Altermagnetic Mn5Si3: Spin Symmetry and Transport

• Altermagnetic Mn₅Si₃ is a collinear, compensated antiferromagnet exhibiting d-wave spin-splitting driven by crystal-symmetry‐protected band textures.
• Experimental studies reveal controlled variant-specific angular switching of anomalous Hall and Nernst effects in high-quality epitaxial thin films.
• Nonrelativistic exchange-splitting and finite Berry curvature in Mn₅Si₃ highlight its potential for low-dissipation spintronic device applications.

Altermagnetic Mn₅Si₃ is a prototypical d-wave altermagnet—an epitaxially stabilized, collinear, compensated antiferromagnet featuring zero net magnetization yet exhibiting robust anomalous Hall and Nernst effects due to its unique real-space and momentum-space spin symmetries. In contrast to both conventional ferromagnets and classical antiferromagnets, Mn₅Si₃ demonstrates that nonrelativistic exchange-splitting and crystal-symmetry-protected band spin textures can drive finite Berry curvature phenomena, advancing the scope of spintronic applications based on light-element compounds.

1. Crystal Structure and Magnetic Phases

Mn₅Si₃ crystallizes in a hexagonal unit cell (space group P6₃/mcm; a ≈ 6.93 Å, c ≈ 4.77 Å at 110 K) in its paramagnetic phase, with two inequivalent Mn sites: Mn1 (Wyckoff 4d, typically weakly magnetic or nonmagnetic) and Mn2 (Wyckoff 6g, strongly magnetic). Within the basal plane, four out of six Mn2 sites per unit cell carry ordered moments, forming two crystallographically inequivalent “checkerboard” sublattices with alternating spin orientation (Rial et al., 2024).

Upon cooling, bulk Mn₅Si₃ exhibits a complex sequence of magnetic phase transitions:

• At $T_{N2} \simeq 95$–100 K, the material enters a collinear antiferromagnetic (AF1) phase with orthorhombic symmetry. The moments remain strictly antiparallel and collinear, with negligible net moment.
• Below $T_{N1}^* \simeq 45$–65 K, a noncollinear antiferromagnetic (AF2) phase emerges, marked by noncoplanar triangular spin arrangements and the loss of inversion symmetry (1904.02277).
• Thin films grown epitaxially on Si(111) stabilize the collinear configuration across a broad temperature range (10–300 K), as epitaxial strain pins the lattice in the high-symmetry hexagonal phase (Badura et al., 2024).

A hallmark of the altermagnetic phase in Mn₅Si₃ thin films is the existence of three inequivalent “variants” for the checkerboard-type magnetic ordering, each defined by a distinct in-plane Néel vector orientation and related by 120° rotations about 0001. The atomic site configurations, combined with anisotropic local environments (trigonal prism vs. antiprism), ensure the up- and down-spin sublattices are linked only by a 180° rotation, establishing the requisite reduced symmetry for altermagnetism (Leiviskä et al., 2024).

2. Altermagnetic Symmetries and Band Structure

Altermagnetic order in Mn₅Si₃ arises from the reduced spin symmetry group $G_\text{spin}$, which allows for nonrelativistic, intrinsic spin splitting in the electronic structure, despite complete compensation of local moments and vanishing global magnetization. Unlike antiferromagnets, whose sublattices are connected by translation or inversion (prohibiting net Berry curvature), and ferromagnets (which allow a Hall vector by symmetry due to nonzero M), Mn₅Si₃ features sublattices related exclusively by rotation. This symmetry enables a momentum-space “d-wave” spin-splitting pattern, with alternate sign lobes in the Brillouin zone (Badura et al., 2024, Leiviskä et al., 2024).

First-principles density functional theory (DFT) calculations (VASP, PBE+SOC, a = 6.901 Å, c = 4.795 Å) show pronounced anisotropic spin splittings of Mn d states across the BZ. The band structure exhibits hot spots of large Berry curvature near avoided crossings, even in the collinear AFM phase, a direct consequence of broken time-reversal symmetry in momentum-space and the absence of global inversion/translation symmetry (Badura et al., 2024). The calculated ground-state moment is ≈40 mμ_B/f.u., consistent with experiment.

Each of the three variants supports distinct monoclinic magnetic point-group symmetries; their selection can be controlled by field rotation during growth or device operation, as confirmed by variant-dependent anisotropic Hall measurements (Rial et al., 2024).

3. Anomalous Hall and Nernst Effects

The key observation in Mn₅Si₃ is the emergence of spontaneous, symmetry-protected anomalous Hall (AHE) and anomalous Nernst effects (ANE) in the absence of conventional net magnetization (Leiviskä et al., 2024, Badura et al., 2024).

Anomalous Hall Effect (AHE)

Thin Mn₅Si₃ films, patterned into Hall bars, display an AHE conductivity $\sigma_\text{AHE}$ that is maximized for the out-of-plane Néel vector orientation and vanishes or exhibits step-like changes as the Néel vector is rotated between in-plane symmetry axes via applied magnetic fields (up to ~2 T to saturate). The field- and angle-dependent AHE measurements show nontrivial, quantized switching behavior that cannot be accounted for by conventional cos θ forms or by simple magnetization lag, but is accurately captured by the underlying crystal and magnetic symmetries. High epitaxial quality is required to resolve this anisotropy; in impure or structurally disordered samples, the AHE reduces to a standard cos θ dependence (Leiviskä et al., 2024).

