APPLIED 11 , 014033 ( 2019 ) One-Dimensional Magnonic Crystal With Cu Stripes for Forward Volume Spin Waves

A one-dimensional magnonic crystal for forward volume spin waves (FV SWs) is demonstrated using eight pairs of Cu stripes fabricated on a 1-mm wide × 14-mm long × 10.2-μm thick yttrium iron garnet (YIG) waveguide and a SW absorber of 30-nm-thick Au film. The development of this crystal is challenging due to strong spectral oscillations caused by edge reflections and process difficulties associated with YIG magnonic crystals. A magnonic band gap with a depth of −4.6 dB is observed at a frequency of 1.80 GHz for a FV SW excited by a 50-μm-wide microstrip line, which is in good agreement with simulation results using three-dimensional modeling in the radio frequency region. The obtained performance is illustrated by plotting the depth of the respective band gaps vs the pair number of the stripes. This value is compared with that obtained in previous studies.


I. INTRODUCTION
One dimensional (1D) magnonic crystals (MCs) for controlling the propagation of spin waves (SWs) have been widely studied and reviewed [1][2][3][4][5][6][7][8][9][10][11][12][13], primarily because of the unique properties of such crystals, e.g., the guiding and filtering of SWs [14][15][16][17], confinement of SWs [18][19][20][21], and slowing (phase shifting) of SWs.MCs are based on phase interference of SWs, and many applications have been proposed or are in development based on the advantages of MCs for controlling SWs.In particular, MCs can be used in SW integrated circuits (ICs), including logic gates [22][23][24][25][26][27][28].SW ICs have attracted attention as next-generation computing elements that generate only a few Joules of heat during propagation.For these applications, forward volume SWs (FV SWs) are the most suitable mode because of their in-plane isotropy.FV SWs propagate in out-of-plane magnetized media without changing their wavelength, even in curved, oblique, or rectangular waveguides [22,24].Hence, the use of phase interference including MCs with FV SWs is significantly promising.However, only a few experimental studies [29] have researched MCs using FV SWs, although many experimental reports have described two modes-specifically, surface SWs (S SWs) [30][31][32][33][34][35] and backward volume SWs (BV SWs) [3,29,[36][37][38].This is mainly because of the significant noise in the FV SW configuration, which makes it difficult to observe a magnonic band gap (MBG) in experiments that employ low damping materials (yttrium iron garnets, YIG) as waveguides.In this study, we demonstrate a 1D MC for FV SW propagation in YIG film by introducing a noise suppression technique based on metallization [22,39,40].The radio frequency (rf) powers used for exciting SWs in this study are in the linear region, and the SWs are dipolar SWs because the wavenumber is in the order of mm [8].The observed MBG is analyzed using an rf simulation and compared with previous reports on MCs.

A. YIG waveguide
First, we calculate the single-mode propagation of FV SWs without periodic structure.A 10.2-µm-thick 14mm-long YIG line is used as a SW waveguide in a three-dimensional (3D) simulator (CST Microwave Studio 2016 SP7) based on the finite integration technique (FIT) [41,42].The parameters used in the simulation are the saturation magnetization 4π M s = 1749 G, relative permittivity r = 15.3, gyromagnetic ratio γ = 2.8 MHz/Oe, and magnetic damping α = 7.4 × 10 −4 .The internal magnetic field H in = 622 Oe is perpendicularly (z direction) applied to the YIG waveguide.This YIG is placed onto two microstrip lines (MSLs).Cu with a thickness of 18 µm, width of 50 µm, and conductivity σ of 5.96 × 10 7 S/m is used to fabricate the MSL.The MSL is placed onto a dielectric substrate ( r = 4.4) with a thickness t d = 0.5 mm, and the backside of the dielectric substrate is covered by Cu and set as ground level.These parameters are the same as those used in our prior simulation [40].
To ensure single-mode propagation of the FV SW and to maximize the input amplitude of the SW, the dispersion curve of the SW in the YIG waveguide is calculated before modeling using magnetostatic equations [8].The wavevector in the width (y) direction k m of the SW in the waveguide is quantized as where w is the width of YIG, and the x-directional wavevector k is expressed with the thickness (z) direction wavenumber k z as [43] Using the boundary conditions [8], the dispersion curve is derived as follows: where t YIG is the thickness of YIG (= 10.2 µm).μ is the diagonal component of the permeability of YIG and is expressed as: where f is frequency [8].In Eq. ( 3), k z t d is sufficiently large, hence tanh(k z t d ) ≈ 1.Therefore, Eq. ( 3) can be converted to Figure 1(a) shows a plot of Eq. ( 5) for m = 1 and 2 at f = 1.8 GHz.When w is between approximately 0.75 and approximately 1.25 mm, a single-mode SW can be obtained.Hence, a width w of 1 mm is used in all subsequent simulations and experiments.The wavenumber k is 3.7578 mm −1 and the wavelength λ is 1.672 mm for w = 1 mm.The dispersion curves for w = 1 mm with various m are shown in Fig. 1(b).A single mode is obtained in the frequency range between approximately 1.780 and approximately 1.815 GHz for m = 1.The spectral robustness is approximately 35 MHz, which is sufficiently large for the experiments.
Based on these estimations, the waveguide feature is determined and 3D simulations are conducted.Figures 1(c) and 1(d) show the calculated distribution of an absolute value of the x-directional magnetic-flux density |b x | as the amplitude of FV SW at the surface of the YIG waveguide for w = 1 and 2 mm, respectively.Disordered propagation is observed during multimode propagation (w = 2 mm).MCs are based on phase interference; hence, such a disordered propagation hinders the exhibition of a MBG.However, in contrast, the 1-mm-wide waveguide exhibits a monotonically decaying amplitude relative to the direction of propagation.Hence, a single-mode propagation of FV SW is obtained with a 1-mm-wide YIG waveguide in simulation.

