 =|c1,2|2 of the cQED modes (top panel) and magnonic modePm = |cm|2 (bottom panel) in the case of linear sweep of theresonance magnon frequency ωm(t) = ω0 + ρt. Adapted fromRef.162.

Figure 8(b) illustrates another interesting possibilityof quantum information manipulation in hybrid magnon-cQED systems, by constructing a magnonic hybrid split-ter that can be used to create entangled magnon statesat the two right ports when a single magnon excita-tion is input from one left port. The entanglement isachieved in the central part of the circuit, which repre-sents a directional magnon coupler and operates similarly

to a half-transparent mirror in optics. The entangledmagnon state will be transferred to the qubits in thecQEDs via magnon-photon coupling, leading to entan-gled qubit states. The same circuit, when excited at bothinput ports with single-magnon excitations, can be usedfor generation of multi-magnon entangled states due totwo-magnon interference effect (magnon bunching) in thedirectional magnon splitter. The two main advantages ofusing magnons compared with directly using microwavecircuits are that 1) the magnon frequency can be tunedelectronically in a wide range; 2) magnonic circuits can bemade much smaller in dimension, in the scale of microns,compared with millimeters-cale microwave circuits.

B. Magnonic logic

magnon

node 1

magnon

node 2

Magnonics

Coherent

Magnonics

...

...

(a)

(b)

node 1

node 3 node 5

node 2 node 4

node 1

(initiation)

node i

(detection)

Δt

t

mic

row

ave

in

pu

t

(c)

g12

g13

g23

g24

g35

g45

FIG. 10. Proposed functionality in coherent magnonics withmagnon hybrid system. (a) Comparison between conventionalmagnonics and coherent magnonics. (b) Network of magnonhybrid systems for coherent information processing. (c) Di-agram of microwave pulse sequences for state initiations anddetections.

12

One major task of magnonics is to encode, transferand process information with magnons163,164, treatingmagnonic circuits as microwave circuits but making useof their tunability and nanoscale solid-state integration.With many device concepts based on magnon interfer-ence and phase control, coherent generations and ma-nipulations of magnons are crucial for these operations.Magnon hybrid systems are meant for maintaining co-herence during excitation transduction. Enhanced cou-pling into the strong-coupling regime will bring in newfeatures such as Rabi-like oscillations11. In particular,coherent remote information transduction mediated bymagnon hybrid systems will greatly enhance the func-tionality of magnonics.

Let us compare conventional magnonics with coherentmagnonics based on magnon hybrid systems, as shownin Fig. 10(a). For conventional magnonics, the work-ing mechanism takes a signal generation-detection pro-cess, i.e., magnons excited at one side, propagating andinterfering with each other, and being received at theother side. For coherent magnonics, the working mecha-nism is manifested as a Rabi-like process: magnons thatare excited from one node propagate and excite anothernode, then due to the strong coupling the excitation ofthe second node will generate a reverse flow of excita-tion back to the first node. This process will take placeback and forth until the excitation flow completely de-cays or loses its coherence. By exchanging excitations,the two nodes will maintain coherence and act like en-tangled nodes. Although the number of magnon excita-tions are much greater than one, all the bosonic magnonsare staying in the lowest energy state and cannot be dis-tinguished, which is thus equivalent to entangled singlemagnon states between the two nodes.

Coherent interaction between the signal generator anddetector will create new concepts for device implemen-tation. In conventional magnonics, one typical devicearchitecture is the spin wave logic gate165, in which bi-nary states of magnon propagation are determined bythe gate input. In coherent magnonics, one potentialarchitecture is a network consisting of many magnonnodes that are coherently coupled [Fig. 10(b)]. Sim-ilar to quantum information, an initiation pulse willinject excitations into one magnonic nodes. Rabi-likeoscillation will transfer the excitations to other nodesback and forth as a function of time. The excitationstates of different nodes, including the amplitudes andphases, can be detected by spin rectification with a sec-ond detecting microwave pulse with designed time de-lay ∆t [Fig. 10(c)]. This is similar to the Ramseyinterferometry166,167 but the role of the second π pulse isplayed by the detecting pulse. In quantum information,the calculation process is to take the coupling strengthsamong different nodes as input and measure the ground-state eigenfunction as output. For coherent magnonics,the coupling strength (gij) can be conveniently modi-fied for input. The convergence to a specific groundstate can be achieved by dissipative coupling (e.g., coher-

ent spin pumping favors in-phase eigenmode and dampsout-of-phase eigenmode64). As an example, up to eightmagnonic nodes have been demonstrated for YIG spheresplaced inside a 3D cavity39. There are also many waysin spintronics for rectification readout such as spin Halleffect, Rashba effect and anisotropic magnetoresistance.Furthermore, we note that Rabi-like oscillation, or nuta-tion dynamics of magnons, has been realized168,169, es-pecially in a YIG single nanodisc with very large coneangle169. This opens new opportunity for exploring co-herent manipulation of magnonic states with large evolu-tion bandwidth (nutation frequency) along with long co-herence time, shown as 0.3 GHz for the former and 100 ns(0.01 GHz) for the latter in a 700-nm-diameter YIGnanodisc169. The main challenge for coherent magnonicsis the relatively short coherence time of magnons. How-ever, although the damping of magnons are much largerthan quantum qubits, the coupling strength can also belarger, resulting in a significant cooperativity for coherentinformation processing. Any realistic coherent magnonicsystem can be readily extended to the single quantumlimit for coupling with qubits.

VII. CONCLUSION

Coherent information processing with hybrid systemshas become a new scientific challenge and inspired lotsof interdisciplinary research activities especially for theirapplication in quantum information. The introductionof magnons to the family has provided new freedom forimplementing many dynamic phenomena that have beenpredicted in theory or realized in other dynamic systems,thanks to the convenience in tuning key properties suchas frequency, damping and coupling. For magnetic sys-tems, we have witnesses a tremendous success in turninggreat science into great applications, from the discoveryof giant magnetoresistance (GMR) to the wide use ofhard-disc drives. One important factor for this successis the convenience of integrating magnetic thin-film, het-erostructure devices on circuits for scalable fabrications.Thus on-chip capability of magnon hybrid systems will becrucial for practical applications. Finally we anticipatean important role of magnon hybrid systems in quantuminformation and magnonics, namely, quantum magnonicsand coherent magnonics.

VIII. ACKNOWLEDGEMENT

The preparation of this perspective article was sup-ported by the U.S. Department of Energy, Office of Sci-ence, Basic Energy Sciences, Materials Sciences and En-gineering Division. W. Z. acknowledges support fromAFOSR under grant no. FA9550-19-1-0254. A. H. ac-knowledges support from Quantum Materials for EnergyEfficient Neuromorphic Computing, an Energy Frontier

13

Research Center funded by the U.S. DOE, Office of Sci-ence.

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