Compact tunable YIG-based RF resonators
José Diogo Costa, Bruno Figeys, Xiao Sun, Nele Van Hoovels, Harrie A. C. Tilmans, Florin Ciubotaru, Christoph Adelmann
CCompact tunable YIG-based RF resonators
José Diogo Costa, a) Bruno Figeys, Xiao Sun, Nele Van Hoovels, Harrie A. C. Tilmans,Florin Ciubotaru, and Christoph Adelmann b) Imec, 3001 Leuven, Belgium
We report on the design, fabrication, and characterization of compact tunable yttriumiron garnet (YIG) based RF resonators based on µm-sized spin-wave cavities. Induc-tive antennas with both ladder and meander configurations were used as transducersbetween spin waves and RF signals. The excitation of ferromagnetic resonance andstanding spin waves in the YIG cavities led to sharp resonances with quality factorsup to 350. The observed spectra were in excellent agreement with a model based onthe spin-wave dispersion relations in YIG, showing a high magnetic field tunabilityof about 29 MHz/mT. a) Author to whom correspondence should be addressed. E-mail: [email protected] b) [email protected] a r X i v : . [ phy s i c s . a pp - ph ] J a n ttrium iron garnet (YIG, Y Fe O ) radiofrequency (RF) resonators based on YIGspheres are a well-established technology and are employed in a broad range of applications,including RF filters and oscillators. These technologies benefit from the low intrinsicmagnetic loss of YIG, leading to quality ( Q ) factors of up to several thousand. Moreover,the resonance frequency of filters and oscillators can be tuned over a wide frequency bymeans of an applied magnetic field. Yet, YIG spheres have mm-scale diameters and requireeven larger transducers for input and output RF signals in addition to the system to applymagnetic fields.More recently, the development of thin film deposition techniques, in particular liquidphase epitaxy (LPE), has led to an increased interest in planar YIG resonators. Thishas resulted in considerable reduction of size and form factor, culminating in Q factorsreaching several thousand for groove-based cavities. However, the area of such deviceswas still in the square mm range, with YIG thicknesses of several µm, and usually operatingin a flip-chip configuration.In the last decade, the field of magnonics has seen tremendous progress and spin-wavedevices have been miniaturized to µm and sub-µm dimensions.
Nonetheless, while YIGmicro- and nanostructures have been studied intensively in recent years, the miniaturiza-tion of YIG-based filters and resonators to sub-mm dimensions has received little attentionso far.
Here, we report on the fabrication and characterization of YIG thin film RFresonators that are based on spin-wave cavities with µm lateral dimensions. This approachallows for a compact device design, with Q factors of up to 350 and large magnetic fieldtunability. A model of the spin-wave dispersion relations of the structures is in excellentagreement with the observed resonator spectra. These results show such devices are promis-ing to reduce the footprint of YIG-based filters, while maintaining high Q factors and tunableelectrical output.The devices were based on 800 nm thick (111) YIG films (Innovent Technologieentwick-lung, Jena, Germany) deposited by LPE on (111) gadolinium gallium garnet (GGG) sub-strates. The films showed low Gilbert damping of α ≈ × − . A combination of e-beamlithography, wet etching, and lift-off was used for device fabrication. The spin-wave cavitieswere microfabricated by wet etching (H PO , 130 ◦ C) using a SiO hardmask. After pla-narization by spin-on carbon, the 100 nm thick Au antenna transducers were defined by alift-off process. 2 ONFIDENTIAL confidential
FIGURE 1 (b) Substrate (GGG) H ext (a) Magnetic cavity(YIG)
