Spin pumping in strongly coupled magnon-photon systems

H. Maier-Flaig1,2, M. Harder3, R. Gross1,2,4, H. Huebl1,2,4, S. T. B. Goennenwein1,2,4

1 Walther-Meißner-Institut, Bayerische Akademie der Wissenschaften, 85748 Garching, Germany2 Physik-Department, Technische Universitat Munchen, 85748 Garching, Germany

3 Department of Physics and Astronomy, University of Manitoba, Winnipeg, Canada R3T 2N2 and4 Nanosystems Initiative Munich, Schellingstraße 4, D-80799 Munchen, Germany

(Dated: October 17, 2018)

We experimentally investigate magnon-polaritons, arising in ferrimagnetic resonance experimentsin a microwave cavity with a tuneable quality factor. To his end, we simultaneously measure theelectrically detected spin pumping signal and microwave reflection (the ferrimagnetic resonance sig-nal) of a yttrium iron garnet (YIG) / platinum (Pt) bilayer in the microwave cavity. The couplingstrength of the fundamental magnetic resonance mode and the cavity is determined from the mi-crowave reflection data. All features of the magnetic resonance spectra predicted by first principlecalculations and an input-output formalism agree with our experimental observations. By changingthe decay rate of the cavity at constant magnon-photon coupling rate, we experimentally tune inand out of the strong coupling regime and successfully model the corresponding change of the spinpumping signal. Furthermore, we observe the coupling and spin pumping of several spin wave modesand provide a quantitative analysis of their coupling rates to the cavity.

I. INTRODUCTION

Motivated by the vision of hybrid quantum informationsystems combining the fast manipulation rates of super-conducting qubits and the long coherence times of spinensembles, strong spin-photon coupling is a major goalof quantum information memory applications. Coher-ent information exchange between microwave cavity pho-tons and a spin ensemble was initially demonstrated forparamagnetic systems1–3, but only recently has this con-cept been transferred to magnetically ordered systems,where coupling rates of hundreds of megahertz can beachieved.4–7 Utilizing the flexibility of exchange coupledmagnetically ordered systems, more complex architec-tures involving multiple magnetic elements have alreadybeen developed8,9. Additionally, magnetically orderedsystems allow to study classical strong coupling physicseven at room temperatures.5–10

Moreover, a key advantage of magnetically ordered sys-tems over their paramagnetic counterparts – which hasyet to be fully explored – is the ability to probe mag-netic excitations electrically through spin pumping andthe inverse spin Hall effect. Spin pumping, in general, re-lies on ferromagnet-normal metal (FM/NM) heterostruc-tures and has been demonstrated for a wide variety of ma-terial combinations11. Under resonant absorption of mi-crowaves, the precessing magnetisation in the ferromag-net sources a spin current into the normal metal, where itis converted into a charge current via the inverse spin Halleffect. This spin Hall charge current is then detected.In ferromagnetic insulator (FMI)-based FMI/NM het-erostructures, charge current signals from the rectifica-tion of the microwave electric field are very small12, lead-ing to a dominant spin pumping/spin Hall signal. Thishas led to much research on FMI/NM heterostructures, ofwhich the Yttrium Iron Garnet (YIG)/Platinum(Pt) bi-layers we use are a prime example. Spin pumping is a wellunderstood effect for weak photon-magnon coupling11,13,

i.e. for situations where the decay rates of the cavityand the magnetic system are larger than the photon-magnon coupling strength. However, the large spin den-sity of YIG and the resulting large effective couplingstrength allows one to reach the strong coupling regimealso in typical spin pumping experiments. The exper-imental observation14 and theoretical treatment15,16 ofspin pumping in a strongly coupled magnon-photon sys-tem has only recently been performed. These results sug-gest that combining spin pumping and strong magnon-photon coupling may enable the transmission and elec-trical read out of quantum states in ferromagnets usinga hybrid architecture. Experiments directly linking spinpumping in the weak and strong coupling regime are,however, still missing. Such experiments are one impor-tant step towards understanding the functional principleand key requirements for such a hybrid architecture.

