Cavity-mediated coupling of terahertz antiferromagnetic spin waves in distant crystals

In the regime of strong light-matter coupling, polariton modes are formed that are hybrid light-matter excitations sharing properties of both, an electrodynamic cavity mode and a matter mode. In the recent decade, magnon-polaritons were intensively researched using ferromagnetic materials in the microwave range, with potential applications for quantum technology and sensors. Exploring antiferromagnetic resonance (AFMR) rises magnon-polariton frequencies into the terahertz (THz) range. Here, we are investigating AFMR in hematite (α-Fe₂O₃) owing to its very low spin damping and temperature-dependent frequency above room temperature. We report on coupling of AFMR in two parallel-plane crystal slabs placed next to each other at a well controlled gap, forming a tunable Fabry-Perot type cavity. Frequency of AFMR in each crystal was indepently controlled by changing its temperature. Thus, as a function of temperature difference between the slabs, one expects to observe a crossing of AFMRs from both crystals. We used a continuous-wave spectrometer operating in the range of 0.2-0.35 THz, which is based on a frequency extender to a vector network analyzer. In reflection spectra, collected as a function of temperature difference between the two crystals, we observed avoided crossings of cavity modes and AFMRs from both slabs. Frequencies of cavity modes can be controlled by changing the gap between the crystals. For distances such that one of cavity modes has a frequency close to the crossing point between the AFMRs from both slabs, we observe that they hybridize by showing avoided crossings. This cavity-mediated coupling softens with rising gap between the crystals and is observable up to almost 9 mm, that is 10 times the sum of crystal slabs thicknesses (0.9 mm). We explain our results using classical electrodynamics and a model based on the input-output theory.