The Kitaev quantum spin liquid (KSL) is a theoretically predicted state of matter whose fractionalized quasiparticles are distinct from bosonic magnons, the fundamental excitation in ordered magnets. The layered honeycomb antiferromagnet $alpha$-RuCl$_3$ is a KSL candidate material, as it can be driven to a magnetically disordered phase by application of an in-plane magnetic field, with $H_c sim 7$ T. Here we report a detailed characterization of the magnetic excitation spectrum of this material by high-resolution time-domain terahertz (THz) spectroscopy. We observe two sharp magnon resonances whose frequencies and amplitudes exhibit a discontinuity as a function of applied magnetic field, as well as two broader peaks at higher energy. Below the Neel temperature, we find that linear spin wave theory can account for all of these essential features of the spectra when a $C_3$-breaking distortion of the honeycomb lattice and the presence of structural domains are taken into account.
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