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c 4gµB ηmagηopt G = iθf . (1) − nr Ms r Vopt

The numerical constant µB is the Bohr magneton and c the speed of light. The factors affecting this rate can be separated ~1¤ m in two parts. Firstly, the materials parameters of the embed- DBR magnet material substrate ded magnetic material: the Faraday coefficient θf , refractive b)i) ii) GGG (7 m) YIG/GGG layer index n, gyromagnetic ratio g and saturation magnetization YIG (2¢ m)

BCB (~1£ m) Ms. These parameters can be optimized by materials devel- Au antenna opment, finding new materials and improving the quality of DBR those available. Secondly, the geometry of the optical cavity Au antenna affects the coupling rate through the volumes of the optical sapphire substrate 2 modes Vi Vo = Vopt = ui,o(r) , where ui,o(r) is the iii) DBR ≈ | | u r 2 mode function with normalizationR max ( i,o( ) )=1. The YIG/GGG | | c) lens array overlap is contained in the fill-factors ηmag = Vint/Vmag and lens array ηopt = Vint/Vopt, which are the proportion of the magnetic and optical modes volumes that contribute to the DBRs Vmag Vopt Au antenna coupling through the triple-mode overlap,

50¡ m crack ∗ Vint = drum(r) [u (r) uo(r)]. (2) Z · i × Figure 1. (a) Schematic of the magneto-optical cavity design. The open microcavity consists of two parts: a concave lens milled into a Here, the mode function um is also normalized such that 2 substrate and coated with a DBR, and a planar mirror with magnetic max ( um(r) )=1. This expression includes the effect of | | layer. Left: Cross section of design to show relative dimensions of the mode polarization. To maximize the geometric factors we the lens and beam waist. Right: 3D representation of the device would like a low optical mode volume resonator, with excel- structure. (b)Fabrication of magneto-optical microcavity. (i) Flat lent overlap with the magnon mode, and orthogonal polariza- side of open microcavity. A gold microwave antenna is patterned on tion of all three modes. the DBR surface before the YIG/GGG layer is bonded. (ii) Cross In this paper, we focus exclusively on the minimization of section of flat mirror, showing two-layer BCB bonding polymer. (iii) the optical mode volume. The design is such that lateral pat- Cross-section section of open microcavity, showing microlens array. terning of the continuous YIG layer to confine the magnon (c) Optical image through cavity structure, showing lens array and mode can incorporated at a later stage. microwave antenna.

III. DESIGN

A schematic of our proposed device is shown in Fig. 1(a). single-crystal YIG from a lattice matched GGG growth sub- The mirrors forming the open microcavities are purchased strate. We later bond this layer to the mirror surface with a from Oxford HiQ [30]. They consist of one planar surface spin-on polymer. and one microlens array. Both surfaces have a high qual- ity reflective coating consisting of 22 layers of SiO2 and The advantage of the open microcavity design is that the Ta2O5, deposited by sputtering. This distributed Bragg reflec- polarization splitting is minimized due to the cylindrical sym- tor (DBR) has a reflectivity of 99.8% at its design wavelength metry. In principle, a minor asymmetry can tune the splitting of 1300nm. The microlens array contains 16 lenses with four to match the magnon frequency, given the precise control of different radii of curvature, from 100 µm down to 20 µm, fab- lens profile that has been demonstrated [31]. For an optical ricated by focused-ion-beam milling [31]. The lens array is resonator with an asymmetrical cross-section, the splitting is situated on a raised pedestal to allow alignment of the two typically a fixed fraction of the free spectral range. There- mirrors. fore, as the mode volume shrinks, the frequency separation To embed a high quality, single crystal YIG layer in the mi- can become too large. This can be seen in the whispering crocavity, we avoid deposition techniques such as pulsed laser gallery mode resonators, where a 1mm diameter YIG sphere deposition and sputtering, because the non-lattice matched was chosen to match the splitting to the magnon frequency DBR substrate would lead to poly-crystalline YIG growth [7]. It is not possible to decrease the size of the sphere, be- [32]. Furthermore, post growth annealing to improve the crys- cause the splitting would become too large. This effect can tallinity of those layers requires temperatures above 700 ◦C, also be seen in the rib waveguide geometry [13], where the which has been found to be detrimental to the DBR [33]. In- length of the cavity must be long ( 4 mm) to keep the polar- stead, we use a lift-off technique [34] to remove a layer of ization splitting small. ≈ 3

