Spin waves (SWs) have the potential to reduce the electric energy loss in signal processing networks. The SWs called magnetostatic forward volume waves (MSFVWs) are advantageous for networking due to their isotropic dispersion in the plane of a device. To control the MSFVW flow in a processing network based on yttrium iron garnet, we developed a SW absorber using artificial structures. The mechanical surface polishing method presented in this work can well control extrinsic damping without changing the SW dispersion of the host material. Furthermore, enhancement of the ferromagnetic resonance linewidth over 3 Oe was demonstrated.

Spin wave devices (SWDs) have attracted substantial research interest, because they process information encoded in a pure spin current rather than in electronic charge. Thus, SWDs are potential candidates for use in “beyond complementary metal-oxide semiconductor” devices.1–3 A decade of research has yielded logic-device concepts based on wave interference, and high energy efficiency during operation has been demonstrated.4–6 Such wave-interference-based processing holds great promise for the realization of signal processing networks including multi-input multi-output gates, in which spin waves (SWs) carrying data packets propagate in the device plane.7,8 However, to realize such signal processing networks, SW dispersion isotropy in the device plane is a critical issue. Among the different types of SWs, only magnetostatic forward volume waves (MSFVWs) possess isotropic dispersion property.9 

The recent development of the epitaxial growth technique, which employs pulsed laser deposition, for ultra-thin magnetic insulators such as yttrium iron garnet (YIG) has furthered progress towards the realization of practical SWDs,10,11 because such insulators yield magnetic damping that is several orders of magnitude less than that of metallic magnetic waveguides.12–14 However, because of the long attenuation lengths in YIG waveguides, unexpected standing modes are easily generated due to the SW reflection from the waveguide edge. This issue was recognized decades ago in classical magnetostatic wave devices.15 Waveguide edge tapering is a conventional method of suppressing such standing modes in the magnetostatic backward volume wave (MSBVW) and magnetostatic surface wave (MSSW) geometries,12,16 in which MSSWs are scattered into MSBVWs at the tapered edge, and vice versa. However, in the MSFVW geometry, this damping process is less dominant due to the isotropic dispersion in the device plane. Apart from edge tapering, for which several damping sources have been reported,17–22 remarkable increases in magnetic damping have been achieved experimentally23,24 and investigated theoretically25,26 by employing defective surfaces. Surface defects enable the two-magnon relaxation in magnetic waveguides to be controlled.27,28 However, decades ago, the limited performances of large-scale simulators and automated measurement systems did not enable comprehensive understanding of the relationship between introduced and intrinsic damping. In this study, we investigated the mechanism of the damping induced by surface roughening, and the behavior of MSFVW propagating in a waveguide with a roughened surface was also simulated by using a finite element analysis method based on the experimental setups, with the objective of determining an effective SW absorber design.

In the experiment, 20 mm long and 1.3 mm wide YIG waveguides with three different edge conditions were prepared. A rectangular waveguide and a tapered edge waveguide with a 45° cutting angle were composed of 110μm thick monocrystalline YIG layers, which were epitaxially grown on gadolinium gallium garnet substrates. A polished edge waveguide with a surface roughness Ra of 118 nm was prepared by mechanically polishing the edges of a rectangular waveguide using 600-grit sandpaper. Ra was measured by using a stylus profilemeter (Ryokosha Corp., ET4000). Overviews of these waveguides are depicted in the insets of Figs. 1b–d. These waveguides were placed on a SW transducer consisting of a pair of 50-μm-wide microstrip lines that were separated by 10 mm, and the transmission spectra S21 were observed electrically by a vector network analyzer (Anritsu 37347C). A bias magnetic field H0 of 2.1 kOe was applied perpendicular to the film plane using an electromagnet so that MSFVWs propagated in the waveguide. The measurement setup is depicted in Fig. 1a, and S21 of each waveguide is shown in Figs. 1b–d. For the rectangular and tapered waveguide, sharp transmission ripples are observable, because of the standing mode in the longitudinal direction. As shown in Fig. 1c, edge tapering does not suppress the standing mode as effectively as in the cases of MSSWs or MSFBWs. On the other hand, transmission ripples are much less prominent for the polished-edge waveguide shown in Fig. 1d. Ripples were quantified by their standard deviations σS21 and were suppressed from 5.79 dB to 3.66 dB only in the polished-edge waveguide. The results indicated that waveguide edges with roughened surfaces can effectively suppress standing modes in SWDs utilizing MSFVWs.

FIG. 1.

Effects of conventional edge tapering on SW transmission properties. (a) Experimental setup and simulation model of SW transducer. Both microstrip lines were short-terminatedTransmission properties S21 of MSFVW propagating in (b) rectangular waveguide, (c) tapered edge waveguide, and (d) polished edge waveguideInsets are overviews of waveguides. H0 = 2.1 kOe was applied along z-direction.