In this paper, we present a systematic study of themagnon-photon coupling in magnetic resonance exper-iments in a YIG/Pt bilayer mounted in a commer-cially available EPR cavity. We measure both the mi-crowave reflection spectra and the electrically detectedspin pumping signal in the system. The tuneable cavityquality allows us to systematically move in and out of thestrong coupling regime. Measurements with high mag-netic field and frequency resolution allow us to clearlyobserve the coupling of spin wave modes with the hy-bridized cavity–fundamental FMR mode. We explore adifferent approach as recently used by Zhang et al. 7 : Inour setup, instead of tuning the cavity frequency we tuneits decay rate while the effective magnon-photon couplingrate and the magnon decay rate stay constant. We thusachieve a transition from the strongly coupled regimewhere the decay rates of spin and cavity system are bothconsiderably smaller than the effective coupling rate, tothe weakly coupled regime where the cavity decay rateis much higher than the magnon-photon coupling rate.This regime is also called the regime of magnetically in-

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duced transparency (MIT)7.This paper is organized as follows: In Sec. II we re-

view the general theory of the coupled magnon-photonsystem and the main features of spin pumping in the caseof strong coupling. In Sec. III we describe the experi-mental details of recording the microwave reflection ofthe system as a function of frequency and applied mag-netic field while simultaneously recording the DC spinpumping voltage across the Pt. Finally in Sec. IV wepresent our observation of strong coupling between thecavity mode and both the fundamental magnetic reso-nance and standing spin wave modes. We also demon-strate the transition from strong to weak coupling bytuning the cavity line width and discuss the differencein the experimental spin pumping signature in both thestrong and weak regimes.

II. THEORY

A. Photon-Magnon Dispersion

Conventionally, ferromagnetic resonance (FMR) ismodeled in terms of the Landau-Lifshitz-Gilbert (LLG)equation which describes the dynamics of a magnetic mo-ment in the presence of a magnetic field. In a staticmagnetic field H0, the magnetic moment will precesswith the Larmor frequency ωs. In detail, ωs dependson the static field strength and on its orientation due toanisotropy17. This precessional motion can be resonantlyexcited by a time varying microwave magnetic field H1

with a frequency close to ωs. To observe spin pumpingin FM/NM heterostuctures, the field H0 should be ap-plied perpendicular to the surface normal (i.e. in theinterface plane)11,13,18,19. In this case, the FMR disper-sion (in the absence of crystalline magnetic anisotropy)

is ωs = γµ0

√H0 (H0 +Ms)

20. Here, Ms is the mate-rial specific saturation magnetization, γ is the materialspecific gyromagnetic ratio and µ0 is the vacuum perme-ability. In the limit H0 Ms the resonance frequencyis thus linear in magnetic field. Contrary to the spinresonance frequency ωs, the resonance frequency ωc of amacroscopic cavity is determined by geometrical and di-electric parameters only and therefore does not dependon the magnetic field. However, since the magnonic andthe photonic mode interact in resonance, we expect mod-ifications to the pure FMR and pure cavity dispersions.To be specific, we will observe an anticrossing of theFMR and the cavity dispersion for a sufficiently strongmagnon-photon coupling.

To describe the coupling between the cavity modeand the spin excitation the quantum mechanical Tavis-Cummings model21,22 and classical first principles15 ap-proaches using the input-output formalism5 have success-fully been used. For the dipolar interaction assumedin the models, the single spin-single photon couplingstrength g0 is proportional to the vacuum microwavemagnetic field H0

1 and the dipole moment m of the spin.

In the scope of the Tavis-Cummings model, it has beenshown that the collective coupling strength geff to an en-semble of spins is proportional to the square root of thenumber of polarized spins for the coupling to the vac-cum microwave magnetic field. In a classical theory, Caoet al. 15 derived that this

√N behaviour prevails also for

the magnon-photon coupling in magnetically ordered sys-tems. Here, the total magnetization and thus the fillingfactor of the ferromagnetic material in the cavity, can beused as a measure for the total number of spins.

