Mn5Si3 Altermagnet: Electronic & Magnetic Insights

• Mn5Si3 altermagnetism is defined by symmetry-protected, momentum-dependent spin splitting with zero net magnetization, driving unconventional magnetic and transport behavior.
• Experimental studies reveal pronounced anisotropic anomalous and nonlinear Hall effects, modulated by variant spin arrangements and Berry curvature hotspots.
• Mn5Si3 exhibits notable thermoelectric, Nernst, and optically tunable spin functionalities, positioning it as a prototype for advanced spintronic devices.

Mn₅Si₃ is an intermetallic compound that exemplifies the altermagnetic class of materials, characterized by vanishing macroscopic magnetization yet exhibiting symmetry-protected, momentum-dependent spin splitting of electronic bands. This unique microscopically spin-chiral ordering leads to unconventional magnetotransport, nonlinear magnetoelectric phenomena, and novel thermoelectric and spintronic functionalities fundamentally distinct from both conventional ferromagnets and antiferromagnets. In recent years, Mn₅Si₃ has emerged as a model system for detailed exploration of altermagnetism, with thin-film and bulk studies revealing rich phase diagrams, distinct magnetic variants, and a suite of emergent responses mediated by Berry curvature and quantum geometrical band effects.

1. Magnetic and Electronic Structure of Altermagnetic Mn₅Si₃

The altermagnetic phase in Mn₅Si₃ is rooted in its unique arrangement of Mn moments. Four out of six possible Mn₂ sites in the unit cell order antiferromagnetically in a checkerboard configuration, resulting in three symmetry-related variants rotated by 120°, each with a distinct Néel vector orientation ([2110], [1210], [1120]) (Rial et al., 27 Sep 2024). The moments are collinear within each variant but, crucially, the sublattices are connected only by rotation rather than translation or inversion symmetry, distinguishing altermagnets from traditional antiferromagnets. This symmetry lowers the energy degeneracy between opposite spins at a given $k$-point, causing alternating spin-splitting of the bands in momentum space.

The resulting band structure is spin-polarized in both real and reciprocal space but compensated such that the net magnetization vanishes. First-principles DFT calculations reveal this anisotropic, $d$-wave-like spin splitting, with the effective Hamiltonian

$$H_{\rm AM} = \sum_{\mathbf{k},\sigma} \epsilon(\mathbf{k})\, c_{\mathbf{k}\sigma}^\dagger c_{\mathbf{k}\sigma} + \sum_{\mathbf{k}} \Delta_m(\mathbf{k})\, \sigma\, c_{\mathbf{k}\sigma}^\dagger c_{\mathbf{k}\sigma},$$

where $\Delta_m(\mathbf{k}) = m\cos(2\theta_\mathbf{k})$ models the angular, momentum-dependent splitting (Giil et al., 2023). The symmetry-protected compensation forbids standard net-magnetization-based responses but allows for nontrivial Berry curvature and related effects.

2. Magnetotransport Phenomena: Linear and Nonlinear Hall Effects

The anomalous Hall effect (AHE) in Mn₅Si₃ is pronounced despite the negligible net magnetization, directly evidencing its altermagnetic nature. In high-crystal-quality epitaxial films, the AHE conductivity $\sigma_{\rm AHE}$ shows a step-like, highly anisotropic dependence on the Néel vector orientation relative to the crystallographic axes. Unlike the projection $M_s\cos\theta$ expected from simple angular dependence, $\sigma_{\rm AHE}$ is maximized for out-of-plane field alignment and nearly vanishes for certain in-plane orientations. The AHE anisotropy is stringent on structural order, vanishing in films with degraded crystallinity (Leiviskä et al., 4 Jan 2024, Rial et al., 27 Sep 2024).

Beyond the linear regime, a magnetic nonlinear Hall effect (MNLHE) has been uncovered, with Hall conductivity $\sigma_H$ showing a quadratic magnetic-field dependence,

$$\sigma_H = \operatorname{sgn}(H)\, \sigma_0 + \sigma_1 H + \operatorname{sgn}(H)\, \sigma_2 H^2,$$

where the quadratic term arises from the combination of chiral next-nearest-neighbor hopping, small canting moments, and Haldane-like phases. The MNLHE is nonanalytic, flipping sign under field reversal, and is unsaturated up to at least $60\,\mathrm{T}$ (Han et al., 7 Feb 2025). This effect is a direct consequence of the alternating-sign Berry curvature in Mn₅Si₃ and fundamentally distinguishes MNLHE from classical NLHEs driven by electric fields.

