Magnetic percolation threshold of the antiperovskite magnetic lattice

Determine the magnetic percolation threshold of the lattice formed by the one-third-occupied transition-metal X-sites in the antiperovskite X$_3$BA structure, whose nearest- and next-nearest-neighbor coordination numbers are eight and six, respectively.

Background

The lithium-rich antiperovskites (Li2M_2M)ChO contain transition-metal and lithium ions randomly distributed over the X-sites of the X3_3BA antiperovskite structure. Consequently, only one-third of the X-sites carry magnetic ions, placing the magnetic subsystem near the percolation threshold. The observed long-range antiferromagnetic order is interpreted as evidence that this filling lies slightly above the threshold.

The paper notes that the relevant magnetic lattice is not a standard lattice for which the percolation threshold is already established. Instead, the authors compare its coordination numbers with those of the body-centered cubic lattice and use an approximate formula for an estimated threshold of approximately 0.26. A rigorous or otherwise reliable determination of the threshold would clarify the basis for interpreting the one-third-filled compounds as weakly above the percolation limit.

References

They form a lattice whose magnetic percolation threshold has not been reported in the literature yet.

— Magnetism in antiperovskite (Li$_2$\textit{M})\textit{Ch}O (\textit{M} = Fe, Mn, Co; \textit{Ch} = S, Se) diluted magnets with fixed 1/3 filling: the key role of magnetic anisotropy  (2608.13111 - Zheng et al., 13 Aug 2026) in Section “Discussion of $T_{\rm N}$”