Resolve the energetic ordering of near-degenerate magnetic states

Determine the exact energetic ordering of the competing magnetic configurations in MnGa$_3$ and Mn$_9$Ga by applying tighter-convergence density-functional-theory calculations than those used in the present study.

Background

The study identifies MnGa3_3 and Mn9_9Ga as compositions with nearly degenerate competing magnetic orderings, with energy differences below 1–2 meV per atom. These differences are smaller than the stated numerical precision of the density-functional-theory calculations, so the calculated ground-state ordering is not reliably distinguishable at the current convergence settings.

Resolving the ordering requires tighter numerical convergence and is relevant both for establishing the true magnetic ground state and for assessing whether these compositions can support field-induced switching between competing magnetic phases, a prerequisite for their proposed magnetocaloric behavior.

References

Furthermore, the $\Delta E$ values for MnGa$_3$ and Mn$_9$Ga fall below the 1--2~meV/atom numerical precision of the \ac{DFT} calculations (Sec.~\ref{sec:dft}), so their exact energetic ordering cannot be resolved without tighter convergence criteria.

— Orbital fingerprinting of magnetism across the Mn-Ni-Ga Heusler ternary  (2609.19835 - Hawthorne et al., 17 Sep 2026) in Section 3, subsection “Magnetocaloric candidates” (Sec. \ref{sec:mce})