C. Design of the magnonic crystal
The pitch of the Cu stripes is determined using the following values.The length of the bare YIG area L YIG is 418 µm (= λ YIG /4), the length of the Cu-YIG area L Cu−YIG is 836 µm (= λ Cu−YIG /4), and the eight pairs of Cu lines are introduced onto the YIG waveguide as shown in Fig. 2. The lattice constant is 1.254 mm.The edges of the YIG waveguide outside the MSLs are covered by 30-nm-thick Au films, which function as SW absorbers for suppressing edge reflections and spectral noise [22,39,40,46].The length of the Au L Au−YIG is 1.8 mm, the distance between the edges of the Au film and the edges of the MSL is 0.2 mm, the conductivity of the Au is 4.56 × 10 7 S/m, and the position and thickness of the SW absorbers are as discussed and specified in Ref. [40].
The calculated transmission spectra of the FV SW with and without SW absorbers and with and without MCs are shown in Fig. 3.In Fig. 3

A. Sample preparation
An MC similar to the one simulated in the last section is lithographically prepared as shown in Fig. 4 The bias magnetic field H 0 is perpendicularly applied to the sample using an electromagnet controlled using a proportional integral derivative (PID) method.The Gauss meter used in this setup is a F. W. Bell 7030 instrument and the current source is a Keysight N5750A.Transmission spectra are then obtained, followed by spin wave spectroscopy by varying the magnetic field.

B. Observation of the magnonic band gap
Figure 5(a) shows the obtained transmission spectra of the YIG waveguide with and without the MC.The bias magnetic field H 0 is 2.30 kOe.It can be seen that the simulated spectra shown in the previous section overlap.As per our design specifications, the MBG is generated at f = 1.80 GHz, which is in excellent agreement with the results of our simulation.The depth of the MBG is approximately −4.6 dB in the experiment and approximately −3.3 dB in the simulation.The difference between the experiment and simulation results may be due to the imperfectness of the sample and the modeling mesh-size limitation in the simulation.The large insertion loss is mainly due to an impedance mismatch at the 50-µm-wide MSLs.This can be improved in the future by optimizing the design of these antennas.
Figure 5(b) shows the FV SW spectroscopy image with varying magnetic fields from 2.25 kOe to 2.35 kOe with 0.5-Oe steps.The observed kinks in the SW spectroscopy might be caused by the PID control error including the quantization error of an analog digital (AD) converter.In the red region, the FV SW is not excited.The blue area shows the propagation of the FV SW.Within this region, the right blue line corresponds to the observation and illustrates the MBG.The slope of this line is equal to the gyromagnetic ratio γ of 2.8 MHz/Oe; thus, this strongly indicates the obtained results are due to the FV SW.The many lines observed in the high-frequency region are due to higher modes generated by the MSL.

