Coherent Two-Dimensional Terahertz Magnetic Resonance Spectroscopy of Collective Spin Waves

We report a demonstration of two-dimensional (2D) terahertz (THz) magnetic resonance spectroscopy using the magnetic fields of two time-delayed THz pulses. We apply the methodology to directly reveal the nonlinear responses of collective spin waves (magnons) in a canted antiferromagnetic crystal. The 2D THz spectra show all of the third-order nonlinear magnon signals including magnon spin echoes, and 2-quantum signals that reveal pairwise correlations between magnons at the Brillouin zone center. We also observe second-order nonlinear magnon signals showing resonance-enhanced second-harmonic and difference-frequency generation. Numerical simulations of the spin dynamics reproduce all of the spectral features in excellent agreement with the experimental 2D THz spectra.

Figure 1

(a) The canted AFM order in YFO leads to a net magnetization $\mathbf{M}$ along the crystal $c$ axis. ${\mathbf{S}}_1$ and ${\mathbf{S}}_2$ are the ${\mathrm{Fe}}^{3+}$ electron spins ordered along the crystal $a$ axis. The AF mode is the amplitude oscillation of $\mathbf{M}$ while the F mode is the precession of $\mathbf{M}$. (b) Single THz pulses transmitted through the sample followed by FID signals from the AF (blue) and F (red) modes. (c) FT magnitude spectra of the FID signals from both magnon modes, showing magnon resonances at $f_{\mathrm{AF}}=0.527\mathrm{THz}$ and $f_{\mathrm{F}}=0.299\mathrm{THz}$.

Figure 2

(a) Schematic experimental geometry. Two THz pulses delayed by $\tau$ with magnetic field polarization parallel to $\mathbf{M}$ excite the AF mode. At each delay $\tau$, ${\mathbf{B}}_{\mathrm{NL}}(t,\tau )$ copolarized with input THz magnetic fields is measured by EOS as a function of $t$. Rotating the sample about the crystal $a$ axis by 90° such that $\mathbf{M}$ is perpendicular to the THz magnetic fields allows the measurement of the F mode. (b) AF mode magnon signals induced by THz pulse $A$ (${\mathbf{B}}_A$, blue) and $B$ (${\mathbf{B}}_B$, red) individually. (c) Magnon signal with the presence of both THz pulses at $\tau =3.7\mathrm{ps}$ (${\mathbf{B}}_{AB}$, black) and the nonlinear signal (${\mathbf{B}}_{\mathrm{NL}}$ magnified $50\times$, magenta). (d) FT magnitude spectrum of the oscillatory signal in ${\mathbf{B}}_{\mathrm{NL}}$ reveals ${\chi }^{(3)}$ and ${\chi }^{(2)}$ peaks at $f_{\mathrm{AF}}$ and $2f_{\mathrm{AF}}$.

Figure 3

Normalized 2D time-time plots of ${\mathbf{B}}_{\mathrm{NL}}(t,\tau )$ from the AF (a) and F (b) mode magnons, respectively. Amplitudes exceeding $\pm 0.8$ are saturated in the color map.

Figure 4

2D THz magnetic resonance spectra of magnons in YFO. (a),(b) Experimental (a) and simulated (b) AF mode 2D magnitude spectra. ${\chi }^{(3)}$ spectral peaks include rephasing (R), nonrephasing (NR), pump-probe (PP), and 2-quantum (2Q) peaks. ${\chi }^{(2)}$ peaks include second harmonic generation (SHG) and THz rectification (TR) peaks. (c),(d) Experimental (c) and simulated (d) F mode 2D magnitude spectra showing the full set of ${\chi }^{(3)}$ peaks. The artifacts are due to the signal double reflections in the sample. Each spectrum is normalized to its maximum amplitude. Amplitudes above 0.5 in (a) and (c) are saturated in the color map.