α-MnTe: A Model Altermagnet

• Altermagnetic MnTe is a hexagonal NiAs-structured antiferromagnet whose layered architecture produces momentum-dependent spin splitting without net magnetization.
• Epitaxial growth on substrates like InP and GaAs enables tight control over stoichiometry, strain, and defect levels, influencing weak ferromagnetism and Berry-curvature transport.
• Advanced spectroscopic and transport techniques reveal symmetry-enforced spin degeneracies, large anomalous Hall responses, and tunable optical and spin-current effects.

α-MnTe is a hexagonal NiAs-type manganese telluride whose compensated A-type antiferromagnetic order supports momentum-dependent spin splitting without net magnetization, making it a canonical model system for altermagnetism. Its combination of layered crystal structure, Néel temperature near room temperature, semiconductor-like electronic structure, and compatibility with epitaxial growth has made it a central platform for symmetry analysis, angle-resolved photoemission, anomalous transport, optical spectroscopy, neutron and X-ray microscopies, scanning-probe imaging, and atomic-scale structural studies (Rooj et al., 5 Feb 2025, Yamamoto et al., 25 Feb 2025, Sheokand et al., 25 May 2026).

1. Crystal, magnetic, and symmetry setting

Bulk α-MnTe crystallizes in the hexagonal NiAs structure with space group $P6_3/mmc$ and point group $D_{6h}$. Refined structural parameters reported for bulk single crystals are $a = 4.1483(1)$ Å and $c = 6.7162(3)$ Å, with Mn at $2a\,(0,0,0)$ and Te at $2c\,(1/3,2/3,1/4)$. The stacking sequence along $c$ follows $ABAB\ldots$, giving a layered architecture in which close-packed Te layers host Mn in octahedral sites (Yamamoto et al., 25 Feb 2025, Sheokand et al., 25 May 2026).

Magnetically, α-MnTe is an A-type antiferromagnet: Mn moments are ferromagnetically aligned within each basal plane and antiferromagnetically stacked along the $c$-axis. The order parameter is commonly written as $L = S_1 - S_2$, while the net magnetization is $D_{6h}$0. The moments lie in the $D_{6h}$1 plane, the system has easy-plane anisotropy, and three in-plane easy axes produce a six-domain manifold once time-reversal-related antiphase states are included (Zhang et al., 24 Oct 2025, Yamamoto et al., 25 Feb 2025).

The altermagnetic character follows from the fact that the opposite spin sublattices are not paired by pure inversion or translation. In ideal hexagonal MnTe, different studies describe the relevant symmetry in complementary ways: one magnetic-space-group analysis without spin–orbit coupling gives $D_{6h}$2, whereas transport analyses with the Néel vector fixed in the basal plane use $D_{6h}$3, and a spin–orbit-coupled treatment with easy axis along $D_{6h}$4 yields $D_{6h}$5 (Rooj et al., 5 Feb 2025, Betancourt et al., 2024). This dependence on symmetry setting is intrinsic to MnTe: the detailed label changes with the assumed magnetic configuration, but the common outcome is the same—spin-split bands in a collinear, magnetically compensated state.

2. Symmetry-enforced spin splitting

The central theoretical result for ideal hexagonal MnTe is partial, rather than complete, spin degeneracy in momentum space. A magnetic-space-group analysis finds full spin degeneracy on the $D_{6h}$6 and $D_{6h}$7 planes, while generic points away from those planes are spin split, except on symmetry-enforced nodal lines such as $D_{6h}$8, $D_{6h}$9, and $a = 4.1483(1)$0 in reciprocal-space coordinates. A minimal symmetry-adapted Hamiltonian capturing this pattern is (Rooj et al., 5 Feb 2025)

$a = 4.1483(1)$1

with eigenvalues

$a = 4.1483(1)$2

The zeros of the spin-splitting term reproduce the symmetry-protected degeneracy on the $a = 4.1483(1)$3 and $a = 4.1483(1)$4 planes and along additional nodal lines (Rooj et al., 5 Feb 2025).

