Tunable Spin Wave Nonreciprocity in a Magnetic System With Two Rectangular Blocks

Nonreciprocity and propagation of spin waves are key properties to develop spin - based electronics, such as magnetic memory, spin information and logic devices. To date, a nonreciprocity ratio cannot be manipulated in a system, while large values are achieved because of the geometrical magnetic configuration. In this study, we suggest a new magnetic system with two blocks, in which the nonreciprocity 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 tunable nonreciprocity. Thus, this study provides a new path to enhance the application of spin waves in spin - based electronics.


Introduction
There has been great interest in spin-based electronics because of its high potential for application to new electronic devices, such as signal processing and data storage. One of the data storage devices is magnetic random access memory (MRAM), which manipulates spin states using spin transfer torque [1][2][3] or spin orbit torque [4][5][6] . In signal transfer and processing applications, magnonics, which use spin waves as information carriers, have attracted considerable attention. Due to the absence of charge carrier transportation, spin wave devices have some advantages such as low power consumption and high processing speed 7 . In addition, many studies have proposed magnonic switches, transistors, and logic devices in recent years [8][9][10][11][12] .
One of the interesting properties of spin waves in device applications is the nonreciprocal propagation of spin waves. The magnetostatic surface spin wave (MSSW), which moves coplanar with and perpendicular to the magnetized direction, propagates with directional dependent intensity due to the asymmetry of the induced field. Such characteristics are called spin wave nonreciprocity. Thus, spin wave nonreciprocity can provide additional degrees of freedom for the control of signal propagation 12,13 . Spin wave nonreciprocity has large potential for applications in switches and logic devices due to selectively unidirectional spin wave propagation 12 , while in devices that require bidirectional signal propagation, the spin wave intensity should be the same in both directions 14 .
Spin wave nonreciprocity is quantified by comparing the spin wave intensities propagating in different directions. Manipulation of the intensity ratio, defined as the nonreciprocity ratio, is the main target in recent studies [14][15][16] . Various parameters have been utilized to control the spin wave nonreciprocity: the frequency of microwaves, magnitude of the external field, excitation antenna width and film thickness 14,17 . The nonreciprocity ratio values were reported to be small (0.4~0.7). Moreover, the wave propagation direction with a larger amplitude could not be controlled. To overcome these problems, Kwon et al. studied a bilayer of tantalum and permalloy and found that it gives a large value of nonreciprocity (~ 60) and a preferred direction of spin propagation 16 . Deorani et al. also suggested a system with two antennas on both sides of a permalloy film, and obtained a nonreciprocity ratio larger than 50 18 . However, magnetic film systems have no flexibility to change the nonreciprocity ratio and the wave propagation direction once the system is fabricated. It would be of great interest to find a way to control the nonreciprocity ratios and direction in a system.
Here, we suggest two bar-type permalloy(Ni80Fe20) blocks that have different widths and are located on a line with a narrow separation (~ 0.3 μm). Because the two blocks have their own frequency range for spin excitation, the excitation characteristics would have a significant dependence on the RF frequency. Thus it is found that both the spin wave nonreciprocity 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. A schematic diagram of the BLS measurement setup is shown in Fig. 1(a). 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

Results and discussion
The dispersion relation is calculated by considering both dipole-dipole and exchange interactions 19,20 . The spin wave frequency of mode number n on a thin film can be expressed as 20 where is the exchange constant, 2 = 2 + 2 is an in-plane component of the wave is the saturation magnetization, and is an external field. The demagnetization factor where is the thickness and is the width of the film. In equation (1), ( ), which represents a quantized matrix element of the dipole-dipole interaction can be written as where ( ) is The exchange constant and gyromagnetic ratio of the permalloy used in this calculation are The calculated dispersion relations of the spin wave with mode number n = 1 for the blocks are shown in Fig. 2(a). 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, a spin wave with a wavevector larger than 3.31 μm -1 would not be excited.
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. 2(a)). 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 can be a valid way to manipulate the spin wave nonreciprocity and direction 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. 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. 3(a)). At the frequencies of 7.8 GHz and 7.9 GHz, the spin waves are observed to be excited only in the narrower block (Figs. 3(b) and (c)). As the frequency increases (Figs. 3(d) and (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. 3(f)), the BLS spectrum clearly shows the spin wave excitation in both blocks with almost the same intensity. With a further increase in frequency (Figs. 3(g), (h) and (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 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 spin wave nonreciprocity and propagation direction 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 nonreciprocity ratio, is plotted in Fig. 4.

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 nonreciprocity 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 nonreciprocity 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.