photo- IV. FABRICATION diodes tunable laser obj. lens photo- MW amps. We start with a YIG film of thickness 2 µm grown by liq- tilt/roll xyz diode port 2 uid phase epitaxy on a gadolinium gallium garnet (GGG) sub- port 1 H0 half-wave linear obj. half-wave pol. beam strate [35]. The lift-off is achieved by inducing spontaneous vector network plate polarizer lens plate splitter analyser delamination as follows. The sample is first subjected to a electromagnet high dose ion implantation 5 1016 cm−2 with He ions at × 3.5MeV [36]. The penetration depth is approximately 9 µm, Figure 2. Experimental setup. The output polarization of a 1270- with straggle 1 µm, creating a narrow layer in which the lat- 1370 nm tunable laser is controlled via a linear polarizer and a half- tice is substantially≈ damaged [37]. Annealing at 470 ◦C for wave plate, before being separated into a local oscillator and cavity 1min leads to delamination of a bilayer consisting of the 2 µm drive. After passing through the cavity, the optical signal orthogonal of YIG and around 7 µm of GGG . This delamination occurs to the input polarization is recombined with the local oscillator and due to the slight lattice mismatch and different coefficient of measured on a high frequency photodiode. The transmission through expansion of YIG and GGG [38]. The lattice mismatch leads the cavity is measured via the light with the same polarization as to a membranewith 10-mm radius of curvatureat room tem- the input on a dc photodiode. A vector network analyzer drives the ∼ magnetic modes and measures the microwave signal from the fast perature. photodiode. The YIG wafer is diced into 1mm square chips post im- plantation, but prior to delamination. Post delamination, the thin membrane is manipulated using a small piece of 25 m µ at elevated temperatures. The oven temperature is ramped to thick Kapton film, where it is held in place by static. 250 ◦C at 1 ◦/min, for a 1hr soak. After allowing the oven To bond the YIG/GGG membrane to the mirror surface, we to cool to room temperature, the clamp is removed and the use BCB cyclotene [39], a polymer used as a dielectric in mi- Kapton film peeled from the mirror surface. This leaves the croelectronics, adhesive wafer bonding [40] and planarization YIG/GGG layer secured to the device. applications [41]. It has excellent optical properties [42], al- During the bonding process, there is some re-flow of the lowing its use, for example, in bonding active III-V devices to BCB cyclotene to the top surface of the YIG/GGG membrane. silicon photonic wafers [43]. To remove this, a 3 min Ar/CF4 reactive ion etch descum is Prior to bonding, a strip-line antenna is patterned on to the performed. surface of the mirror using photo-lithography and lift-off as shown in Fig. 1(b). A titanium adhesion layer of 7nm is de- posited under 100nm of gold, with a final 7nm of titanium above. This final layer is required to avoid the poor adhesion V. EXPERIMENTAL SETUP of BCB cyclotene to gold [44]. We prepare the mirror surface with solvent cleaning in an For measurement, the planar mirror is glued over an aper- ultrasonic bath. The device is then soaked in DI water, be- ture on a PCB patterned with input and output coplanar fore a 2min plasma cleaning process in a reactive ion etcher. waveguides, which are connected to semi-rigid coaxial cables. This is followed by a further 2min soak in DI water. The sur- The on-chip strip-line antenna is then wire-bonded to the PCB face is primed with an adhesion promoter AP3000 [44]. The waveguides for microwave measurement and excitation of the BCB cyclotene is deposited and spun for 30s at 6000 RPM, magnon modes in the YIG. The PCB is mounted on a circu- followed by 1min on a hot plate at 150 ◦C to remove the sol- lar stub which sits in an xyz-translation lens mount. The lens vent. We use a double layer of BCB cyclotene [43]. The first array is similarly mounted on a circular stub in a tilt-yaw lens layer is partially cured with a 2min anneal at 250 ◦C on a holder, for full control of the cavity geometry. strip annealer. This layer remains ‘tacky’ and bonds well to a The device is mounted in an electromagnet, with magnetic second layer of BCB cyclotene, but is viscous enough to pre- field applied orthogonal to the cavity length. Light is focused vent pinch-through under the membrane during curing, where into and out-of the cavity using two aspheric lenses mounted there can be significant re-flow of the polymer [43]. The sec- on xyz stages. The cavity is selected by scanning the laser ond layer of BCB is spun under the same conditions. to the correct position. The input laser is an external cavity Separately, the YIG/GGG layer is prepared with a 2min diode laser with linewidth 1MHz. The input polarization plasma ash to activate the surface, before a 12hr evaporation is set with a rotatable Glan-Thompson≈ prism. On the output, of AP3000 is performed in a desiccator. The membrane is a rotatable half-wave plate is used to select the measurement removed from the desiccator immediately prior to bonding. basis on a polarizing beam splitter. From the beam splitter, The bonding is performed in a simple spring-loaded clamp. the transmitted signal with the same polarization as the input The Kapton tape bearing the YIG/GGG membrane is placed light field is measured with a dc photodiode. The polariza- on the mirror, with the YIG layer in contact with the BCB tion scattered light is focused into a single mode fiber, and cyclotene. The clamp is closed to the point where the layer is combined with a local oscillator directly from the laser in a held in place with minimal pressure and then heated on a hot 50:50 fiber coupler. One output of this coupler is measured plate to 150 ◦C. The pressure is then increased to the required on a fast photodiode (12GHz bandwidth) connected via a mi- load. The assembly is then transferred to an oven at 150 ◦C crowave amplifier to a vector network analyzer (VNA). The under nitrogen flow to prevent oxidation of the BCB cyclotene VNA is also used to drive the magnetization dynamics via the 4 a) 0.6 enough to explain the observed splittings. We note that by fab- 0.5 ricating arrays of lenses with varying ellipticity, it would be 0.4 possible to obtain microcavities with a specific splitting. This FSR 0.3 would enable the triple resonance condition to be achieved. 0.2 We extract the total dissipation of the optical mode from the linewidth of peak (Fig. 3(c)) κ/2π = 11 GHz. This corre- (arb. units) 0.1 sponds to a Q-factor of 20,000 and Finesse of 600. 0.0 transmitted intensity The expected external loss rate can be estimated from the