Logarithmic magnetic viscosity (“magnetic aftereffect”) and nanometer-scale Barkhausen steps have also been observed in time-resolved Hall effect measurements, evidencing domain relaxation and discrete flips of the Hall vector in the altermagnetic regime (Skobjin et al., 6 Jun 2025).

Effect	Origin in Mn₅Si₃	Distinguishing Features
Anomalous Hall Effect	Berry curvature from compensated, collinear altermagnetic order	Strong anisotropy; persists with vanishing net moment
Magnetic Nonlinear Hall	Chiral NNN hopping; Zeeman-induced Berry curvature modulation	Quadratic field dependence; nonanalytic
Barkhausen Effect	Domain switching of Hall vector	Steps in dynamic Hall voltage

3. Thermoelectric Phenomena and Nernst Responses

The anomalous Nernst effect (ANE), previously forbidden in collinear, compensated magnets by Kramers degeneracy, is realized in Mn₅Si₃ due to the alternating spin-splitting band structure. Berry curvature “hot spots” near the Fermi level—created by band-crossings in the presence of altermagnetic order—enable a spontaneous, nonvolatile ANE even for perfectly collinear Néel vectors (Badura et al., 19 Mar 2024, Han et al., 20 Mar 2024). Measured Nernst coefficients reach $\sim$microvolts per kelvin, with sizable Nernst conductivities $\alpha_{yx}$ despite only tens of m$\mu_B$ per formula unit in net magnetization. Mn doping shifts the Fermi level and enhances the ANE by a factor of six, demonstrating the sensitivity of thermoelectric responses to Berry curvature topology.

Moreover, a “spin splitting Nernst effect” has been theoretically predicted for altermagnets: under a longitudinal temperature gradient, electrons with opposite spins are transversely deflected in opposite directions, forming a pure transverse spin current. This effect, unlike conventional spin Nernst responses, requires neither spin–orbit coupling nor net magnetism, and is characterized by symmetric coefficients, $N_{s,xy}=N_{s,yx}$ (Yi et al., 4 Sep 2025). The effect is tunable by Fermi energy, temperature, transport direction, and system dimensions.

Thermoelectric effects extend to junctions: in altermagnet–superconductor systems, the proximity-induced momentum-dependent spin splitting in the superconductor produces a sizable thermoelectric response. Spin-selective tunneling and broken particle–hole symmetry (induced by the altermagnet) yield Seebeck coefficients and figures of merit comparable to ferromagnet-based devices, while maintaining stray-field–free operation—highly advantageous for cryogenic applications (Sukhachov et al., 15 Apr 2024).

4. Topological Magnetism, Majorana Modes, and Optical Control

Altermagnetic Mn₅Si₃ plays a pivotal role in emergent topological phases when integrated into heterostructures. In heterostructures with conventional $s$-wave superconductors and two-dimensional topological insulators, the interplay between pairing, altermagnetic exchange (as a Dirac mass), and geometric boundaries leads to domain-wall formation and localization of zero-energy Majorana corner modes (MCMs). The location and presence of MCMs are tunable by the Néel vector orientation and by uniaxial strain, which modifies hopping parameters and mass profiles along sample edges. Only the out-of-plane (z) component of the Néel vector opens a Dirac mass and supports MCM formation (Li et al., 2023).

Detection and manipulation of the Néel vector in Mn₅Si₃ are enabled via combined tunneling conductance and optical absorption studies in bilayers with topological or crystalline valley-edge insulators. Changes in the Néel vector orientation induce topological phase transitions (from first-order to trivial insulators or to second-order SOTIs with corner modes), tune band gaps (observable via absorption onset), and determine the presence of robust or valley-protected edge states, all measurable with practical spectroscopies (Ezawa, 14 Mar 2024).

Optical-control paradigms are further extended by polarization-selective photoexcitation. Ultrafast (sub-100 fs) pump pulses cause redistribution of orbital occupations, renormalizing onsite energies through Coulomb and Hund’s exchange interaction. This process enhances the relative conduction-band spin splitting by up to a factor of four, providing all-optical tuning of altermagnetic spin splitting on femtosecond timescales, orders of magnitude faster than any magneto-acoustic or domain manipulation (Rajpurohit et al., 26 Sep 2024).