The characteristic fingerprint of strong coupling is theformation of an observable anti-crossing of the cavity andthe spin dispersion relation close to resonance. Note,that the presence of stong coupling and the accompaniedvisible anti-crossing of the dispersion relations requiresthat the effective coupling geff exceeds the loss rates ofthe spins (γs) and the cavity (κi + κe). Experimentally,we tune the spin resonance frequency ωs across the cavityresonance frequency ωc via an externally applied staticmagnetic field. The coupled system can most simply bemodelled in the vicinity of the resonance frequency usingtwo coupled harmonic oscillators, where the resonancefrequency is5:

ω± = ωc +∆

2± 1

2

√∆2 + 4g2

eff (1)

Here, ∆ = γ (µ0H0 − µ0Hres) is the spin-cavity detuningwith Hres statisfying the spin resonance condition for agiven cavtiy frequency ωc.

In ferromagnetic films, additional magnetic modes, so-called perpendicular standing spin waves modes, appeardue to magnetic boundary conditions. For the conditionwhere the magnetization is pinned at least at one sur-face of the film (and in the absence of any anisotropiesor magnetic gradients) the magnon spectrum can easilybe calculated20. The difference of the resonance field ofthe nth-mode from the fundamental mode Hn

res −H1res is

proportional to n2. Cao et al. 15 also calculated the ex-pected coupling strength for different modes and foundthat the coupling decreases with increasing mode numberas geff ∝ 1/n. This can be understood when consideringthe microwave mode profiles and the fact that the spa-tial mode profile of the microwave field H0

1 in a cavityis typically homogeneous and in phase throughout thethickness of the (thin film) sample. Therefore only everysecond mode can be excited and the effective magnetiza-tion to which the microwave can couple to is reduced toMn .

B. Spin pumping and strong coupling

Spin pumping in ferromagnet/normal metal bilayersin the weak coupling regime is well understood11,13,19:An additional mechanism which damps the magnetiza-tion precession becomes available by spin pumping, asthe precessing magnetisation is driving a spin currentinto the adjacent normal metal.13 In electrically detected

3

VNA 9-10 GHZLNA1 ADC

A B

electro

magnet

feedline

DC lines

YIG sample

sample holder

DC meas. lines

cavity

geff

κiκe γspγi

H0

cryostat

A-B

FIG. 1. Block diagram of the experimental setup and samplemounting. (Inset) Schematic of the coupling scheme illus-trating cavity decay due to intrinsic losses viz. losses to thefeedline κc = κi +κe, spin system decay consisting of intrinsicdamping and spin pumping damping γi = γs + γsp as well thecollective coupling rate geff

spin pumping, this spin current is then converted into acharge current via the inverse spin Hall effect (ISHE). Forelectrical open circuit conditions, one thus obtains a volt-age which scales as11,19 VSP ∝ g↑↓λSD tanh tN

2λSDsin2 θ.

It, thus, contains information on the spin mixing con-ductance g↑↓, the spin diffusion length λSD, the mag-netization precession cone angle θ and depends on thethickness of the normal metal layer tN. The maximalprecession cone angle θ and thus the maximal expectedspin pumping voltage depends on the microwave powerbut also on the coupling strength between cavity and spinsystem. For strong coupling, the cone angle is expectedto be reduced as compared to the weak coupling case dueto the hybridized nature of the excitation at its maximalintensity.

The other contributions in the equation for VSP arematerial constants: The spin mixing conductance g↑↓ de-scribes the the transparency of the ferromagnet/normalmetal interface und limits the spin pumping efficiencygenerally; the spin diffusion length λSD in conjunctionwith the normal metal thickness tN accounts for a spinaccumulation in the normal metal and reduces the spinpumping efficiency if tN / λSD.