1280 1300 1320 1340 1360 DBR reflectivity R = 0.9986 as κext = 2∆ωFSR log R − input laser wavelength (nm) [46], giving κex/2π 3GHz. Using these values, and 0.5 ≈ b) c) κ = κext + κint, we can estimate the internal dissipation rate 0.4 0.4 κint/2π =8 GHz. This is consistent with the transmitted in- 2 2 0.3 0.3 tensity on resonance κext/κ 0.07. If this internal dissipa- tion were solely due to absorption≈ in the YIG layer, we would 0.2 0.2 expect κint = κabs = (αc/nYIG )(tYIG /L) 1 GHz. The dis- 0.1 0.1 ≈

(arb.units) crepancy suggests that other dissipation mechanisms play a 0.0 0.0 role. A likely source is the surface roughness on the GGG top transmitted intensity -50 -25 0 25 50 -100 -50 0 50 100 surface, where the crack propagates during lift-off. This could laser detuning (GHz) laser detuning (GHz) be alleviated by post-bonding polishing. The choice of mirror reflectivity was conservative to en- Figure 3. Transmission spectroscopy of optical modes. (a) Wide sure good coupling to the cavity. If the scattering losses can wavelength scan, showing free spectral range. Insets show mode be eliminated, then the mirror reflectivity could be increased, profile imaged in transmission. (b) Measurement of polarization of while keeping the system over-coupled. In this case, the min- modes. The linear polarization can be set so that only one mode is imum possible dissipation rate would be κabs 1 GHz - as excited. This device had a smaller polarization splitting ≈16 GHz. achieved in WGM cavities [6, 8]. ∼ (c) Measurement of polarization splitting and optical linewidth of device used in BLS measurements. The linear polarization is set so that both modes are probed. This device is also measured in (a). VII. BRILLOUIN LIGHT SCATTERING microwave antenna. Next, we use homodyne detection to measure the magnon- scattered light, emitted from the microcavity with opposite linear polarization to the input. The input laser wavelength VI. CHARACTERIZATION is fixed and set to the lower wavelength optical mode, with frequency ωi. The VNA is used to drive the magnon modes We first characterize the optical modes of the microcavi- via the microwave antenna, as well as detect the signal at the ties. The transmitted intensity is measured as a function of same frequency from the fast photodiode, where the scattered input laser wavelength, and angle of input linear polarization, light is combined with a local oscillator taken from the input as shown in Fig. 3. A measurement over a wide wavelength laser. range (Fig. 3(a)) is used to determine the free spectral range A measurement using this method is shown in Fig. 4(a),as a

