Quantized Spin Excitations in a Ferromagnetic Microstrip from Microwave Photovoltage Measurements

Quantized spin excitations in a single ferromagnetic microstrip have been measured using the microwave photovoltage technique. Several kinds of spin wave modes due to different contributions of the dipole-dipole and the exchange interactions are observed. Among them are a series of distinct dipole-exchange spin wave modes, which allow us to determine precisely the subtle spin boundary condition. A comprehensive picture for quantized spin excitations in a ferromagnet with finite size is thereby established. The dispersions of the quantized spin wave modes have two different branches separated by the saturation magnetization.

Figure 1

(a) Schemetic drawing of the Py microstrip and the measurement circuitry. (b) Top view micrograph of a device with Py strips placed in slots between the ground (G) and signal (S) lines of a coplanar waveguide. (c) Typical photovoltage spectra measured at different microwave frequencies (from 4.5 to 5.5 GHz with a step size of 0.1 GHz). Arrows indicate FMR, SSW for the quantized number $p=2$ (S2 and S2’) and SSW for $p=3$ (S3 and S3’), respectively. The dashed line indicates $H=M_0$. All curves are normalized with the FMR amplitude and vertically offset for clarity.

Figure 2

(a) Quantized MSFVM and (b) DESW modes found near FMR ($p=0$) and SSW ($p=2$), respectively. The spectra are measured at different microwave frequencies and are vertically offset. They are normalized either to FMR or SSW ($p=2$). (c) The measured dispersions (symbols) of the quantized MSFVM and (d) DESW modes are compared with the calculated results (dotted lines). The inset in (d) illustrates the spin waves in the microstrip quantized along both $y$ and $z$ directions.

Figure 3

Dispersions of FMR ($p=0$) and SSWs ($p=2$ for S2 and S2’, $p=3$ for S3 and S3’, $p=4$ for S4 and S4’) measured (solid marks) in the entire magnetic field range. Open symbols show the measured lower branches of the DESWs at $H<M_0$. Upper branches at $H>M_0$, which are too close to the FMR and SSW, are not shown here for brevity but are plotted in Fig. 2 instead. Solid lines are calculated for the SSWs with $p=0$, 2, 3, and 4. Dotted lines are calculated for the DESWs with $p=2$. The dashed line indicates $H=M_0$.