III. EXPERIMENTAL DETAILS

A. Sample preparation

In our experiments we used YIG/Pt heterostruc-tures grown by liquid phase epitaxy on (111)-orientedGadolinum Gallium Garnet (GGG) substrates. The YIG

film thickness was 2.8 µm. In order to produce a highquality interface between YIG and Pt, and thus a largespin mixing conductance g↑↓, we followed the work ofJungfleisch et al. 23 and first treated the YIG surfaceby piranha etching for 5 minutes in ambient conditions.Thereafter, the sample was annealed at 500 C for 40 min-utes in an oxygen atmosphere of 25 µbar. Under highvacuum, it was then transferred into an Electron BeamEvaporation (EVAP) chamber where 5 nm Pt was de-posited. The exact Pt thickness was determined usingX-Ray reflectometry. However, we note that for our anal-ysis the Pt layer thickness is of minor importance as itwas consistently larger than the spin diffusion length λSD

of Pt such that the Pt layer simply serves as a perfect spinsink.

In order to achieve collective strong coupling betweenmagnons and cavity photons, the number of magneticmoments must be sufficiently high. Therefore, we dicedthe sample into several pieces of different lateral dimen-sions. Magnetic resonance experiments in the strong cou-pling regime showed that the

√N scaling of the coupling

strength discussed in Section II is indeed obeyed uponcomparing samples with different volume and thus dif-ferent total magnetic moment. In the following, we willfocus on a sample with lateral dimensions 2 mm× 3 mmwhich, with the effective spin density ρS = 2.1×1022 µB

cm3

of iron atoms in YIG24, contains on the order of 4× 1017

spins. Finally, the sample was mounted on a PCB samplecarrier and wire bonded as depicted in the inset of Fig. 1.The carrier itself was mounted on a sample rod which al-lowed the sample to be accurately positioned in the elec-trical field node of a Bruker Flexline MD5 dielectric ringcavity in an Oxford Instruments CF935 gas flow cryo-stat. Shielded DC cabling allowed for the measurementof the ISHE voltage. The detailed design blueprints ofthe sample rod and chip carrier can be retrieved online25.

B. Experimental setup

The Bruker cavity exhibits a TE011 mode with an elec-tric field node at the sample position. Its quality factorQ = ω/∆ωFWHM

c (∆ωFWHMc being the full width half

maximum line width of the cavity) is dominated by thedissipative losses in the dielectric and its finite electricalresistance (κi) as well as radiation back into the cavityfeed line (κc). By changing the cavity’s coupling ratio tothe feed line, unloaded coupled quality factors Qc from 0to 8000 can be achieved. This allows tuning in and outof the strong coupling regime easily. Using the gas flowcryostat, different temperatures can be stabilized. All thefollowing experiments have, however, been performed atroom temperature.

To measure ferromagnetic resonance (FMR) the cavitywas connected to the port of an Agilent N5242A vectornetwork analyzer (VNA). The driving power of 15 dBmexcites at maximum on the order of NPh = 1.3×1014 pho-tons in the cavity which is considerably smaller than the

4

number of spins in the sample (4 × 1017). In this case,the theory presented in Sec. II is well justified26. Thefrequency dependent cavity reflection S11 was measuredwhile sweeping the external field µ0H that is created bya water cooled electromagnet. The IF bandwidth waschosen to be 100 Hz which leads to a frequency sweeptime of approximately 2 s for each magnetic field step. Acalibration of the microwave leads up to the resonator’sSMA connector was performed. The calibration did notinclude the feed line inside the resonator mount, whichgave rise to a background signal in the reflection param-eter. However, by utilizing the full complex S-parameterfor the background subtraction with the inverse map-ping technique outlined by Petersan and Anlage 27 anda subsequent Lorentzian fit to the magnitude, a reliablemeasurement of Q is still possible, even for a completelyuncalibrated setup. We note that even though standingwaves in the mirowave feed line will not appear in thecalibrated reflection measurement they will still changethe total power in the cavity and therefore may compli-cate the electrically detected DC spin pumping signal.Uncalibrated measurements did not show sharp feed lineresonances in the frequency range studied here but onlysmooth oscillations with an amplitude of less than 1 dBand there was no correlation in the DC signal resolved.In order to fit the data and as it improves clarity, we onlydiscuss calibrated measurements in the following.

