Antiferromagnetic Resonance and Terahertz Continuum in $\alpha \text{−}{\mathrm{RuCl}}_3$

We report measurements of optical absorption in the zigzag antiferromagnet $\alpha \text{−}{\mathrm{RuCl}}_3$ as a function of temperature $T$, magnetic field $B$, and photon energy $\hslash \omega$ in the range $\sim 0.3$–8.3 meV, using time-domain terahertz spectroscopy. Polarized measurements show that threefold rotational symmetry is broken in the honeycomb plane from 2 to 300 K. We find a sharp absorption peak at 2.56 meV upon cooling below the Néel temperature of 7 K at $B=0$ that we identify as the magnetic-dipole excitation of a zero-wave-vector magnon, or antiferromagnetic resonance (AFMR). With the application of $B$, the AFMR broadens and shifts to a lower frequency as long-range magnetic order is lost in a manner consistent with transitioning to a spin-disordered phase. From a direct, internally calibrated measurement of the AFMR spectral weight, we place an upper bound on the contribution to the dc susceptibility from a magnetic excitation continuum.

Figure 1

(a) Optical density $\alpha (\omega )d$ with $\mathbf{E}$ parallel to axis $\mathbf{a}$ (blue) and axis $\mathbf{b}$ (red) at $T=4\mathrm{K}$. Inset: polar plot of the transmitted terahertz electric field amplitude at 294 K as a function the rotation angle of a sample positioned between crossed polarizers. The principal axes are marked by dashed lines. (b) Zigzag antiferromagnetic order on the honeycomb lattice, with the $\mathbf{a}$ and $\mathbf{b}$ axis directions denoted by the blue and red arrows.

Figure 2

(a) Coherent magnon emission measured in the time domain at 2, 4, 6, and 8 K on an expanded vertical scale. Inset: time trace of the transmitted terahertz $\mathbf{E}$ field at 2 K (blue) and 15 K (red). The 2 K pulse shows coherent magnon radiation while the 15 K pulse does not. (b) Resonance amplitude (left-hand scale) with $\mathbf{B}(\mathrm{t})\perp \mathbf{a}$ (blue) and $\mathbf{B}(\mathrm{t})\perp \mathbf{b}$ (red) and the FWHM along $\mathbf{a}$ (right-hand scale) as a function of temperature. The dashed lines are a guide to the eye. (c) The absorption spectrum at 4 K as a function of the magnetic field. (d) Absorption spectra with the dc $B$ field parallel to the terahertz field $\mathbf{B}(\mathrm{t})$, both at 45° between the $a$ and $b$ axes. The zero-field spectrum is subtracted. (e) Dependence of the AFMR energy (left-hand axis) and inverse quality factor ${\mathrm{\Gamma }}_R/{\omega }_R$ (right-hand axis) on the magnetic field. (f) The solid black and red circles show the static magnetic susceptibility $\chi (0)$ and the contribution to $\chi (0)$ from the $\mathbf{q}=\mathbf{0}$ spin wave, respectively, as a function of the magnetic field. The shaded region between indicates the maximum contribution from a magnetic excitation continuum.

Figure 3

Absorption spectra interpreted as optical conductivity, with $\mathbf{E}$ parallel to $\mathbf{b}$.