10 µmAntennaYIG CavityMeanderLadder H ext wh (c) FIG. 1. (a) Schematic of a YIG cavity resonator. Examples of standing spin-wave modes inside theYIG cavity are represented by dashed lines. (b) Inductive antennas used in this study: meander andladder antennas. (c) Optical micrograph of a meander antenna resonator. The red box indicatesthe position of the YIG cavity with width w and height h . Figure 1(a) depicts a schematic of a YIG cavity resonator. Spin-wave cavity modes(dashed lines) are excited inside the cavity by inductive antennas. Two distinct types ofantennas were used in this study: meander and ladder structures [Fig. 1(b)]. Both meanderand ladder antennas consisted each of N identical wires [ N = 4 in Fig. 1(b)] with a widthof 1 µm and a pitch of 2 µm. Figure 1(c) shows an optical micrograph of processed deviceincluding a meander antenna. The dashed red line indicates the region where the YIG cavity( × µm ) is located. The difference between the two types of antennas lies in the directionof the RF current: while in ladder antennas, currents in wires flow in the same directionwith the same phase, currents in adjacent meander antenna wires have a phase shift of π , i.e. they flow in opposite directions. Hence, local magnetic fields are always in the samedirection for ladder antennas but alternating for meander antennas.The RF response of the devices was assessed by measuring the RF reflection ( S -parameter) using a Keysight E8363B network analyzer (input RF power − dBm) at fre-quencies between 10 MHz and 15 GHz. During the measurements, an external magnetic fieldof µ H ext = 145 mT was applied along the antenna wires [see Fig. 1(c)]. Figure 2(a) shows as3 ONFIDENTIAL confidential
FIGURE 2 h = 64 µm h = 128 µm h = 256 µm (b) f (GHz) (a) h = 64 µm h = 128 µm h = 256 µm | S | ( d B ) FIG. 2. RF characteristics of YIG cavity resonators with ladder antennas for different cavity heights h and constant width w = 16 µm. (a) Measured magnitude of the S -parameter vs. frequency.(b) Smith chart representation of the RF measurements matched to a 50 Ohm impedance ( f = 10 MHz to 15 GHz) . In all cases, µ H ext = 145 mT. an example the return loss of three ladder-antenna resonators ( N = 8 ) with different cavityheights ( w = 16 µm) after de-embedding the contact pad parasitics. Sharp resonances areobserved at frequencies between 6.1 and 6.2 GHz, followed by a series of weaker resonancesat higher frequencies. A Smith chart representation of the device impedances is shown inFig. 2(b). The intrinsic Q factor of these devices varied between about 200 and 350, whichwas obtained for the largest device. The RF absorption by the YIG cavity increased with h due to the increasing magnetic cavity volume.4 ONFIDENTIAL
FIGURE 3 f (GHz) f (GHz) k ( r a d / µ m ) k ( r a d / µ m ) (b)(a) (c) (d) (e) (f) R e [ S ( H e x t ) – S ( ) ] H RF R e [ S ( H e x t ) – S ( ) ] Fouriertransform
FIG. 3. RF characteristics of YIG cavity resonators ( × µm cavity size) with (a) ladder and(c) meander antennas. (b) schematic representation of the studied devices (top) and the generatedexternal magnetic field (bottom). Dispersion relations for the resonators with (d) ladder and (f)meander antennas, with DE (solid lines), BV (dashed lines), and excited cavity modes (stars). µ H ext = 145 and 164 mT for ladder and meander antenna resonators, respectively. (e) Excitationspectrum for ladder (blue line) and meander antennas (red line). We now discuss in more detail the different resonance spectra for devices including bothladder and meander antennas. Resonator spectra are shown in Figs. 3(a) and 3(c) forladder ( µ H ext = 145 mT) and meander ( µ H ext =
163 mT) antennas, respectively. Thecavity area was × µm in both cases and all applied magnetic fields were sufficient tosaturate the magnetization. In addition to the main resonance, the spectra showed severaladditional weaker resonances that are well separated in the case of the ladder antenna. Thisbehavior can be understood by considering the spin-wave dispersion relations in the YIGcavity. In this geometry, two types of spin-wave modes can be generated: (i) backward5olume (BV) modes with the wavevector parallel to H ext ; and (ii) Damon-Eshbach (DE)modes with the wavevector perpendicular to H ext . The corresponding dispersion relations(saturation magnetization M s = 130 kA/m, exchange constant A = 3 . pJ/m, α = 1 × − )are represented in Figs. 3(d) and 3(f) for the two devices and µ H ext = 145 mT and 163mT, respectively. The dashed and solid lines represent dispersion relations for propagatingBV and DE spin waves, respectively.In a cavity, the boundary conditions impose that the wavenumber can only assume dis-crete values of k = nπ/L with n the mode number