The DC voltage from the sample was measured alongthe cavity axis and thus perpendicular to the externalmagnetic field and the sample normal. It was ampli-fied with a differential voltage amplifier model 560 fromStanford Research Systems. The amplifier was operatedin its low noise (4 nV/

√Hz) mode and set to a gain of

2× 104. The analog high-pass filter of the amplifier wasdisabled, however, a low-pass filter with a 6dB roll-off at1 kHz was employed. Limiting the bandwidth of the am-plifier by filtering is required in order to achieve a goodsignal-to-noise ratio. Care has, however, to be taken asthe lineshape may be quickly distorted by inappropriatesettings and thus the signature of spin pumping might bemasked. High-pass filtering can easily lead to a dispersivelike contribution to the signal, whereas low-pass filteringwill give rise to asymmetric line shapes depending on theratio of IF bandwidth and low-pass frequency. We madesure that no such distortions contribute to the presentedmeasurements. The amplified voltage signal was finallyrecorded using the auxiliary input of the VNA simulta-neously with the cavity reflection S11.

IV. RESULTS AND DISCUSSION

We first focus on the case of the so-called critical cou-pling of the feed line to the cavity in which most FMRexperiments are conducted. In this case, the internal lossrate of the cavity equals the loss rate to the feed line andthe quality factor is Qc = Qinternal/2. Note that insertinga sample and holder into the cavity will reduce the cavity

275 267 259Static magnetic 0H (mT)

259 267 275180 0 180V

9.509.559.609.659.709.759.80

0.2 0.4 0.6240 0 240

9.559.609.659.709.759.80

|S |11VDC (µV)

5 7 9 11=n

Freq

uenc

y(G

Hz)

(a)

(b)

2gef

f/2π

= 6

4 M

Hz

FIG. 2. (a) Reflection parameter S11 recorded while sweepingthe magnetic field. Strong coupling of the collective spin ex-citations is indicated by a clear anticrossing, spin wave modesto the low field side of the main resonance are visible. Blacknumbers indicated the spin wave mode number. (b) Simul-taneously recorded DC voltage. Fundamental and spin wavemodes are visible where the latter couple less strongly andthus pump spin current more efficiently. Insets: Detail ofn=5 spin wave mode including the dispersion relation of thestrong coupling between the fundamental FMR mode and thecavity as solid red line and the anti-crossing of this hybrid andthe spin wave mode (#5) as white lines.

Q by an amount which depends on the sample and holderdetails such as conductivity and dielectric losses. Basedon our measured loaded Qc = 706, the cavity decay rateis calculated to be κc/2π = ωr

2π/2Qc = 6.8 MHz.Strong coupling of the magnon and cavity system man-

ifests itself in a characteristic anti-crossing of the (mag-netic field independent) cavity resonance frequency andthe magnon dispersion that is (approximately) linear inmagnetic field. This anti-crossing corresponding to twodistinct peaks in a line cut at the resonance field, are im-mediately visible in the reflection spectrum in Fig. 2. Theminimal splitting gives the collective coupling strengthgeff/2π = 31.8 MHz of the fundamental mode to the cav-ity. Taking into account the number of spins in thesample, the single spin coupling rate is on the order ofg0/2π = 0.1 Hz which is in agreement with experimentson paramagnetic systems28.

In our setup, even the coupling of higher order spinwave modes to the cavity can be resolved. We numberthe spin waves as noted in Fig. 2 taking into accountthat with an uniform driving field only odd modes canbe excited. Analysis of the resonance position of the spinwave modes reveals that Hn

res − H1res in our sample is

proportional to n rather than n2. This indicates a non-square like potential well. Similarly, complicated modesplittings have been reported in literature29. The low-est order spin wave mode that can be easily observed inour setup is shown in the inset of Fig. 2 (a) in detail.

