arXiv2026
Thin-film Mn$_5$Si$_3$ is a prominent altermagnetic candidate owing to its metallicity, demonstrated anisotropic anomalous transport, and proposed $d$-wave exchange splitting that could enable spin-polarized transport. Its postulated altermagnetic structure has zero propagation vector, unlike the bulk collinear antiferromagnetic AFM2 phase, which orders at the $M$ star. We analyze both phases using Landau theory, first-principles paramagnetic-instability calculations, and Monte Carlo simulations. AFM2 appears in Landau theory as a symmetry-protected inversion-even, permutation-odd mode at a single arm of the $M$ star. At $Γ$, the same intracell pattern belongs to the collinear sector of an $E_{2g}$ order parameter; both phases require higher-order terms for their selection. Disordered-local-moment calculations identify the leading exchange instability at $M$, and the resulting classical Heisenberg model orders at the bulk experimental temperature scale into the orthogonal $3M$ phase favored by single-site entropy. Magnetostructural coupling to $E_{2g}$ deformations favors single-$M$ AFM2 ordering. The estimated homogeneous-strain contribution to the relevant quartic coefficient is about a quarter of the competing entropic term near the bulk transition, while internal $E_{2g}$ relaxations are expected to provide additional stabilization. The $Γ$-point $E_{2g}$ mode, whose Landau theory contains the altermagnetic sector, is substantially weaker and further suppressed by epitaxial strain comparable to that reported for Mn$_5$Si$_3$/Si(111) films exhibiting anomalous transport. The same strain reduces the leading magnetic exchange scale. These results explain the bulk $M$-point instability but strongly disfavor relocating the propagation vector from $M$ to $Γ$ in a moderately strained bulklike Mn$_5$Si$_3$ film, leaving the identity of the Hall-active phase unresolved.