C. Comparison and discussion
The obtained depth of the MBG is compared with that of previous reports including those using the other two modes (S SW and BV SW), as shown in Fig. 6 and Table I.The color of the plots indicates the mode, and the shape of the plots indicates the type of structure used to realize the MCs.From the figure, it is evident that this study is one of a few reports on MCs for FV SW and the depth is comparable to that of the other modes.Because of the small number of Cu-stripe pairs, the depth in the experiment at −4.6 dB is not as large; however, this is similar to the results of the simulation.Hence, the increase in the number of stripes should increase the depth of the MBG.
In contrast, one can note that the only other report using FV SW, shown as (n) [29], does not show a large depth of MBG because that study focused only on the spectral position of MBG, not on depth.Hence, introducing the noise suppression technique and 3D-designing technique shown in this paper will increase the depth.In addition, Fig. 6 does not consider the observed frequency, applied field, properties of YIG, and measurement setup (i.e., the dynamic range of the network analyzer).This accounts for the large deviation displayed in the figure .The simplest way to maximize the depth of MBG is to maximize the number of structures, and the maximum value can be determined by the propagation length of SWs.Therefore, to increase the depth of MBG, the suppression of insertion losses of the input and output ports using an impedance-matching technique and/or meander antenna should be effective.In addition, decreasing the damping factor of the SW waveguide material (including YIG) and its in-plane uniformity, and development of a precise nanoor micropatterning procedure for YIG would also help increase the propagation length of SWs and the depth of MBG.

IV. CONCLUSION
A 1D MC is demonstrated using Cu stripes fabricated on 10.2-µm-thick YIG film based on FV SWs.This is a report of MBG for FV SWs using a periodically metallized YIG waveguide.The MBG is designed by combining magnetostatic equations and the FIT using a 3D model.At f = 1.80 GHz, a MBG with a depth of approximately −4.6 dB is observed experimentally, which is close to the depth of −3.3 dB observed in the simulation.The calculated results demonstrate the importance of the SW absorber in order to obtain a distinct MBG.This is an important component for controlling FV SWs when realizing SW ICs in the future.

FIG. 1 .
FIG. 1.(a) Calculated wavenumber as a function of the width of the YIG waveguide at a frequency of 1.8 GHz.(b) Dispersion curve of the FV SW at w = 1 mm.(c),(d) Calculated amplitude distribution of the FV SW in YIG waveguides with widths of w = 1 and 2 mm.The thickness of the YIG t YIG is 10.2 µm and the saturation magnetization of 4π M s is 1749 G.The internal magnetic field in the YIG is H in = 622 Oe.

L
FIG. 2. 1D MC model containing eight pairs of Cu stripes.This model is used when simulating the FV SWs.(a) Overview of the simulation model and (b) an enlargement of the region close to the MSL and SW absorbers.The length of Au-YIG, Cu-YIG, and YIG are shown as L Au−YIG , L Cu−YIG , and L YIG , respectively.

FIG. 3 .
FIG. 3. (a) Calculated transmission spectra of the FV SW propagating in the YIG waveguide without SW absorbers and (b) with SW absorbers.The blue lines represent the transmission through the bare YIG waveguide, while the red lines indicate transmission through the YIG with the MC.

FIG. 4 .
FIG. 4. Process for preparing the MC.(a) Overview of the fabricated sample.(b, c) The bare YIG is cut with a dicing saw.(d) Cu-Ti is deposited onto the YIG.(e) The resist is exposed by a mask aligner.(f) The Cu-Ti is etched.(g) Resist coating for SW absorbers.(h) Au-Ti deposition.(i) Lift-off step.

FIG. 5 .
FIG. 5. (a) MBG for the FV SWs using an MC composed of Cu stripes on a YIG waveguide.The bias magnetic field H 0 is 2.30 kOe.The blue line and circles show the transmission spectra of the YIG waveguide.The red line and circles represent that of the YIG with the MC.(b) SW spectroscopy image of the MBG with a varying applied magnetic field H 0 .The inset shows the wide range of the same spectra.

TABLE I .
Comparison of the depth of the MBGs.All data are obtained from experimental reports shown with evaluable units.The number of structures means the number of metal lines, grooves, or a pair of notches in the waveguides.The depths show that of the first-order MBGs.The first-order MBGs for S SW and FV SW are observed at the lowest frequency, and those for BV SW are observed at the highest frequency.