Thickness-dependent magnon spin transport in antiferromagnetic insulators: Crossover from a quasi-three-dimensional to quasi-two-dimensional regime

Motivated by the recent observation of giant room-temperature magnon spin conductivity in an ultrathin ferromagnetic insulator [X.-Y. Wei et al., Nat. Mater. 21, 1352 (2022)], we investigate thickness-dependent magnon spin transport in thin antiferromagnetic insulators (AFIs). We study the prototypical AFI hematite, known for its exceptionally low magnetic damping and two distinct magnetic phases: a low-temperature uniaxial easy-axis phase and a high-temperature biaxial easy-plane phase. Using stochastic micromagnetic simulations, we investigate thickness-dependent magnon spin transport across both magnetic phases. Our results uncover a crossover from quasi-three-dimensional to quasi-two-dimensional magnon spin transport at a critical thickness, determined by the frequency or energy of the excited magnons. Below this critical thickness, we observe a pronounced enhancement in the magnon diffusion length in both magnetic phases. This rise is attributed to a change in the effective magnon density of states, reflecting the reduced phase space available for scattering in the thinner, quasi-two-dimensional regime. Understanding and controlling long-distance magnon spin transport in AFIs is crucial for developing next-generation spintronic nanodevices, especially as materials approach the two-dimensional limit.