This symmetry structure produces a marked contrast between nodal-plane and off-nodal-plane spectroscopy. In vacuo ARPES on near-ideal MnTe films measured at $a = 4.1483(1)$5 eV probes the $a = 4.1483(1)$6 nodal plane and therefore sees only the weak, symmetry-allowed spin splitting there; the same study emphasizes that the predicted large nonrelativistic splitting, $a = 4.1483(1)$7 eV, requires access to regions away from the nodal planes (Zhang et al., 24 Oct 2025). By contrast, ARPES on $a = 4.1483(1)$8 UC MnTe/InP films reported a bulk-band splitting of $a = 4.1483(1)$9 meV near the $c = 6.7162(3)$0-like $c = 6.7162(3)$1 point, together with surface states crossing $c = 6.7162(3)$2, and identified this as a large altermagnetic splitting arising from the interplay of altermagnetic order and spin–orbit coupling (Zhou et al., 10 Feb 2026).

MnTe is also described as a g-wave altermagnet in the direct-space sense. A partial-wave decomposition of the on-site spin density identifies a ferroically ordered g-wave form factor around Mn, coexisting with antiferroic magnetic dipoles (Jaeschke-Ubiergo et al., 13 Mar 2025). At the same time, recent atomic-scale structural studies argue that ideal uniform $c = 6.7162(3)$3 symmetry is not realized everywhere: local inversion-symmetry-breaking distortions lower the spin-space-group symmetry, admit d-wave altermagnetic components, and, in the lowest-symmetry $c = 6.7162(3)$4 setting, even allow an s-wave contribution associated with net magnetization (Ren et al., 26 May 2026). Accordingly, the precise harmonic classification of spin splitting in MnTe is now understood as structure dependent rather than globally fixed.

3. Epitaxy, stoichiometry, and structural symmetry breaking

Thin-film MnTe has been realized by molecular beam epitaxy on both InP(111)A and GaAs(111)B. On GaAs(111)B, growth at $c = 6.7162(3)$5C with a Te-rich Mn:Te flux ratio of $c = 6.7162(3)$6 produced $c = 6.7162(3)$7 nm films with an epitaxial relation $c = 6.7162(3)$8-MnTe$c = 6.7162(3)$9GaAs(111), phase-pure $2a\,(0,0,0)$0 X-ray reflections, uniform Mn and Te signals by EDX, and late-stage streaky RHEED consistent with a smooth epitaxial morphology (Sheokand et al., 25 May 2026). On InP(111)A, optimized growth windows of substrate temperature $2a\,(0,0,0)$1C and Te/Mn flux ratio $2a\,(0,0,0)$2 yielded $2a\,(0,0,0)$3 nm films with rocking-curve full-width-at-half-maximum $2a\,(0,0,0)$4 for $2a\,(0,0,0)$5, roughness $2a\,(0,0,0)$6 nm, sharp MnTe/InP interfaces by STEM, and Néel temperatures of $2a\,(0,0,0)$7 K for 35 nm and $2a\,(0,0,0)$8 K for 100 nm films (Zhang et al., 24 Oct 2025). A separate phase-diagram study on InP(111) further showed that phase-pure $2a\,(0,0,0)$9-MnTe is stabilized by higher Te/Mn flux ratios and elevated growth temperatures (Shao et al., 12 Feb 2026).

Stoichiometry is a critical variable. One MBE study on InP reported near-ideal stoichiometry together with a vanishingly small laterally averaged magnetization, $2c\,(1/3,2/3,1/4)$0 kA/m at 20 K, and an equally good alternative model in which any residual magnetization is confined to a $2c\,(1/3,2/3,1/4)$1 nm interfacial region (Zhang et al., 24 Oct 2025). Another study, by contrast, found naturally Mn-rich MnTe films with $2c\,(1/3,2/3,1/4)$2 in $2c\,(1/3,2/3,1/4)$3, native metallicity with $2c\,(1/3,2/3,1/4)$4 in the valence band, and a net ferromagnetic moment of $2c\,(1/3,2/3,1/4)$5 emu cm$2c\,(1/3,2/3,1/4)$6 within the MnTe layer, together with a strong anomalous Hall response dominated by that defect-induced ferromagnetism (Chilcote et al., 2024). These two regimes establish that weak ferromagnetism in MnTe films is not a single phenomenon: it can be suppressed to near-zero values in near-stoichiometric films, confined to interfaces, or amplified by Mn excess.