FIG. 1.

Effects of conventional edge tapering on SW transmission properties. (a) Experimental setup and simulation model of SW transducer. Both microstrip lines were short-terminatedTransmission properties S21 of MSFVW propagating in (b) rectangular waveguide, (c) tapered edge waveguide, and (d) polished edge waveguideInsets are overviews of waveguides. H0 = 2.1 kOe was applied along z-direction.

Close modal

Next, to confirm the effect of the roughness-induced magnetic damping, we prepared four samples with different Ra values and film thicknesses. The geometrical properties of the prepared samples are summarized in Table I. Each of the samples was a 1.3 mm × 1.3 mm square cut from the same wafer. The ferromagnetic resonance (FMR) linewidths ΔH of these samples were measured using a vector network analyzer–FMR setup with a 50Ω matched microstrip through line.29 Figures 2a–d show the measured complex susceptibility spectra χ=χ+iχ of the samples used. H0=2.3 kOe was applied perpendicular to the film plane, and the background spectrum was subtracted based on a reference measurement conducted at H0=3.3kOe. The value of χ at frequency f and in an effective magnetic field Heff can be expressed in FMR form as30 

χ(f)=γ24πMS(4πMS+Heff)fr2f(fiΔf),
(1)

where γ=2.8MHz/Oe is the gyromagnetic ratio, 4πMS is the saturation magnetization, fr=γHeff is the FMR frequency, and Δf is the frequency-swept linewidth. According to Eq. (1), the imaginary parts of the susceptibility spectra χ were fit using a Lorentzian function, and the ΔH=Δf/γ values were estimated. As a result, ΔH was found to have broadened following mechanical polishing and was estimated to have increased from 2.4 Oe to 7.1 Oe in the 10μm thick samples (#S1 and #S2) and from 4.6 Oe to 6.7 Oe in the 110μm thick samples (#S3 and #S4). The FMR frequency fr was down-shifted slightly by mechanical polishing, indicating the change of the demagnetization field, which is sensitive to changes in film thickness.

TABLE I.

Geometric parameters and measured magnetic damping constants of YIG samples.

SampleThickness (μm)Ra (nm)αΔH0 (Oe)
#S1 10 0.2 2.50×104 2.17 
#S2 10 94 2.51×104 5.97 
#S3 110 0.1 2.07×103 0.59 
#S4 110 118 2.23×103 3.99 
SampleThickness (μm)Ra (nm)αΔH0 (Oe)
#S1 10 0.2 2.50×104 2.17 
#S2 10 94 2.51×104 5.97 
#S3 110 0.1 2.07×103 0.59 
#S4 110 118 2.23×103 3.99 
FIG. 2.

Susceptibility χ spectra of (a) unpolished 10 μm thick sample #S1, (b) polished 10 μm thick sample #S2, (c) unpolished 110 μm thick sample #S3, and (d) polished 110 μm thick sample #S4. H0 = 2.3 kOe was applied. Red and blue dots represent real (χ′) and imaginary (χ″) components, respectively. (e) FMR frequency fr dependence of ΔH. Triangles and circles correspond to polished and unpolished samples, respectively. Open and closed symbols represent 10 and 110 μm thick samples, respectively. Dashed lines are linear fits determined using FMR frequency region fr > 1.5GHz.

FIG. 2.

Susceptibility χ spectra of (a) unpolished 10 μm thick sample #S1, (b) polished 10 μm thick sample #S2, (c) unpolished 110 μm thick sample #S3, and (d) polished 110 μm thick sample #S4. H0 = 2.3 kOe was applied. Red and blue dots represent real (χ′) and imaginary (χ″) components, respectively. (e) FMR frequency fr dependence of ΔH. Triangles and circles correspond to polished and unpolished samples, respectively. Open and closed symbols represent 10 and 110 μm thick samples, respectively. Dashed lines are linear fits determined using FMR frequency region fr > 1.5GHz.

Close modal

It is also important to investigate experimentally the origin of this scattering mechanism. In general, ΔH is described as a sum of intrinsic and extrinsic processes, specifically,31 

ΔH(fr)=2αfr/γ+ΔH0,
(2)

where α denotes the Gilbert damping constant, and ΔH0 is the extrinsic process. Since ΔH depends on fr, the variation of ΔH with fr was measured in this experiment by sweeping H0 from 1.2 kOe to 2.5 kOe in 20 Oe increments, and the results are shown in Fig. 2e. The obtained curves were linearly fit using Eq. (2), and the dotted lines overlaid on the measured data in Fig. 2e represent these linear fits. Error was caused in the lower-frequency regime by the inhomogeneity of Heff;32,33 thus, this regime was ignored, and the fit curves were determined using fr > 1.5 GHz.

