Tunable asymmetric spin wave excitation and propagation in a magnetic system with two rectangular blocks

Asymmetric spin wave excitation and propagation are key properties to develop spin-based electronics, such as magnetic memory, spin information and logic devices. To date, such nonreciprocal effects cannot be manipulated in a system because of the geometrical magnetic configuration, while large values of asymmetry ratio are achieved. In this study, we suggest a new magnetic system with two blocks, in which the asymmetric intensity ratio can be changed between 0.276 and 1.43 by adjusting the excitation frequency between 7.8 GHz and 9.4 GHz. Because the two blocks have different widths, they have their own spin wave excitation frequency ranges. Indeed, the spin wave intensities in the two blocks, detected by the Brillouin light scattering spectrum, were observed to be frequency-dependent, yielding tuneable asymmetry ratio. Thus, this study provides a new path to enhance the application of spin waves in spin-based electronics.

www.nature.com/scientificreports/ the excitation characteristics would have a significant dependence on the RF frequency. Thus, it is found that both the spin wave asymmetry ratio and propagation direction can be controlled by the applied excitation RF current.

Experimental details
Spin wave propagation was detected using a Brillouin light scattering (BLS) spectroscopy system. The BLS spectroscopy is an optical tool that uses inelastic scattering of photons with some quasiparticles, similar to Raman spectroscopy, working between photons and phonons. The BLS spectroscopy has the advantage of investigating excitations in the GHz frequency regions where, in general, spin waves prevail 22 . A schematic diagram of the BLS measurement setup is shown in Fig. 1a. To obtain a high-resolution image of spin wave propagation, a spatially resolved micro-BLS (μ-BLS) system is used. An Ar + ion laser (λ = 514.5 nm) is used as the monochromatic light source. The scattered light from the sample was transferred to a Fabry-Perot interferometer with two etalons. High contrast of the signal is obtained as the light is transferred through both etalons. The spatial interval of the measurement is set to 100 and 200 nm for the x-and y-directions, respectively. The sample surface and laser spot were visualized by a CCD camera for real-time measurement observation. SEM images of samples A and B are shown in Fig. 1b,c, respectively. Sample A consists of two rectangular blocks one with a width of 1.61 μm and the other with a width of 3.14 μm, which have a gap of 0.3 μm between them. Sample B consists of two identical rectangular blocks with a width of 3.09 μm and the same gap. The blocks are multilayers of Ta(3 nm)/Ni 80 Fe 20 (20 nm)/SiO 2 (5 nm). The RF microwave current antenna covers the gap across the two blocks, as shown in Fig. 1. The antenna is a stack of SiO 2 (40 nm)/Ta(3 nm)/Cu(150 nm)/Ta(5 nm) layers. Blocks and antennas are patterned by an e-beam lithography process.
A spin wave is generated with an applied field of H x = 800 Oe along the x-direction. An RF microwave current with a power of P = 100 mW flows through the antenna in the same direction as the external field.

