Integration and characterization of micron-sized YIG structures with very low Gilbert damping on arbitrary substrates

The growth of high-quality thin film yttrium-iron-garnet (YIG) is very challenging. Even today, very low Gilbert damping (⁠$α≤5×10−4$⁠) is only achieved for deposition on gadolinium-gallium-garnet (GGG), which is almost perfectly lattice-matched to YIG (see the overview in the study by Schmidt et al.¹). Nevertheless, for many experiments, a GGG substrate is not suitable. GGG exhibits a strong paramagnetism that even increases below $70 K$⁠.² This results in an enlarged Gilbert damping in a thin YIG film due to the coupling of the YIG with the substrate. As a consequence, many experiments, which aim, for example, for the investigation of the strong coupling of magnons and microwave photons,^3–9 are limited to bulk YIG fabricated by liquid phase epitaxy (LPE) or to macroscopic YIG spheres. Until now, this problem prevents experiments in hybrid quantum magnonics on YIG microstructures. Furthermore, experiments using YIG microstructures and integrated microwave antennas on GGG are difficult because of its strong paramagnetism that comes into effect especially at low temperatures.² Unfortunately, there has also not been any successful attempt to grow high-quality YIG with reasonably low Gilbert damping on other substrates. Thus, a method to fabricate thin high-quality YIG microstructures on GGG along with a subsequent transfer on a different substrate would lead the way toward many new promising experiments and applications. We have developed a process that allows us to transfer YIG microstructures from GGG onto another substrate. Although the process is not suitable for mass fabrication, it, nonetheless, enables a class of experiments, which until today seemed unthinkable.

Our method is based on a fabrication process¹⁰ using room-temperature (RT) pulsed laser deposition (PLD), liftoff, and annealing, which yields freely suspended YIG structures, whereby we apply the process in order to fabricate bridges or doubly clamped beams. The suspended parts of these structures exhibit extraordinarily low Gilbert damping and linewidth in ferromagnetic resonance (FMR). For similar structures, a ferromagnetic resonance (FMR) linewidth at 9.6 GHz of $μ0ΔHHWHM=140 μT$ and a Gilbert damping of $α≈2×10−4$ were demonstrated. These values are comparable to those best obtained for epitaxial YIG thin-film material grown by PLD or sputtering (cf. overview in the study by Schmidt et al.¹). Using this process, we fabricate an array of 500 000 bridges of span-size $1.5×5 μm2$ on a GGG substrate. The bridges are arranged in an array with a periodicity of $5 μm×25 μm$⁠. We then mask the spans of the bridges by aluminum oxide using electron beam lithography, e-beam evaporation, and liftoff. [Fig. 1(b)]. Using argon ion milling allows one to remove the part of the bridge that connects the span to the substrate leaving the masked YIG as a microslab-like platelet embedded in aluminum oxide (AlOx) [Fig. 1(c)]. Dissolving the mask in ammonia water lifts the 500 000 YIG microplatelets from the substrate and immerses them in the solution. The wet etchant is then stepwise replaced by water, yielding a watery suspension of uniform monocrystalline YIG platelets [Fig. 1(d)]. By drop-casting, the YIG platelets can now be transferred to any substrate. After drying, the platelets stick to the substrate and even remain in place during subsequent spin-coating of further resist layers. The drop-casting is a statistical process where a small amount of solution is spread over a large area of the sample. The large number of fabricated platelets ensures that in the end of the process, a reasonable number of structures can be found in the area of interest that can be of the order of $100×100 μm2$ or smaller. Still, in some cases, the drop-casting process needs to be repeated several times. With the help of additional lithography, the platelets can be integrated in complex devices or applications.