The slopes of the curves remain almost unchanged by mechanical polishing for both the 10 and 110μm thick samples. The resulting α and ΔH0 values are also listed in Table I. The large difference in α might be due to the difference between the qualities of the two crystals. The extrinsic process ΔH0 was increased by mechanical polishing from 2.17 Oe to 5.97 Oe (+3.8Oe) and from 0.59 Oe to 3.99 Oe (+3.4Oe) for the 10- and 110μm thick samples, respectively. Therefore, the roughness-induced scattering mechanism can be explained as an extrinsic process. The scattering potential may be explained by the fluctuation in the effective magnetic field that is caused by the demagnetization effect, which was introduced by the rough surface in this case. Hence, the ΔH0 enhancements in the 10μm thick samples were larger than those in the 110μm thick samples because the modulation of demagnetization field introduced by roughness would have more significantly affected the thin films.

Finally, the ΔH0 dependence of the propagating MSFVW absorption was calculated by using a finite element simulation (ANSYS HFSS version 15). The simulation model was the same as the experimental setup shown in Fig. 1a except for the rf connector. In this simulation, the SW waveguide had the typical electromagnetic properties of monocrystalline YIG: 4πMS=1760G, relative permittivity εr=15.3, and γ=2.8MHz/Oe. Based on the measurements shown in Fig. 2e, α=2.07×103 was employed. Heff was set to 500 Oe within the waveguide and was oriented along the z-axis, so that the MSFVW propagated along the x-axis. In Figs. 3a–c, the edge regions of both waveguides (#A1 and #A3) were set to have finite ΔH0, while ΔH0 was set to 0 in region #A2. An MSFVW was injected from the microstrip line antenna on the #A1 side. The amplitude of the propagating MSFVW at 2 GHz was displayed as a magnetic field perturbation Hx. As ΔH0 increased, the intensity of the interfering wave in #A1 remarkably decreased. Figure 3d shows the measured σS21 as a function of ΔH0, as well as a fit curve that was obtained by using the exponential function σS21=R0exp(ΔH0/η)+σ0, where η is defined as the damping value that reduces the ripple to 1/e. It was determined that η=3.33Oe, R0=5.51Oe, and σ0=2.25dB. The experimentally obtained values presented in Figs. 1b and 1d are indicated by triangles in Fig. 3d and agree well with the fitting. Residual ripple σ0 mainly consisting of a standing mode along the y-direction because the exchange contribution was ignored, so the effect of the perpendicular standing SW could also be ignored. These results indicate that there is a room for further reduction of the transmission ripples σS21 by optimizing the mechanical polishing conditions.

FIG. 3.

Simulated MSFVW amplitude variation with ΔH0. MSFVW amplitude distributions at 2 GHz in YIG waveguides with ΔH0 values of (a) 1 Oe, (b) 5 Oe, and (c) 50 Oe. Finite ΔH0 values were defined in regions #A1 and #A3. (d) ΔH0 dependence of σS21 at frequencies ranging from 1.9 GHz to 2.1 GHz. Open circles represent simulated results, and closed triangles indicate experimental results. Dashed line is exponential fit.

FIG. 3.

Simulated MSFVW amplitude variation with ΔH0. MSFVW amplitude distributions at 2 GHz in YIG waveguides with ΔH0 values of (a) 1 Oe, (b) 5 Oe, and (c) 50 Oe. Finite ΔH0 values were defined in regions #A1 and #A3. (d) ΔH0 dependence of σS21 at frequencies ranging from 1.9 GHz to 2.1 GHz. Open circles represent simulated results, and closed triangles indicate experimental results. Dashed line is exponential fit.

Close modal

In conclusion, roughness-induced scattering was introduced to suppress standing SWs in the MSFVW geometry of a YIG waveguide. Mechanical polishing of the YIG surface resulted in enhancement of the local extrinsic magnetic damping of the SW waveguide to more than 3 Oe. Realization of precise surface roughness control and complex structure fabrication are outside the scope of this work, but these goals will be achieved using photolithography and chemical etching (or similar techniques) in the future.34 The present results will contribute to fundamental research on SWDs utilizing MSFVWs in low-damping SW waveguides and the realization of SWD networks.

We acknowledge support from the Japan Society for the Promotion of Science (JSPS) KAKENHI Nos. 26706009, 26600043, 26220902, 25820124, and 15H02240, JST PRESTO. TG acknowledges the assistance from the Murata Science Foundation. NK acknowledges a Grant-in-Aid for JSPS Fellows (No. 15J07286).

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