Counter-rotating standing spin waves: A magneto-optical illusion

We excite perpendicular standing spin waves by a laser pulse in a GaMnAsP ferromagnetic layer and detect them using time-resolved magneto-optical effects. Quite counterintuitively, we find the first two excited modes to be of opposite chirality. We show that this can only be explained by taking into account absorption and optical phase shift inside the layer. This optical illusion is particularly strong in weakly absorbing layers. These results provide a correct identification of spin waves modes, enabling a trustworthy estimation of their respective weight as well as an unambiguous determination of the spin stiffness parameter.

Figure 1

(a) Reference frame. (b) Dependence of the TRMO signal $\delta \beta$ on the probe beam linear polarization with respect to the sample crystallographic axes. (c) Time dependence of $\delta {\theta }_{\exp }$ and $\delta {\varphi }_{\exp }$. Inset: Fourier transform amplitude of $\delta {\theta }_{\exp }$. (d) Optically detected magnetization trajectory. (e), (f), (g) Decomposition of the experimental magnetization trajectory (d) into two oscillating signals at frequencies $f_0=2.36$ GHz and $f_1=3.90$ GHz and a nonoscillating signal, respectively.

Figure 2

(left) Magnetization trajectory in the depth of the ferromagnetic layer for the $p=0$ (a), $p=1$ (b), $p=2$ (c) PSSW modes and corresponding detected trajectory in (g), (h), (i) assuming that the optical signal would result from a depth-averaged amplitude. (right) (d), (e), (f) Theoretical effective magnetization trajectory in the depth of the ferromagnetic layer taking into account the optical phase factor and corresponding optically detected trajectory in (j), (k), (l). $L=50$ nm, $\lambda =700$ nm, and the other parameters are given in the Appendix.

Figure 3

Theoretical optically detected direction of rotation of the magnetization vector for $p=0$, 1, and 2 PSSWs modes from the amplitude ratio $r_p$ of $\delta {\theta }_p^{\mathrm{opt}}$ and $\delta {\varphi }_p^{\mathrm{opt}}$ (see text). The dashed line indicates the layer thickness. $\lambda =700$ nm, $\eta =3.67,\kappa =0.1$.

Figure 4

(a) Reference frame: light propagates along $z,\mathbf{M}$ is the magnetization vector, $\beta$ denotes the angle or the linear incident polarization with the $x$ axis. (b) Multilayer scheme.