Here, we show one example of how a YIG platelet can be integrated into a coplanar waveguide (CPW) geometry to achieve in-plane excitation and high sensitivity in FMR. As a substrate, we use sapphire onto which $150 nm$ of Au with a Ti adhesion layer was deposited by electron beam evaporation. Sapphire is chosen because of its excellent properties for high-frequency measurements. Before the drop-casting, a layer of PMMA is spun onto the unpatterned metal surface. The suspension is subjected for a few seconds to ultrasonic agitation to ensure a homogeneous suspension of the YIG platelets, and by using a pipette, a single drop of the suspension is then put onto the sample. After the drop-casting, the YIG platelets are typically flat on the sample surface but randomly oriented. Once a suitable YIG platelet is identified, we heat the sample up to $250 °C$⁠, which is well above the glass transition temperature of the PMMA,¹¹ causing the YIG platelet to slightly sink into the PMMA film [Fig. 2(a)]. By electron beam lithography, we then cross-link the PMMA at the end of the selected bridge, defacto welding the bridge to the Au surface [Fig. 2(b)]. Using the PMMA layer under the YIG has several advantages compared to direct deposition on the Au surface. No spin coating is required before the bridge is fixed, and after removing the non-crosslinked PMMA, the sample surface is also now clean from the possible residue of the drop-casting process. In addition, spare bridges, which were transferred onto the first PMMA film during the drop-casting, are now lifted off the substrate and do not hinder further processing or characterization. It should be noted that there is most likely a gap of $10−40 nm$ between YIG and Au, and so the system corresponds rather to a bridge with a YIG platelet as a span and two pedestals of PMMA as posts. Only now, the CPW structure is fabricated, allowing us to align it accurately with respect to the YIG platelet. The CPW is defined using electron beam lithography, AlOx evaporation, and liftoff to mask the intended area of the CPW and the YIG platelet. By argon ion milling, we remove the unmasked Au and Ti. After removing the AlOx mask, we end up with a CPW perfectly aligned with the YIG platelet and also matching in terms of size and shape [Fig. 2(c)]. The final structure is shown in Fig. 3 as a false-color SEM image.

In order to assess the sensitivity of our experiment, we now perform FMR measurements. In addition to room temperature characterization, we also investigate spin dynamics at low temperature. As mentioned, a GGG substrate can deteriorate the damping of thin film YIG at low temperatures,^12,13 an effect that may be circumvented by our process. For the measurements at 295 K, the sample is contacted by RF probes that provide a good electrical contact. The external magnetic field is applied in-plane, whereby the magnetic field is modulated with a frequency of 187 Hz. For measurements at low temperatures, the samples are bonded and inserted into a ⁴He bath cryostat. The cryostat is placed inside an electromagnet that can be rotated in the sample plane. Here, the magnetic field is modulated at 10 kHz using an air coil of a few turns of Cu wire wound around the sample holder inside the cryostat. The measurements are performed at $T=5 K$ because this temperature is the lowest that can be precisely stabilized in the cryostat over the long necessary time span. During the measurements, the external magnetic field is oriented along the long side of the platelet. FMR is measured by sweeping the magnetic field at constant RF frequency at an RF power of $−21 dBm$⁠. The transmitted RF signal is rectified, and the modulation of the external field allows for lock-in detection to increase the measurement sensitivity. With the YIG platelet centered on the waveguide, the exciting RF field is oriented in the sample plane and homogeneous over the YIG platelet. As a consequence, we can only excite standing spin-wave modes with an uneven number of antinodes that have non-zero magnetization.

Figure 4 shows two resonance curves obtained at 4 GHz at 295 K and at 5 K, respectively. In both cases, we observe an extended spin-wave spectrum with a large number of backward-volume modes (BVMs). These discrete modes are caused by the finite size of the YIG platelet and correspond to standing spin-wave modes as observed in a previous experiment.¹⁰ Because of the complexity of the spectrum and the overlap of multiple modes, it is difficult to obtain a linewidth or even extract a Gilbert damping from measurements at different respective frequencies. A closer look at the shape of the main resonance line indicates that it is not a single line but composed of at least two separate lines if not more (Fig. 6). At 5 K, the spectrum is noisier than that at room temperature, a fact that is attributed to the different setups used for the measurements. But still, the details of the spectrum are similar to those at room temperature. The major difference to the room temperature measurement is the change in the resonance field that appears due to the increasing saturation magnetization.¹⁴ From micromagnetic simulations and the position of the main resonance, we infer the saturation magnetization of $μ0Meff≈180 mT$ at room temperature and of $μ0Meff≈251 mT$ at 5 K. This increase in saturation magnetization at low temperature is in good agreement with the literature.¹⁵ 

We perform TRMOKE experiments on the YIG in order to obtain more detailed information about the local structure of the excited modes. Further details of this technique are given in the work of Tamaru et al.¹⁶ and Neudecker et al.¹⁷ Again, the measurements are performed with the external magnetic field oriented along the long side of the platelet. TRMOKE allows us to locally image magnon modes in terms of both intensity and phase.¹⁰ To perform the spatially resolved imaging, the frequency was set to 4 GHz at an RF amplitude of −25 dBm. The real and imaginary part of the dynamic susceptibility were detected in a pointwise manner, while the magnetic field was kept constant for each picture (Fig. 5).