Anomalous Nernst Effect (ANE)

Epitaxial Mn₅Si₃ thin films exhibit a sizable anomalous Nernst coefficient $S_{yx}$, reaching up to μV/K scale (e.g., $S_{yx}=−(3±2)$ μV/K at 58 K, $−(0.04±0.01)$ μV/K at 216 K, for 20 nm films). The extracted anomalous Nernst conductivity $\alpha_{yx}$ (in A/(K·m)) aligns semi-quantitatively with DFT predictions based on the intrinsic Berry curvature of the spin-resolved bands (Badura et al., 2024). The low-temperature limit matches $$(\pi^2/3)(k_B^2T/e)(d\sigma_{xy}/d\epsilon)|_{\epsilon=\mu}$$ (Mott relation).

A summary of the key Hall and Nernst transport characteristics:

Observable	58 K	216 K	Net moment per f.u.
$S_{yx}$ (μV/K)	-3 ± 2	-0.04 ± 0.01	45 ± 20 mμ₋B (58 K); 10 ± 8 mμ₋B (216 K)
$\alpha_{yx}$ (A/K·m)	0.11 ± 0.08	0.015 ± 0.005	DFT: 0.25 (58 K), 0.12 (216 K)

These transport effects demonstrate that intrinsic Berry curvature mechanisms, enabled purely by the symmetry of the spin texture and band structure, can yield strong AHE/ANE without heavy elements or net magnetization (Badura et al., 2024).

4. Magnetic Variant Control and Experimental Methodologies

The three altermagnetic variants, each corresponding to a distinct in-plane Néel vector direction ([2̄110], [1̄210], [11̄20]), are structurally related by 120° rotations. Nanoscale Hall-cross devices (down to 100 nm scale) fabricated from high-quality epitaxial films allow the isolation and identification of variant-dominated responses (Rial et al., 2024). Rotating the applied field within various planes produces distinct angular dependencies—two-state or four-state step-wise AHE switching—diagnostic of the underlying variant and plane of field rotation.

The minimal theoretical Hamiltonian required to explain these switching phenomena includes:

• Atomic site-dependent magnetic anisotropy,
• Bulk Dzyaloshinskii–Moriya interaction (DMI), which induces slight moment canting ($m \approx 0.05\,μ_B/$u.c.),
• Zeeman coupling to external H.

The resulting hysteresis and plateaus in normalized $\rho_{AHE}(\theta, \varphi)$ as a function of field angle match the variant-specific free-energy landscapes and confirm the symmetry origin of altermagnetic transport anisotropy (Rial et al., 2024).

5. Phase Diagram, Topological Effects, and Thermodynamic Properties

In addition to the collinear (altermagnetic) and noncollinear antiferromagnetic phases, the phase diagram of Mn₅Si₃ also includes an intermediate ferromagnetic-like phase at lower temperatures, marked by a slight net moment and dominated by conventional skew-scattering AHE (1904.02277). The noncollinear AF2 phase supports large Berry curvature and a topological anomalous Hall effect, with a Hall conductivity of order 50–100 Ω⁻¹ cm⁻¹.

The loss of inversion symmetry in AF2 gives rise to finite scalar spin chirality $$(\chi_{ijk} = \mathbf{S}_i \cdot (\mathbf{S}_j \times \mathbf{S}_k) \neq 0)$$ on Mn2 triangles, localizing Berry curvature “hot spots” at avoided crossings. The magnitude and sign of such effects are set by the chiral configuration of local moments.

Thermodynamic signatures include the inverse magnetocaloric effect ($\Delta S_M < 0$) in AF2, reflecting magnetic fluctuations and entropy changes under field, further confirming unconventional spin thermodynamics associated with altermagnetic ordering (1904.02277).

6. Implications, Applications, and Future Directions

Mn₅Si₃ exemplifies a new material platform for "all-light-element" spin physics, demonstrating that collinear, compensated antiferromagnets can host strong, symmetry-protected transverse transport coefficients, driven by nonrelativistic mechanisms and requiring neither net M nor strong spin–orbit coupling (Badura et al., 2024, Rial et al., 2024). Potential applications include:

• Low-dissipation, stray-field-free spintronic memory and logic elements,
• Miniaturized thermoelectric generators and heat-flux sensors,
• High-frequency antiferromagnetic devices utilizing rapid switching and absence of magnetostatic cross-talk,
• Variant-selective devices exploiting the three-fold symmetry and associated domain boundaries for information encoding and manipulation.

The ability to rotate the Néel vector with moderate fields (<2 T), control AHE/ANE responses without net magnetization, and directly image domains via anomalous Nernst microscopy establishes Mn₅Si₃ thin films as both a canonical altermagnet and an experimental testbed for future research in compensated spintronics, valleytronics, and topological transport phenomena (Badura et al., 2024, Leiviskä et al., 2024, Rial et al., 2024).