5

It exhibits the largest effective coupling (3 MHz) of allspin wave modes. The red and white lines in Fig. 2 (a)correspond to the harmonic-oscillator model (Eqn. 1) forthe fundamental mode and the lowest order spin wavemode, respectively. As the spin wave couples to an al-ready hybridized sytem, we superimposed the dispersionωc = ωr (B) of the hybridized system of fundamentalmode and unperturbed cavity as the ”cavity” mode inthe modelling of the spin wave mode couplings.

In order to quantify the coupling strength of the higherorder modes which only interact weakly with the hy-bridized cavity–fundamental FMR mode, we follow theapproach of Herskind et al. 30 . For each field, we fita Lorentzian to the magnitude of the cavity absorp-tion. From this fit we extract the resonance frequencyωc and the half width half maximum of the absorption∆ω which, in the weakly coupled spin waves reads as30

∆ω = ∆ωc + geffγs/(γ2s + ∆2

).

The coupling of the spin waves to the already hy-bridized cavity resonance decreases with the order of themode. This can be understood by taking into accountthat the effective magnetization to which the homoge-neous microwave field can couple decreases with increas-ing mode number. The extracted values, gn=7,9,11,13 =[3.65, 2.49, 1.64, 1.16] MHz, match accurately with the ex-pected 1

n dependence of the coupling strength15.We attribute the pronounced feature that is seen to

the right of the anti-crossing to an unidentified spinwave mode. A similar feature was found in otherexperiments14 and has been interpreted in the same man-ner. In our data, we can clearly distinguish between thefundamental mode and this additional mode – simplyby remembering that the relative intensity and couplingstrength is expected to be higher for the fundamentalmode. Possible origins for the additional mode are an in-homogeneous sample or a gradient in the magnetic prop-erties across the film thickness31. This would be consis-tent with the unusual spin wave mode splitting. Lastly,we note that the recorded signal in the reflection parame-ter is completely symmetric upon magnetic field reversal.

The simultaneously recorded DC voltage is shown inFig. 2 (b). Contrary to the reflection parameter, the volt-age signal reverses sign on reversing µ0H0. The lineshapethat we record for all modes is completely symmetric asfar as they can be clearly distinguished from each other.We thus conclude that we observe a signal purely causedby spin pumping and not by any rectifying effect. In aFMI/NM bilayer (ρYIG ≥ 10 GΩ m)32 rectification canonly arize from a change of the spin Hall magnetoresis-tance (SMR) in the normal metal. According to modelcalculations12 this effect is negligible for the system weinvestigate because of the small magnitude of the SMReffect (< 0.1%). This notion is further corroborated bythe fact that the change in lineshape expected for rectifi-cation type signals is not visible in our data. Apart fromthe spin wave modes which are clearly resolved in theDC voltage signal, we can also clearly see the electrically

detected spin pumping voltage originating from the hy-bridized system of cavity and fundamental FMR mode(the main anti-crossing). The hybridized cavity eigen-modes can, however, pump spin current into the normalmetal only very inefficiently and thus the DC voltage weobserve is very low.

The upper panels of Fig. 3 show the change in cav-ity reflection as we gradually increase the coupling of thecavity to the feed line and thus increase the cavity decayrate. Starting from the critically coupled case (inter-nal cavity losses are equal to losses into the feedline) inthe left panel to a highly overcoupled cavity (losses intothe cavity feed line dominate the cavity’s decay rate) inthe right panel, we clearly see an increase in the cavitylinewidth up to the point were the unperturbed cavityis no longer recognizable. Correspondingly, the cavitydecay rate increases from left to right and, in turn, themicrowave magnetic field strength H1 in the cavity de-creases. For the already weakly coupled spin wave modesthe spin pumping voltage decreases with decreasing mi-crowave magnetic field strength H1 resp. available mi-crowave power(indicated by the higher S11 parameter)in the cavity. The DC spin pumping voltage amplitudecorresponding to the fundamental mode (lower panels ofFig. 3) does, however, not decrease for lower Q-factorsbut stays approximately constant. Considering that theabsorbed power of the cavity-spin system stays approxi-mately constant when changing the cavity decay rate ascan easily be seen in the line cuts in the upper panels ofFig. 3 this behaviour can also be understood.