Results and discussion
The dispersion relation is calculated by considering both dipole-dipole and exchange interactions 23,24 . The spin wave frequency of mode number n on a thin film can be expressed as 24 (1) ω 2 n = ω n H + αω M k 2 ω n H + αω M k 2 + ω M F(kL) , www.nature.com/scientificreports/ where α is the exchange constant, is the gyromagnetic ratio, M s is the saturation magnetization, and H ex is an external field. The demagnetization factor N x is where t is the thickness and w is the width of the film. In Eq. (1), F(kL) , which represents a quantized matrix element of the dipole-dipole interaction can be written as where P(kL) is The exchange constant and gyromagnetic ratio of the permalloy used in this calculation are α = 2.7975 × 10 −17 m 2 and γ 2π = 2.8 × 10 −3 GHz/Oe, respectively. The measured saturation magnetization is 816 Oe.
The calculated dispersion relations of the spin wave with mode number n = 1 for the blocks are shown in Fig. 2a. It shows that the dispersion has a clear dependence on the block width, i.e., the upper dispersion curve (in red) for the block with a width of 3.14 μm and the lower curve (in black) for that with a width of 1.61 μm. Thus, the ferromagnetic resonance frequency in the wider block is found to be 8.06 GHz, and that for the narrower block is 7.80 GHz. It is known that the spin wave wavelength should be larger than the width of the microwave antenna for efficient excitation 15 . Considering the 1.9 μm width antenna used in this study, we found that the spin wave amplitude with a wavevector larger than 3.31 μm −1 diminishes significantly. As a result, the spin wave frequency, which is allowed in the narrower block, is found in a range of 7.80 ≤ ω ≤ 9.15 GHz (denoted by a black arrow in Fig. 2a). The allowed frequency for the wider block is also found in a range of 8.06 ≤ ω ≤ 9.51 GHz (denoted by a red arrow).
The measured BLS intensities for the two blocks are plotted in terms of the frequency in Fig. 2b. It is clear that the BLS intensity is strong in the frequency ranges for each block and decreases rapidly outside the ranges. Thus, significant asymmetric intensity is expected near both ends of the frequency ranges. If the RF frequency is larger than 9.15 GHz, the spin wave in the wider block is excited while the spin wave in the narrower block is negligible. The opposite situation occurs if the RF frequency is smaller than 8.06 GHz. This means that the spin waves in the field ranges of 7.80 GHz ≤ ω ≤ 8.06 GHz and 9.15 GHz ≤ ω ≤ 9.51 GHz are excited only in the narrower and wider blocks, respectively. The waves propagate in a specific direction, i.e., upward in the narrower block and downward www.nature.com/scientificreports/ in the wider block. On the other hand, in a frequency range of 8.06 ≤ ω ≤ 9.15 GHz, the spin waves are excited in both blocks at the same time and propagate along both directions. This implies that frequency modulation can be a valid way to manipulate the spin wave excitation and propagation in this geometry.
To observe spin wave propagation, spatial profiles of the spin waves in sample A with various frequencies are observed and plotted in Fig. 3. Spin wave intensities collected by BLS measurement system at each point are mapped. At a frequency of 7.6 GHz, no spin wave excitation is observed except for the spin wave of the edge mode in the wider block (Fig. 3a). At the frequencies of 7.8 GHz and 7.9 GHz, the spin waves are observed to be excited only in the narrower block (Fig. 3b,c). As the frequency increases (Fig. 3d,e), the spin waves in the wider block, as well as in the narrower block, start to be excited. At a frequency of 8.8 GHz (Fig. 3f), the BLS spectrum clearly shows the spin wave excitation in both blocks with almost the same intensity. With a further increase in frequency (Fig. 3g-i), the BLS intensity in the narrower block decreases while the intensity in the wider block remains strong. The observations in Fig. 3 are consistent with the discussion on spin wave excitation based on www.nature.com/scientificreports/ the dispersion relation. Asymmetric spin wave excitations are clearly observed depending on the frequency. This means that in the two block system (sample A), the asymmetric spin wave excitation and propagation are manipulated by frequency variation. From the data in Fig. 3, the spin wave intensity ratio between the narrower and wider blocks, defined as the asymmetry ratio, is plotted in Fig. 4. The data, indicated by red square symbols, represent the spin wave excitation in the narrower block and wave propagation upward. The data, represented by black circle symbols, are for the excitation in both blocks and bidirectional propagation, and those by blue triangles are for the excitation in the wider block and propagation downward. The asymmetry ratio changes from 0.276 to 1.43 in a system (sample A in this study), and the wave propagation direction also changes with the variation of frequency.
For comparison, spatial profiles of spin wave excitation in the two blocks with the same dimension (sample B) are plotted in Fig. 5. At low frequencies of 7.6 GHz and 7.9 GHz, no excitation of the main mode wave, other than the edge mode, is observed in either the upper or lower blocks (Fig. 5a,b). At the frequencies of 8.4 GHz, 8.8 GHz and 9.4 GHz (Fig. 5c-e), the spin excitation in both blocks is observed with slight intensity differences. The intensity difference is likely due to asymmetric field application, induced by the antenna, which is also  www.nature.com/scientificreports/ observed in other studies 15,16,19 . Thus, the characteristics in sample B cannot be utilized for the control of asymmetric spin wave excitation and propagation, as reported in previous research 16 .

Conclusion
We investigated the spin wave characteristics in a magnetic system of two blocks, which have different width dimensions (1.61 and 3.14 μm) and are separated with a small gap (0.3 μm). We found that the spin wave excitation and its propagation can be controlled by adjusting the excitation frequency. The spatial BLS spectrum shows that the spin wave is excited only in the narrower and wider blocks at low ( ≈ 7.9 GHz) and high frequencies ( ≈ 9.4 GHz), respectively, and in both blocks at frequencies ( ≈ 8.8 GHz) between them. As a consequence, the spin wave propagation direction is determined to be unidirectional downward and upward at low and high frequencies, respectively, and bidirectional at the frequencies between them. These observations are found to be consistent with the analytical dispersion relations for the two blocks. The asymmetry ratio, defined as the BLS intensity ratio of the spin wave in the blocks, is determined to be in the range between 0.26 and 1.43, depending on the excitation frequency.
The two-block system shows a new function of tunable nonreciprocal effects of asymmetric spin wave excitation and propagation without structural modification. Compared to the pre-existing system, the discovery in this study affords an additional degree of freedom in signal processing. Our system will provide a new possibility for the applications of spin-based electronics, such as spin logic devices, switch devices, and spin wave-based data transporting systems.