The spatially resolved measurements show several standing BVMs with the fundamental mode with only one antinode [Fig. 5(a)] and three standing BVMs with antinodes distributed along the bridge in Figs. 5(b)–5(d).¹⁰ As expected, all observed modes exhibit an uneven number of antinodes. Again, it is not possible to extract a precise value for the linewidth for this sample. Using the method described in Ref. 10, we have performed micromagnetic simulations using mumax3¹⁸ to reproduce the observed spin-wave patterns. We find a reasonable agreement in the magnetic field and frequency for all modes when we use a saturation magnetization of $μ0Meff=176 mT$⁠. The fact that this value is higher than that observed by Heyroth et al.¹⁰ may be due to additional anisotropies that are included in M_eff. The anisotropy of thin film YIG is known to depend on strain, and releasing the bridge from the substrate removes or at least strongly modifies any strain that may initially have been present in the YIG. Another platelet from the same batch was transferred into the gap of a CPW. In this geometry, the out-of-plane RF field allows for TRMOKE measurements with the external field applied perpendicular to the long side of the platelet. This results in a larger spacing between the resonance lines and yields the spectrum shown in Fig. 6. The resonance field is slightly shifted compared to the measurements shown in Fig. 5. At 4 GHz, we observe two superimposed lines that can be fitted by two lorentzian line shapes. We obtain a linewidth of $μ0ΔHHWHM≈195 μT$⁠. Even for large-area thin films, there are only two publications from other groups that show a smaller linewidth at this frequency.^19,20 For untransferred bridges (on GGG), we have already measured a smaller linewidth; however, it is unclear whether the original sample produced for the drop-casting was of similar quality. In any case, the magnetic quality is only weakly affected by the transfer, if at all.

In summary, we have demonstrated that it is possible to transfer high-quality thin-film YIG microstructures onto other substrates and to integrate them into complex experiments while retaining the extraordinary magnetic quality. Notably, we are able to measure FMR spectra at $5 K$ with many details. This process opens up routes toward a multitude of experiments that formerly seemed completely out of reach. As we have shown in Ref. 10, the 3D patterning process is not limited to linear bridges. Besides, we can also make frames, rings, circular drums, tables, or other arbitrarily shaped flat structures that would allow us to use the transfer technique presented here. This possibility to fabricate high-quality 2D patterned YIG films on different substrates and integrate them into more complex devices would give access to concepts of magnonics as presented, for example, in Refs. 21–23. The main restriction appearing in this context is merely the size. With the increasing structure size, the yield of the initial 3D patterning process is reduced and also the writing time increases linearly with the area. On the other hand, we need a large number of structures to have enough statistical hits in the drop-casting process. A low concentration of YIG structures in the suspension would make the drop-casting a hopeless procedure, and thus, there is a trade-off between the structure size and number. Further options arise from the possibility to apply various kinds of processing to the structures prior to the transfer. A new kind of YIG-based hybrid structure/heterostructure may be obtained by integrating the YIG into layer stacks. Before masking the free-standing YIG with AlOx and detaching it from the substrate, we can deposit additional layers on top of the YIG. After drop-casting, 50% of the structures will have these additional layers on the substrate side. In a next step, more layers can be deposited on the free YIG that is now at the top. In this way, multilayers can be created, which contain a YIG film that is no longer at the bottom of the layer stack as typical for YIG grown on GGG but where the YIG is one of the inner layers of a functional stack. It should be noted that few limitations exist with respect to the materials that can be used and that even lithographical patterning for these materials on both sides of the YIG is possible. Various applications come to mind: simple metal/YIG/metal stacks can be realized as have been used for magnon drag experiments.²⁴ Metal/ferroelectric/YIG/metal stacks can give access to electric field-controlled anisotropy and magnetization phenomena.²⁵ Even metal/piezoelectric/YIG/metal capacitors can be fabricated that will allow us to control the YIG magnetization dynamics or anisotropy by strain. A unique feature of this experiment would be that the strain in the YIG is no longer counteracted by the comparatively thick substrate on which the YIG is grown, but the YIG can have the same thickness as the piezoelectric material. Moreover, the possible use for hybrid quantum magnonics at mK temperatures should be stressed. As van Loo et al.¹² and Mihalceanu et al.¹³ have shown, the damping of thin film YIG increases at low temperatures, mainly because of interaction with the GGG substrate. In our case, the YIG platelet is no longer on the substrate. Even more, it has never been in direct contact with GGG, and so contamination effects can also be excluded, making high performance at mK temperatures even more likely. Finally, these isolated structures may also be suitable for the formation of magnon-based Bose–Einstein condensates.²⁶ 

We wish to acknowledge the support of TRR227 Project B02 WP3 and Project B01.