Terahertz Optomagnetism: Nonlinear THz Excitation of GHz Spin Waves in Antiferromagnetic ${\mathrm{FeBO}}_3$

A nearly single cycle intense terahertz (THz) pulse with peak electric and magnetic fields of $0.5\mathrm{MV}/\mathrm{cm}$ and 0.16 T, respectively, excites both modes of spin resonances in the weak antiferromagnet ${\mathrm{FeBO}}_3$. The high frequency quasiantiferromagnetic mode is excited resonantly and its amplitude scales linearly with the strength of the THz magnetic field, whereas the low frequency quasiferromagnetic mode is excited via a nonlinear mechanism that scales quadratically with the strength of the THz electric field and can be regarded as a THz inverse Cotton-Mouton effect. THz optomagnetism is shown to be more energy efficient than similar effects reported previously for the near-infrared spectral range.

Figure 1

(a) Schematic of the ${\mathrm{FeBO}}_3$ crystal structure and experimental geometry. THz and optical pulses are focused onto the ${\mathrm{FeBO}}_3$ crystal. The diameter of the probe beam is significantly smaller than that of the THz beam. The external magnetic field ${\mathbf{B}}_{\mathrm{ext}}$ is along the $x$ axis. $\mathbf{L}$ and $\mathbf{M}$ are antiferromagnetic and magnetization vectors, respectively. $\tau$ is a controllable time delay between the THz pump pulse and the optical probe pulse. o.a. denotes the optical axis (along the $z$ axis). (b) Ellipticity acquired by linearly polarized light at the wavelength of 800 nm upon propagation along the o.a. as a function of magnetic field applied in the sample plane. (c) Static polarization rotation acquired by linearly polarized light at the wavelength of 800 nm upon propagation through the tilted crystal as a function of magnetic field. The crystal tilt and the orientation of the magnetic field are shown in panel (a). (d) Waveform of the THz electric field and the corresponding Fourier spectrum (inset).

Figure 2

Optically detected THz-induced spin dynamics in ${\mathrm{FeBO}}_3$. (a) Probe polarization rotation vs time delay $\tau$. Here, the THz pump polarization (direction of the THz electric field) is along the $y$ axis and the optical probe polarization is along the $x$ axis. The crystal was tilted around the $y$ axis over 10°, as shown in Fig. 1. $B_{\mathrm{ext}}=40\mathrm{mT}$, $T=6\mathrm{K}$. (b) Corresponding Fourier spectrum of the waveform shown in (a). Both the high frequency q-AFM and the low frequency q-FM modes of magnetic resonance in ${\mathrm{FeBO}}_3$ are clearly seen. The damping constants are 0.1 and 0.004 for the q-FM and q-AFM modes, respectively. Behavior of $\mathbf{M}$ for q-AFM (longitudinal oscillation) and q-FM (precession) modes are shown as insets next to the corresponding spectral maxima. (c) The dependencies of the q-AFM (open blue circles) and the q-FM mode (closed red circles) frequencies on the external magnetic field. Solid lines are fits based on theoretical dependencies for ${\omega }_{\mathrm{AFM}}$ (blue curve) and ${\omega }_{\mathrm{FM}}$ (red curve) [26]. (d) The dependencies of the amplitudes of q-AFM (open blue circles) and q-FM (closed red circles) modes on the THz electric field. The blue and red curves correspond to linear and quadratic fits, respectively.

Figure 3

(a) Optically detected THz induced spin dynamics in ${\mathrm{FeBO}}_3$ measured for different angles $\alpha$ between the THz electric field and the $y$ axis. $\alpha$ is shown near each curve. The crystal was tilted around the $y$ axis over 10°, as shown in Fig. 1. $B_{\mathrm{ext}}=40\mathrm{mT}$, $T=6\mathrm{K}$. (b) Normalized Fourier amplitudes of the q-AFM (open blue circles) and q-FM (closed red circles) modes from panel (a). Change of sign of the amplitude indicates phase changes. The experimental data are fitted by $\sim \cos \alpha$ (blue curve) and $A+B\sin 2\alpha$ (red curve) (c) Waveforms of the magnetization dynamics after deducing the odd (upper panel) and even (lower panel) parts with respect to the polarity of the applied magnetic field $\pm 40\mathrm{mT}$. (d) Fourier spectrum of the odd (higher panel) and even (lower panel) waveforms from panel (c). (e) The dependence of the amplitude of the q-FM mode on its frequency. Hyperbolic fit is shown by the red curve.

Figure 4

(a) Optically detected THz induced spin dynamics at different temperatures, indicated near the curves. In the experiment the crystal was tilted around the $y$ axis over 10°, as shown in Fig. 1. $B_{\mathrm{ext}}=40\mathrm{mT}$. (b) Frequencies of the q-AFM (open blue circles) and q-FM (closed red circles) modes of the waveforms from panel (a).