∆ωFSR /2π 6.7 THz. A number of spatial modes result- function of microwave drive frequency and applied magnetic ing from the≈ lateral confinement of the microlens are visible. field. When the microwave drive is resonant with a magnon These can be identified by imaging in transmission, see insets mode with frequency ωm within the microcavity, the magnons of Fig. 3(a). The coupling to these higher order modes is min- created scatter with the input optical photons to create optical imized by optimizing the transmitted intensity on resonance photons at a frequency ωi ωm. When combined with the ± through the lowest order mode. local oscillator ωLO = ωi, and mixed on the photodiode, this By measuring the transmitted intensity as a function of the results in a microwave signal at ωm, resulting in the bright angle of linear polarization,we can find the axes of the orthog- lines in Fig. 4(a). The power plotted± is the optical power at onal, linearly polarized modes, and the splitting between the the photodiode, using the responsivity of the photodiode and two. An example of this measurement is shown in Fig. 3(b), amplification of the amplifier chain to convert from the mea- where the polarization splitting is 16 GHz. This splitting sured microwave power at the VNA. To check this conversion, varies with different lens arrays, and is related to slight asym- we measure the noise equivalent power of the photodiode in metries in the nominally-cylindrical fabricated lens. In the darkness, and compare to its specified value. device used for BLS measurements shown in this paper, the To confirm that the modes result from the embedded mag- splitting is 32 GHz, as shown in Fig. 3(c). Because the ap- netic material, we compare the optical measurement to a stan- plied magnetic field from the electromagnetis limited to <1 T, dard inductive ferromagnetic resonance (FMR). This is made we are unable to reach the triple resonance condition. We note via the reflected microwave power to the output port of the that the frequency splitting due to the magnetic linear birefrin- VNA, and is shown in Fig. 4(b). The change in microwave re- gencein YIG [45] is estimated as 900MHz. This is not large flection coefficient ∆ S11 with magnetic field is plotted over ∼ | | 5 a) b) The peak measured optical power of the BLS signal is

