Semiclassical model of magnons in double-layered antiferromagnets

The stability and magnonic properties of double-layered antiferromagnets are investigated using two model systems, a linear chain (LC) and a more complex chain of railroad trestle (RT) geometry, and the results are confronted with properties of the real material CrN. The spin-paired order ($\cdots{+}{+}{-}{-}\cdots$) in LC requires alternating ferromagnetic and antiferromagnetic (AFM) exchanges, whereas in RT, an analogous order remains stable even when all interactions are AFM within certain analytical constraints. The rock-salt structure of CrN evokes clear magnetic frustration since Cr atoms in a face-centered cubic lattice form links to twelve nearest neighbors (NNs) all equivalent and AFM. Nonetheless, the magnetostructural transition to an orthorhombically distorted phase below $T_\text{N} = 287~\text{K}$ leads to four different NN Cr-Cr distances and consequently, to a large diversification of the exchange strength, which suppresses the frustration and allows for stable double-layered AFM order of CrN. This behavior originates from a competition at each NN link between Cr-Cr direct exchange and 90$^\circ$ Cr-N-Cr superexchange, both exhibiting specific power-law dependences on the interatomic distance. Finally, based on the $\textit{ab initio}$ calculated exchange parameters, the magnon spectrum and temperature evolution of ordered magnetic moments are derived.