Helicity-Changing Brillouin Light Scattering by Magnons in a Ferromagnetic Crystal

Brillouin light scattering in ferromagnetic materials usually involves one magnon and two photons and their total angular momentum is conserved. Here, we experimentally demonstrate the presence of a helicity-changing two-magnon Brillouin light scattering in a ferromagnetic crystal, which can be viewed as a four-wave mixing process involving two magnons and two photons. Moreover, we observe an unconventional helicity-changing one-magnon Brillouin light scattering, which apparently infringes the conservation law of the angular momentum. We show that the crystal angular momentum intervenes to compensate the missing angular momentum in the latter scattering process.

Figure 1

(a) A spherical crystal (0.5 mm in diameter) of yttrium iron garnet is placed in the gap of a magnetic circuit which consists of a pair of cylindrical permanent magnets, a coil, and a yoke. A coupling loop coil above the YIG sphere is used to excite magnons. By a set of a quarter-wave plate and a polarization beam splitter either left or right circularly polarized light is chosen for the input and the output. (b) Light from a cw laser is separated into two paths by an optical fiber splitter. An electro-optic modulator (EOM) in the upper path is used to calibrate signals and an acousto-optic modulator in the lower path is used to generate a local oscillator. The signal and the LO are combined and the resultant signal is sent to a power meter and a high-speed photo detector followed by a spectrum analyzer after a microwave amplifier. (c) Schematic representation of the relevant frequencies. The carrier light at ${\mathrm{\Omega }}_C$ is scattered into the sidebands at ${\mathrm{\Omega }}_R$ and ${\mathrm{\Omega }}_B$. The beat signals appear at ${\omega }_R$ and ${\omega }_B$ with respect to the LO at ${\mathrm{\Omega }}_L$.

Figure 2

(a) and (b): Microwave reflection spectrum for the Kittel mode under the external magnetic fields (a) ${\mathit{H}}_{\text{ext}}\parallel ⟨100⟩$ and (b) ${\mathit{H}}_{\text{ext}}\parallel ⟨111⟩$. The blue points show the measured reflection amplitude whereas the red curve shows the Lorentzian fitting. (c)–(f): Scattering efficiencies of the Stokes sideband (red bars) and the anti-Stokes sideband (blue bars) by two magnons [(c),(d)] and one magnon [(e),(f)] for four distinct polarization sets under ${\mathit{H}}_{\text{ext}}\parallel ⟨100⟩$ [(c),(e)] and ${\mathit{H}}_{\text{ext}}\parallel ⟨111⟩$ [(d),(f)]. The height of the color bar shows the mean scattering efficiency and the difference between the top of the black wire frame and the bar represents a standard deviation estimated from measurements repeated six times. $R_i$ ($L_i$) represents the right-circular (left-circular) polarization for the input field, while $R_o$ ($L_o$) represents right-circular (left-circular) polarization for the output field.

Figure 3

Energy-level diagrams relevant to the Brillouin scattering. The states are labeled by the electronic ground and excited states $|g⟩$ and $|e⟩$, respectively, with the number of magnons as $|n⟩$. The green arrows represent the input carrier with the angular frequency of ${\mathrm{\Omega }}_C$ and the red and blue arrows represent the Stokes and anti-Stokes sidebands with ${\mathrm{\Omega }}_R$ and ${\mathrm{\Omega }}_B$, respectively, for the $L_i\to R_o$ configuration. $\mathrm{\Delta }$ denotes the frequency detuning between the light and the $|g⟩\leftrightarrow |e⟩$ transition. The horizontal dashed arrow connects the identical states due to the ambiguity emerged from the crystal angular momentum $3\hslash$.