1.2nW. Given the local oscillator power PLO = 65 µW and input≈ microwave power 1 mW, the total conversion efficiency is calculated to be 8 10−16. This low value is to be ex- pected, since the microwave× coupling and magnon mode over- lap in this devices have not been engineered. Therefore, to show the value of design we separate the coupling rate Eq. 1 into an optical part Gopt and the magnetic fill-factor ηmag, G = Gopt√ηmag, and estimate the obtained rate for the fab- ricated cavity. The optical mode volume for a Gaussian beam can be esti- mated as [29] Figure 4. (a) Brillouin light scattering signal. The mixed power with the local oscillator, incident on the fast photodiode. A magnetic field 2 Vopt = πw1L/4, (3) independent background has been subtracted. (b) Microwave mea- surement of magnetic modes, via |S11| using the vector network an- where L is the cavity optical path length and w1 is the alyzer. 2 beam waist on the flat mirror surface. We estimate w1 = (λ/π)√βL(1 L/β) in the parallax approximation, where β is the radius− of curvature of the lens. With the parameters of the same range as Fig. 4(a). We have confirmed that the res- the measured device, L 12 µm and β = 70 µm, this yields onances in Fig. 4(b) results from the YIG layer in FMR mea- 3 V 100 µm . This corresponding≈ to G 50 kHz. surements over a wider magnetic field. The fact that the slope opt opt The≈ magnon mode overlap in the device measured≈ is poor. with magnetic field is the same in both measurements con- Taking the whole area of the cracked film part, we estimate firms that the optical signal results from Brillouin light scat- η 10−3, reducing the coupling rate to G 50 Hz. tering in the YIG. The band of resonances also has the same ∼ ≈ Compared to the whispering gallery mode Vopt upper limit in both measurements. The differences in the re- 3 ≈ 5000 µm , and the waveguide device of Ref. 13 Vopt sponse – in particular, that the microwave reflection spectra 5 3 ≈ has more resonances than the optical BLS – can be explained 10 µm , the optical mode volume achieved here is a signif- by the fact that, in the inductive measurement, the entire strip- icant improvement. However, the microwave coupling and line is probed, whereas the optical measurement is only sensi- magnon confinement are lacking, severely limiting the con- tive to the region of the YIG film below the lens. The large version efficiency. The waveguide device [13] has optimized number of resonances in the inductive measurement is due magnon modes ηmag 1 and optimized microwave coupling through an microwave≈ resonator, and even WGM mode de- to strain inhomogeneity across the film from the film trans- −5 fer process. vices (ηmag 10 ) benefit from impedance matched mi- crowave coupling≈ to the Kittel mode [5]. The magnon modes observed in the optical measurement depend on overlap with both the microwave and optical fields [47]. The Kittel mode has the correct symmetry to fulfill these requirements, and we tentatively assign the strongest scatter- VIII. CONCLUSIONS ing to this uniformmode. There are two other modes at higher frequency visible in Fig. 4(a). The mode spacing of these is We propose and demonstrate an open magneto-optical cav- too large to be due to perpendicular standing spin waves, given ity device with optical mode volume limited by the thickness the thickness of the YIG film [48]. A possible candidate for of an embedded magnetic layer. This design is tunable, has these modes would be magneto-static surface spin waves [49] the correct polarized modes, and a significantly reduced opti- with wavevector set by the width of the microstrip antenna cal mode volume compared to previous devices [5–7, 13]. [50]. However, the robust identification of these modes re- We envisage that simple improvements in the demonstrated quires further measurement and will be the subject of future device design should enable the strong-coupling regime to be work. reached. By removing the GGG from the device via polish- A fit to the Kittel mode in the BLS measurement gives a ing, the cavity length can be reduced to 3um, and using the linewidth of Γ 20 MHz, a value larger than is typical for lowest radius of curvature lens β = 22 µm, the resulting mode ≈ 3 high quality YIG thin films [51]. This is expected, because the volume would be Vopt 7 µm (from Eq. 3). Combining this current device has imperfections in the YIG layer due to the with lateral patterning≈ of the YIG layer to confine a magnon ion-implantation process, and strain disorder from the bond- mode to a disk with diameter 5 µm, it should be possible to ing process, such as the cracks visible in Fig. 1(c). These im- achieve G = 200 kHz using the open microcavity design. perfections can be improved by further fabrication processes. If we combine this with the discussed improvements in the Firstly, the damage from ion-implantation can be alleviated magnon and optical linewidth to Γ=1 MHz and κ =1 GHz, via annealing [52]. Secondly, the strain disorder can be re- respectively, this would lead to a single photon cooperativity duced by polishing the GGG from the back of the YIG/GGG of C = 4G2/Γκ = 10−4. We would then require an opti- bi-layer. It has also been possible to transfer a YIG layer cal pump power of 5 mW to achieve the strong coupling crack-free. regime √nG > κ, Γ≈. In order to achieve cooling of magnetic 6

2 mode via optical damping, Γopt = 4nG /κ [53, 54] compa- that antiferromagnetic materials could also be embedded in rable to the magnetic damping would require only 1 µW the microcavity in order to explore the interaction of optical input power [10]. ≈ photons with THz magnon modes [18, 58]. Finally, it will be necessary to couple microwaves effi- ciently into the resulting small volume of magnetic material. Elsewhere, we have demonstrated that this is possible using ACKNOWLEDGEMENTS low impedance microwave resonators [55]. With careful mi- crowave circuit optimization it is possible to achieve coupling We are grateful to Aurilien Trichet and Jason Smith (Ox- to femtolitre magnetic volumes [56], to match that possible ford HiQ) for advice on open microcavities, Roger Webb with open optical microcavities [29]. (Surrey ion beam centre) for assistance with ion implantation, As well as demonstrating progress towards microwave- and Miguel Levy, Dries Van Thourhout, Koji Usami, Andreas optical conversion [4], it is expected that the enhancement of Nunnenkamp and Paul Walker for useful discussions. This the magnon-photon interaction demonstrated could have sig- work was supported by the European Union’s Horizon 2020 nificant impact in magnonics [57], through the increased mea- research and innovation programme under grant agreement surement sensitivity and in optical modification of the magnon No 732894 (FET Proactive HOT). The data plotted in the fig- dynamics. The versatility of the fabrication method means ures can be accessed at the Zenodo repository [59].

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