Reciprocal excitation of propagating spin waves by a laser pulse and their reciprocal mapping in magnetic metal films

Focused pulse-laser-induced propagating magnetostatic surface spin waves (MSSWs) were investigated using an all-optical space-time-resolved magneto-optical Kerr effect microscope in 20-nm-thick permalloy thin films to clarify reciprocity and symmetry of MSSW emission. The microscope setup was constructed with variable direction of the applied magnetic field, and the corresponding angular dependence was examined. MSSWs were reciprocally emitted from the laser spot, in contrast to the nonreciprocal emission obtained by the antenna method. Specifically, the observed excitation amplitude and phase were independent of the propagation and magnetization directions within experimental error. By transforming the data into wave number–frequency space, the MSSW dispersion relation was clearly identified within the wave number of 2–3 rad/$\mu \mathrm{m}$ and frequency of 10 GHz. These observations are consistent with the model of ultrafast modulation of out-of-plane shape magnetic anisotropy inside the focused laser spot. In addition to confirming the symmetric and reciprocal emission of laser-induced MSSWs, the study demonstrated that this technique can provide all-optical microscopic spectroscopy for MSSW in metals, such as Brillouin light-scattering technique.

Figure 1

Schematic illustration of the coordinate system in this experiment. Both the applied magnetic field $\mathbf{H}$ and macroscopic magnetization vector ${\mathbf{M}}_0$ lie in the $y-z$ plane. The polar angle of $\mathbf{H}$ and ${\mathbf{M}}_0$ are denoted as ${\theta }_H$ and ${\theta }_M$, respectively. The probe laser spot is scanned along the $x$ axis with the origin being defined as the center of the pump laser spot. The $X-Y-Z$ coordinate system is defined as $Z\parallel {\mathbf{M}}_0$ and $X\parallel x$.

Figure 2

The pump-laser-induced change in the Kerr rotation angle $\mathrm{\Delta }{\theta }_K$ measured at a ${\theta }_H$ of $-4^{\circ }$ as a function of the position $x$ for the pump-probe delay time $\mathrm{\Delta }t$ of (a) 0.0, (b) 92.5, and (c) 909.0 ps. The curve is a Gaussian function fitted to the data, and the arrows indicate the spin-wave emission.

Figure 3

Space-time mapping of the pump-laser-induced change in the Kerr rotation angle due to the MSSW for $\mathrm{\Delta }{\theta }_K^{\mathrm{sw}}$ obtained at ${\theta }_H$ of (a) $4^{\circ }$ and (b) $-{14}^{\circ }$. The arrows are a visual guide showing the spatiotemporal evolution of the MSSWs. The time dependence of $\mathrm{\Delta }{\theta }_K^{\mathrm{sw}}$ at ${\theta }_H$ of $4^{\circ }$ obtained at (c) $x=\pm 2.1\mu \mathrm{m}$ and (d) $x=\pm 4.5\mu \mathrm{m}$. Similar data at ${\theta }_H$ of $-{14}^{\circ }$ obtained at (e) $x=\pm 1.6\mu \mathrm{m}$ and (d) $x=\pm 3.2\mu \mathrm{m}$. Open (solid) circles represent the data recorded at $x>0\mu \mathrm{m}$ ($x<0\mu \mathrm{m}$). Solid curves in (c), (d), (e), and (f) are the calculated data fitted to the experimental ones.

Figure 4

Field angle dependence of (a) the average wave number $k_0$, (b) the frequency $f_0$ for the sinusoidal change in the MSSW packet, and (c) the group velocity $v_g$ with different propagation directions. Solid line in (a) is a visual guide, and solid curves in (b) and (c) are the calculated data.

Figure 5

The frequency $f$ and wave number $k_x$ map of the spectrum density for the pump-laser-induced change in the Kerr rotation angle due to the MSSW, $\mathrm{\Delta }{\theta }_K^{\mathrm{sw}}$; (a) the real part and (b) the imaginary part at ${\theta }_H=4^{\circ }$, and (c) the real part and (d) the imaginary part at ${\theta }_H=-{14}^{\circ }$. The thin, thick, and dashed curves in (a) and (b) [(c) and (d)] are the calculated data of the dispersion relation of MSSW for different magnetic field angles of $3^{\circ }, 4^{\circ }$, and $5^{\circ }$ ($-{12}^{\circ }, -{13}^{\circ }$, and $-{14}^{\circ }$), respectively.

Figure 6

The theoretical frequency $f$ and wave number $k_x$ map of the spectrum density for the pump-laser-induced change in the Kerr rotation angle due to the MSSW, $\mathrm{\Delta }{\theta }_K^{\mathrm{sw}}$; (a) the real part and (b) the imaginary part at ${\theta }_H=4^{\circ }$, and (c) the real part and (d) the imaginary part at ${\theta }_H=-{14}^{\circ }$.

Figure 7

The theoretical frequency $f$ and wave number $k_x$ map of the spectrum density for the pump-laser-induced change in the Kerr rotation angle due to the MSSW, $\mathrm{\Delta }{\theta }_K^{\mathrm{sw}}$. The data computed at ${\theta }_H=4^{\circ }$ with the different size of the demagnetization area ${\sigma }_m$ and probe beam ${\sigma }_p$. Panels (a), (c), and (e) [panels (b), (d), and (f)] are the real part (the imaginary part) of the data for the case of ${\sigma }_m={\sigma }_p=$ 500, 300, and 150 nm, respectively.

Figure 8

The pump-laser-induced change in the Kerr rotation angle with different positions $x$ and pump-probe delay times $\mathrm{\Delta }t$: (a) uncorrected data $\mathrm{\Delta }{\theta }_K(x,\mathrm{\Delta }t)$ measured at ${\theta }_H=4^{\circ }$. (b) after subtracting the demagnetization $\mathrm{\Delta }{\theta }_K^{\mathrm{sw}}(x,\mathrm{\Delta }t)$, and (c) the change in the Kerr rotation angle due to the demagnetization $\mathrm{\Delta }{\theta }_K^{\mathrm{mag}}(x,\mathrm{\Delta }t)$.