and L the cavity length. The resultingdiscrete spectra are shown as stars in Figs. 3(d) and 3(f). Note that for a rectangular cavity,the effective cavity lengths for BV (here L BV = 32 µm) and DE modes (here L DE = 16 µm)are not equal.A comparison with the experimental spectra in Figs. 3(a) and (c) shows excellent agree-ment with the frequencies of both BV and DE spin-wave cavity modes. Further insight intothe excited resonances, their relative amplitudes, and the dependence on the antenna designcan be gained by considering the excitation efficiency of a spin-wave (cavity) mode, whichis given by Γ n ∝ (cid:12)(cid:12)(cid:12)(cid:12)(cid:90) V H RF ( x ) · m ( x ) dV (cid:12)(cid:12)(cid:12)(cid:12) , (1)with H RF the magnetic excitation field, m ( x ) the dynamic magnetization of the spin-wavemode, and V the cavity volume. In wavevector space, the excitation efficiency is thusgiven by a Fourier transform of the magnetic excitation field. To a first approximation, themagnetic field underneath an antenna wire with width d can be written as H RF ≈ ± I RF / d in the wire region and 0 outside, as shown in Fig. 3(b) for both ladder and meander antennas.Here, I RF is the RF current.The resulting spatial Fourier spectra of the excitation fields transverse to the wires areshown in Fig. 3(e) for both ladder and meander antennas ( N = 8 ). This geometry corre-sponds to the excitation of DE spin-wave cavity modes. The spectra show that ladder an-tennas efficiently excite DE cavity modes with smaller wavenumbers k (larger wavelengths)but cannot excite high- k modes. A similar result is found for the Fourier transform alongthe wires of the ladder antenna (not shown), which couple to BV cavity modes. As a result,the main resonance in the experimental spectrum in Fig. 3(a) can be attributed to a super-position of the DE and BV ferromagnetic resonances—which are nondegenerate due to thefinite dimensions of the rectangular YIG cavity—and the first BV spin-wave cavity mode.6 ONFIDENTIAL
50 100 150 200 250 30046810
Ladder MeanderTunability:Ladder - 29.3 MHz/mTMeander - 28.0 MHz/mT
FIGURE 4 f ( G H z ) µ H ext (mT) FIG. 4. Tunability of YIG cavity resonators. Resonance frequency vs. external magnetic field forresonators ( × µm cavity) with ladder and meander antennas, as indicated. The solid linesrepresent best linear fits to the data. Additional resonances at lower frequency correspond to higher order BV spin-wave modes,whereas only one DE mode was clearly observed at higher frequencies. Note that due tosymmetry reasons, only odd BV cavity modes can be excited.By contrast, meander antennas preferentially excite DE cavity modes with larger wavenum-bers around a maximum determined by the wire pitch. Moreover, due to the opposite direc-tions of the magnetic fields underneath adjacent wires, the meander antenna cannot exciteBV modes since the average magnetic field transverse to the wires is zero. Therefore, thespectrum consists of DE modes with increasing mode number n until the dispersion relationbecomes flat at high k . The main resonance in the spectrum in Fig. 3(c) thus consists of asuperposition of a large number of BV cavity modes with nearly continuous k . As a result,the Q factor of the main resonance is lower for meander antennas than for ladder antennas.Note that the Q factor of resonators with meander antennas can be optimized by reducingthe wire pitch, which reduces the excitation of DE cavity modes with low wavenumbers.One of the key advantages of YIG resonators is their tunability by a magnetic field.This is illustrated in Fig. 4, which shows the dependence of the measured main resonancefrequency on the applied magnetic field for ladder and meander antennas. In both cases,the dependence in the studied magnetic field range was linear with slopes of 29.3 MHz/mT(ladder) and 28.0 MHz/mT (meander). The tunability was very similar to that of devices7 ONFIDENTIAL
