Surface acoustic wave coupled to magnetic resonance on multiferroic ${\mathrm{CuB}}_2{\mathrm{O}}_4$

We observed surface acoustic wave (SAW) propagation on a multiferroic material ${\mathrm{CuB}}_2{\mathrm{O}}_4$ with use of two interdigital transducers (IDTs). The period of IDT fingers is as short as 1.6 $\mu \mathrm{m}$ so that the frequency of SAW is 3 GHz, which is comparable with that of magnetic resonance. In the antiferromagnetic phase, the SAW excitation intensity varied with the magnitude and direction of the magnetic field, owing to the dynamical coupling between SAWs and antiferromagnetic resonance of ${\mathrm{CuB}}_2{\mathrm{O}}_4$. The microscopic mechanism is discussed based on the symmetrically allowed magnetoelastic coupling.

Figure 1

(a) Top view of ${\mathrm{CuB}}_2{\mathrm{O}}_4$ SAW device used in this research. Magnetic field was applied along the surface of the device. (b) Enlarged view of Al IDT. (c) Schematic diagrams of the device. the surface of device is (001) plane of the ${\mathrm{CuB}}_2{\mathrm{O}}_4$ crystal, and SAW propagation direction is parallel to the $\left[110\right]$ axis. (d) Transmission between two IDTs. Solid line is the raw data measured and dashed line shows the transmission due to SAW deduced by the Fourier transformation analysis (see text). (e) Transmission as a function of time obtained by the inverse Fourier transformation. Data in the colored region are used for the Fourier transformation to the SAW transmission $S_{21}^{\mathrm{SAW}}$.

Figure 2

(a) Magnetic field dependence of microwave absorption due to magnetic resonance of ${\mathrm{CuB}}_2{\mathrm{O}}_4$. The external magnetic field is parallel to $\left[110\right]$ axis. Thick line shows the SAW frequency. (b) Magnetic field dependence of microwave absorption at 3.013 GHz due to magnetic resonance. (c) Magnetic field dependence of normalized SAW transmission $S_{21}^{\mathrm{SAW}}/S_{21}^0$ and excitation $-S_{11}^{\mathrm{SAW}}/S_{11}^0$.

Figure 3

(a) Normalized SAW transmissions $S_{21}^{\mathrm{SAW}}$ and $S_{12}^{\mathrm{SAW}}$ as a function of magnetic fields with various directions. Solid lines show the transmission from port 1 to port 2 ($S_{21}^{\mathrm{SAW}}/S_{21}^0$) and dashed lines are transmission for opposite direction ($S_{12}^{\mathrm{SAW}}/S_{12}^0$). (b) Illustration of $xyz$- and $XYZ$-coordinate systems. (c) Magnetic field angle dependence of normalized SAW transmission $S_{21}^{\mathrm{SAW}}$ at ${\mu }_{0}H=40$ mT. Solid line shows $C_1-C_2{cos}^2\varphi$.

Figure 4

(a) Microwave reflection from the SAW device $|S_{11}|\left(f\right)$ at several magnetic fields. The magnetic fields are applied parallel to the SAW propagation direction. The solid line shows the observed data, and the dotted and dashed lines are the result of fitting of magnetic resonance and background, respectively (see text). (b) SAW excitation $-S_{11}^{\mathrm{SAW}}$ at 40 and 200 mT and the difference between 40- and 200-mT values ($\mathrm{\Delta }{S}_{11}$). (c) SAW transmission $S_{21}^{\mathrm{SAW}}$ at 40 and 200 mT and their difference ($\mathrm{\Delta }{S}_{21}$). $\mathrm{\Delta }{S}_{11}$ and $\mathrm{\Delta }{S}_{21}$ in (b) and (c) are multiplied by 5.

Figure 5

Microwave absorption spectra in magnetic fields with various directions within the ($1\overline{1}0$) plane and the fixed magnitude of ${\mu }_{0}H=40$ mT. $\theta$ is defined as the angle between the [001] axis and the magnetic field.