The best measure of the true magnon spectrum andline widths of the spin system can be extracted fromthe highly overcoupled case (right panels of Fig. 3 andFig. 4). There, the magnon-photon coupling is negligi-ble compared to the cavity loss rate and therefore, themagnon-cavity mode hybridization does not distort theline shape. A mode that strongly couples with the cav-ity, on the contrary, can vanish completely in the fixed-frequency spectrum. We finally note that we observethe described anti-crossing due to the magnon-photoncoupling and thus the distortion of the lines in a fixed-frequency experiment (with the cavity tuned to high Q,as usually done in cavity-based FMR experiments) al-ready for sample volumes as small as V = 2× 10−3mm3

in the case of YIG (MS = 140 kA m−1). These samplevolumes are easily achieved for LPE grown samples andwe note that in most cavity FMR experiments33 the ef-fects of the coupling need to be taken into account inorder to yield accurate results especially when automaticfrequency control is employed.

V. CONCLUSIONS

In summary, we presented systematic measurementsof spin pumping in different regimes of the magnon-photon coupling strength. For the fundamental mode ofa YIG/Pt bilayer, strong coupling with an effective cou-

6

0.0 0.4 0.8

260 265 270 275 280 260 265 270 275 280Static magnetic field µ0H0 (mT)

260 265 270 275 280− 250 0 250VDC (µV)

99.559.609.659.709.759.

Freq

uenc

y(G

Hz)

0.160.320.480.64|S11|

−240−80080240

9.559.609.659.709.759.80

VDC (µV)|S11|

FIG. 3. Increasing the coupling of the cavity to the feed line (from left to right) increases the cavity loss rate κc and thus linewidth ∆ω/2π. This enables experimental control of the transition between strong and weak coupling. The line cuts at positivefield (intense colors) and negative field (pale colors) again confirm the symmetry, V (−H0) = −V (H0) and S11(−H0) = S11(H0)and also show the merging of the two dispersion curves during the strong/weak transition.

− 4

− 8

− 12

|S11

|(d

B)

weak couplingstrong coupling

255 260 265 270 275Magnetic Field (mT)

0

50

100

150

VD

C(µ

V)

(a)

(b)

FIG. 4. Line cuts of (a) reflection parameter and (b) DC volt-age at the resonator frequency ωc (H0 = 0). In the stronglycoupled magnon-photon case (green lines), the fundamentalmode vanishes as opposed to the weakly coupled case wherethe magnon spectrum is accurately reproduced

pling strength of geff/2π = 31.8 MHz has been achievedat room temperature in a standard EPR cavity. Thecharacteristics of the coupled magnon-photon system fitwell to the established theory and are consistent withrecent results. Simultaneously, we recorded the electri-cally detected spin pumping signal of the fundamentalmode. We were able to tune the system from the strong

to the weak coupling regime by changing the cavity’s de-cay rate. The evolution of the spin pumping signal of thefundamental mode has been analyzed qualitatively andfollows the predictions of Lotze 16 : In the strongly cou-pled magnon-photon system the spin pumping efficiencyis reduced as the precession cone angle is smaller than inthe weakly coupled case. Additionally, we were able toobserve coupling and electrically detected spin pumpingof several spin wave modes with distinctly different cou-pling strengths and observe for the first time their 1/ndependence predicted by Cao et al. 15 . Furthermore, wedirectly demonstrated the implications of strong couplingon fixed-frequency FMR experiments. We conclude thatsmall sample volumes or an highly overcoupled cavity aremandatory for a qualitatively and quantitatively correctevaluation of the magnon spectrum.

ACKNOWLEDGEMENTS

We thank Christoph Zollitsch and Johannes Lotzefor many valuable discussions and Michaela Lammel forassistance in the sample preparation. M. Harder ac-knowledges support from the NSERC MSFSS program.We gratefully acknowledge funding via the priority pro-gramme Spin Caloric Transport (spinCAT) of DeutscheForschungsgemeinschaft (Project GO 944/4), SFB 631C3 and the priority programm SPP 1601 (HU 1896/2-1).

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