FIGURE 5 f (GHz) R e [ S ( H e x t ) – S ( ) ] R e [ S ( H e x t ) – S ( ) ] (b)(a) w = 16 µm h N = 8 h = 256 µm h = 128 µm h = 64 µm h = 32 µm h = 16 µm h = 8 µm w = 64 µm N = w/2 µm w h = µ m w = 32 µm w = 16 µm w = 8 µm FIG. 5. RF characteristics of YIG cavity resonators with ladder antennas for different cavitydimensions. (a) Different cavity widths w for constant antenna wire density ( N = w/ µm) andcavity height ( h = 40 µm). (b) Different cavity heights for constant cavity width ( w = 16 µm, N = 8 ). In all cases, µ H ext = 145 mT. based on bulk YIG, demonstrating the device miniaturization does not affect tunability.The slight dependence of the tunability on the antenna design can be attributed to thedifferent magnetic field dependence of the relevant spin-wave cavity modes.These results indicate that ladder antennas lead to a better-defined device response witha sequence of well-marked and sharp resonances. In the following, we focus on the signaloptimization of ladder structures. Figure 5(a) shows the frequency response of resonatorswith identical antenna wire width (1 µm) and pitch (2 µm), identical cavity height h = 40 µm, but different cavity width w . Maintaining a constant wire density for increasing w wasachieved by setting the number of wires in each resonator to N = w/ µm. In this case,increasing w leads to two competing effects: (i) an increase of the magnetic volume and8ransducer size; and (ii) the redistribution of the total current in an increasing number ofparallel wires, which lowers the RF magnetic field underneath each individual wire. Whereas(i) increases the RF absorption by the cavity, (ii) reduces the external excitation. Botheffects tend to compete with each other and, as a result, an optimum width of w = 16 µm( N = 8 ) was observed, as shown in Fig. 5(a). As expected, the separation between adjacentDE cavity modes decreased for larger w and several peaks became superimposed for thelargest cavity. Narrower cavities also showed reduced resonator Q factors, possibly due toedge effects or processing imperfections.The effect of varying the cavity height h is illustrated in Fig. 5(b). In this case, longerantennas overlap with a larger magnetic volume without reducing the driving RF magneticfield, leading to increased RF absorption by the longer YIG cavity. Thus, the strongest RFabsorption was obtained for the largest studied cavity with h = 256 µm, in keeping with theresults in Fig. 2(a). The main resonance frequency increased with h in agreement with thechange of the dispersion relation as a function of the cavity length (not shown).In conclusion, we have studied the characteristics of RF resonators based on YIG cavi-ties with areas down to 128 µm ( ≈ − mm ). Both ladder- and meander-type antennaswere used as transducers between the RF and spin-wave domains. The resonators showed Q factors up to 350, depending on the YIG cavity dimensions, and a magnetic field tunabilityof about 29 MHz/mT. The observed frequency dependence of the resonators was in excel-lent agreement with the spin-wave dispersion relations in YIG, indicating that the differenttransducers excited distinctly different cavity modes. While ladder antennas mainly coupledto ferromagnetic resonance, meander antennas excited standing spin-wave modes with largewavevectors. The results show that µm-sized YIG resonators may find applications in futureminiaturized magnetically tunable RF filters. The small device size and form factor of theresonators are particularly promising for future integrated systems in a package combiningdifferent RF components.All data needed to support the conclusions are present in the paper. Additional datamay be requested from the authors. This work has received funding from the imec.xpandfund. The authors would like to thank Patrick Vandenameele and Peter Vanbekbergenfor their support of the project as well as Xavier Rottenberg, Kristof Vaesen, and Barendvan Liempd for many valuable discussions. J.D.C. acknowledges financial support from theEuropean Union MSCA-IF Neuromag under grant agreement No. 793346. FC’s and CA’s9ontributions have been funded in part by the European Union’s Horizon 2020 research andinnovation program within the FET-OPEN project CHIRON under grant agreement No.801055. REFERENCES C. Kittel, Phys. Rev. , 155 (1948). J.F. Dillon, Phys. Rev. , 59 (1958). P.S. Carter, IRE Trans. Microw. Theory Tech. , 252 (1961). P.C. Fletcher and R.O. Bell, J. Appl. Phys. , 687 (1959). J. Helszajn,
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