5. Variants, Symmetry, and Device Implications

The magnetic order in Mn₅Si₃ allows for three symmetry-equivalent “variants” due to possible checkerboard choices of four occupied out of six Mn₂ sites per layer (Rial et al., 27 Sep 2024). Each variant is characterized by a distinct easy-axis and symmetry operation (e.g. $C_2$ along a particular axis), producing unique anisotropies and switching behaviors in the Hall and magnetoresistance data. The experimental ability to rotate the external magnetic field and “select” variants underpins reconfigurable functionality at the domain level (e.g. switchable AHE signals, multistability).

Field rotation and sample geometry (patterned Hall bars) control the dynamical manipulation of variant populations and domain sizes. Hall vector “domain” flips, responsible for Barkhausen jumps, can be as small as 18 nm, revealing mesoscopic control of altermagnetic order and offering possibilities for scalable, robust switching in spintronic memory elements (Skobjin et al., 6 Jun 2025).

The efficiency of collinear spin current (CSC) generation in Mn₅Si₃ is parametrized by a “spin-splitting angle”, $\alpha_{yx}$, reaching values of 0.24—substantially higher than typical spin-Hall angles. Field-free perpendicular magnetization switching is feasible by aligning charge current directions and the Néel vector appropriately, suggesting device designs that integrate CSC sources (altermagnetic layers) with perpendicularly magnetized spin-torque targets for nonvolatile, high-speed, and low-power MRAM systems (Dong et al., 12 Jun 2025).

6. Comparative and Applied Significance

Compared to conventional ferromagnets and antiferromagnets, Mn₅Si₃ demonstrates that Berry curvature and all associated quantum geometric responses are not intrinsically tied to nonzero net magnetization, but to the magnetic symmetry and momentum-space spin splitting. The existence of a large AHE, ANE, spin splitting Nernst effect, and MNLHE in a light-element, collinear, compensated altermagnet such as Mn₅Si₃ provides a new platform for device paradigms where stray-field–free operation, rapid switching, and quantum-geometry-driven responses are central (Han et al., 20 Mar 2024, Han et al., 7 Feb 2025).

The robust proximity-induced functionality in superconductor–altermagnet bilayers (memory, thermoelectricity), combined with dynamical control via light or strain and the emergent topological states in hybrid structures, positions Mn₅Si₃ as a prototype for high-frequency spintronics, energy-efficient memory, and quantum computation elements.

7. Summary Table: Key Altermagnetic Properties in Mn₅Si₃

Property/Phenomenon	Mechanistic Origin	Experimental/Practical Implication	Reference
Anisotropic AHE & MNLHE	Berry curvature, symmetry breaking, chiral hopping	Hall vector rotation, high-field quadratic response	(Leiviskä et al., 4 Jan 2024, Han et al., 7 Feb 2025)
Nonvolatile ANE & Nernst	Band Berry curvature hotspots, tuning by doping	Magnetic-field-immune thermoelectric conversion, Fermi-level tuning	(Badura et al., 19 Mar 2024, Han et al., 20 Mar 2024)
Barkhausen effect, domains	Variant population switching; field-driven relaxation	Domain engineering at ~10 nm scale for memory	(Rial et al., 27 Sep 2024, Skobjin et al., 6 Jun 2025)
Spin splitting Nernst effect	Anisotropic, spin-dependent Fermi surface	Magnonless spin current, symmetry-equal $N_{s,xy}=N_{s,yx}$	(Yi et al., 4 Sep 2025)
Collinear spin current (CSC)	Band splitting via [C₂		mᵧ] operation
Majorana modes, SOTIs	Edge mass domain engineering via Néel vector and strain	Tunable topological parametrics for quantum devices	(Li et al., 2023, Ezawa, 14 Mar 2024)
Ultrafast spin splitting control	Photoinduced orbital renormalization	Femtosecond all-optical spintronic switching	(Rajpurohit et al., 26 Sep 2024)

Mn₅Si₃ thus defines a canonical material platform in the emerging field of altermagnetism, offering a synergy of magnetic symmetry, electronic topology, and quantum transport responses across multiple energy and timescales, with both fundamental and applied ramifications for future condensed-matter, spintronic, and quantum devices.