Observation of terahertz magnon of Kaplan-Kittel exchange resonance in yttrium-iron garnet by Raman spectroscopy

Backscattering Raman spectroscopic investigations were performed on an yttrium-iron garnet single crystal using linearly and circularly polarized light. A terahertz (THz) magnon of the Kaplan-Kittel (KK) exchange resonance was discovered, which had been regarded as unobservable via optical methods. The KK exchange resonance had a 7.8-THz frequency at 80 K, and the polarization selection rule led to an antisymmetric Raman tensor of the $A_2$ mode. Moreover, the assignment of all the Raman-active phonon modes, $3A_{1\mathrm{g}}, 8E_{\mathrm{g}}$, and $14T_{2\mathrm{g}}$, was proposed. This study will stimulate further investigation of the coupling of THz magnons and phonons and pave the way toward THz optomagnonics.

Figure 1

Schematic of the KK exchange resonance mode. (a) Sublattice magnetizations ${\mathbf{M}}_{\mathrm{a}}$ and ${\mathbf{M}}_{\mathrm{d}}$ under effective magnetic fields ${\mathbf{H}}_{\mathrm{a}}$ and ${\mathbf{H}}_{\mathrm{d}}$ in the ground state, respectively. (b) Ferromagnetic and antiferromagnetic vectors $\mathbf{M}$ and $\mathbf{L}$ under effective magnetic fields $\mathbf{H}$ and $\mathbf{h}$ in the ground state, respectively. (c) In the KK exchange resonance, ${\mathbf{M}}_{\mathrm{a}}$ and ${\mathbf{M}}_{\mathrm{d}}$ precess in the clockwise direction. (d) $\mathbf{L}$ also precesses in the same direction, while $\mathbf{M}$ is stationary.

Figure 2

Homemade backscattering Raman-spectroscopy system. The incident light from the 785-nm diode laser (LD785-SEV300, Thorlabs) passes through a collimating lens (CL), half-wave plate (HWP), polarized beam splitter (PBS), bandpass filters (BPF), polarized filter (PF), beam splitter (BS), quarter-wave plate (QWP), and objective lens (OL). The diameter of the focused laser spot equals 25 $\mu \mathrm{m}$. After sample irradiation by the incident polarized light at 40 mW, the scattered light from the sample is polarized using a Glan-Taylor prism (denoted by A). Subsequently, the inelastically scattered light is separated from its elastically scattered counterpart using an edge filter (EF), combination of lenses (L), and pinhole (PH). The scattered light comprising different wavelengths is spatially separated by the grating (1200 g/mm grating blazed at 500 nm) in the monochromator (Acton SpectraPro 2500i, Princeton Instruments) followed by subsequent detection by CCD image sensors (S11501-1007S, Hamamatsu Photonics). The frequency resolution of this Raman system equals 1.0 ${\mathrm{cm}}^{-1}$. The heating caused by the focused laser spot results in a 1–2 ${\mathrm{cm}}^{-1}$ redshift in the Raman spectrum.

Figure 3

Schematics of linearly and circularly polarized configurations for selection rules. The parallel- and crossed-polarized light rays indicate that the polarizations of the incident and selected scattered light are parallel and perpendicular, respectively. R and L represent the right- and left-handed helicities, respectively, of the circularly polarized light.

Figure 4

(a) Full Raman spectra with various polarization configurations at 80 K. For linear polarization, dark and light green spectra represent parallel- and crossed-polarized configurations, respectively. For circular polarization, black, red, blue, and purple spectra represent the RL-, LR-, RR-, and LL-polarized configurations, respectively. (b) Magnification of (a).

Figure 5

YIG (111) Raman spectra in the 240–270-${\mathrm{cm}}^{-1}$ range with (a) RR- and (b) LL-polarized configurations in the 80–140 K temperature range. The red, green, and purple curves fit the magnon and two $T_{2\mathrm{g}}$ phonons, respectively. The blue curve denotes the sum of the red, green, and purple curves. Fitting was performed using a Voigt function that represents the convolution of the Gaussian and Lorentzian functions with full widths at the half maxima of 1.0 and 2.5 ${\mathrm{cm}}^{-1}$, respectively. Unlike other phonon signals, the magnon peaks indicated by arrows represent significant temperature-dependent frequency shifts.

Figure 6

(a) Temperature-dependent frequency shift in the KK mode. The red and black lines with error bars denote the KK mode observed in our Raman spectra with RR- and LL-polarized configurations, respectively. The purple line with squares [25] and orange line with pentagons [28] represent the experimental data for neutron scattering. The blue line with triangles [24] and green line with hexagons [23] indicate the simulation results obtained using different models. The KK mode is fitted with normalized magnetization (yellowish green) [42]. (b) The selection rule for the KK mode of YIG observed with crossed-, RR-, and LL-polarized configurations at 7.8 THz and 80 K.