The structural symmetry of MnTe is also under active revision. Optical polarimetry and phonon calculations have argued for a native inversion-symmetry-breaking distortion that lowers the point group from $2c\,(1/3,2/3,1/4)$7 to $2c\,(1/3,2/3,1/4)$8, with Mn displacements of order $2c\,(1/3,2/3,1/4)$9 of the $c$0-axis lattice parameter (Wu et al., 22 Mar 2025). Atomic-resolution STEM and EMCD go further, reporting ubiquitous inversion-symmetry-breaking local motifs identified as $c$1, $c$2, and $c$3, together with ferroelectric-like PFM signatures (Ren et al., 26 May 2026). A common misconception is therefore that MnTe is structurally exhausted by ideal $c$4; the recent literature instead supports a coexistence of high-quality NiAs stacking with local polar distortions that can modify the allowed altermagnetic harmonics.

4. Experimental identification of altermagnetic order

Bulk altermagnetism in MnTe has been established directly by transmission XMCD spectro-microscopy on a 150–200 nm lamella cut from a bulk crystal. The domain-resolved XMCD spectrum at the Mn $c$5 edges exhibits the characteristic altermagnetic oscillatory fingerprint: across $c$6, the contrast switches sign eight times and the spectrum shows nine peaks of alternating sign, while across $c$7 two sign changes are observed. The measured maximum XMCD contrast is $c$8 of $c$9, in quantitative agreement with the predicted $ABAB\ldots$0, and far larger than the $ABAB\ldots$1 expected for a thin surface shell in a 200 nm lamella (Yamamoto et al., 25 Feb 2025). The same measurements resolved $ABAB\ldots$2 $ABAB\ldots$3m domains in the lamella center, $ABAB\ldots$4 $ABAB\ldots$5m domains near the edges, $ABAB\ldots$6 Néel domain walls of width $ABAB\ldots$7 nm, and cartwheel-like textures consistent with vortex or antivortex winding (Yamamoto et al., 25 Feb 2025).

Polarized neutron diffraction has provided a reciprocal-space bulk probe of the same order. Nuclear–magnetic interference terms were observed at mixed nuclear/magnetic reflections such as $ABAB\ldots$8, $ABAB\ldots$9, $c$0, and $c$1, while pure reflections such as $c$2 and $c$3 showed no interference contribution. The interference terms track the magnetic transition at $c$4 K and reconstruct a net Néel vector $c$5 with modulus $c$6 after either oblique field cooling or $c$7-axis field cooling at $c$8 mT (Liu et al., 20 May 2026). The same work found a spontaneous weak ferromagnetic moment $c$9 per Mn at 100 K, coupled to the altermagnetic order and switchable by milli-Tesla-scale magnetic-field cooling (Liu et al., 20 May 2026).

Near the surface, scanning-probe NV magnetometry has visualized evanescent magnetization and associated domains in epitaxial MnTe films. At 2 K, stray fields remain largely in the range $L = S_1 - S_2$0 G to $L = S_1 - S_2$1 G across thicknesses from 2 to 230 unit cells. The area-normalized RMS magnetization, $L = S_1 - S_2$2, stays nearly thickness independent at $L = S_1 - S_2$3, $L = S_1 - S_2$4, $L = S_1 - S_2$5, and $L = S_1 - S_2$6 for 2, 40, 80, and 230 UC, whereas the volume-normalized $L = S_1 - S_2$7 falls from $L = S_1 - S_2$8 to $L = S_1 - S_2$9, indicating a surface-dominated origin of the weak uncompensated moment (Zhou et al., 24 May 2026). Atomic-resolution EMCD complements this by showing alternating $D_{6h}$00 dichroic signals across successive Mn layers in locally distorted $D_{6h}$01 and $D_{6h}$02 regions, directly correlating local symmetry lowering with collinear in-plane altermagnetic order (Ren et al., 26 May 2026).

5. Transport, Hall responses, and spin currents

In-plane magnetotransport in MnTe follows strict symmetry selection rules. For basal-plane rotation of the Néel vector, the longitudinal and transverse resistivities contain a non-crystalline second-order anisotropic magnetoresistance,

$D_{6h}$03

a fourth-order crystalline term,

$D_{6h}$04

a sixth-order crystalline term,

$D_{6h}$05

and an odd-in-field third-order anomalous Hall contribution,

$D_{6h}$06

which is forbidden in $D_{6h}$07-symmetric collinear antiferromagnets but allowed in altermagnets (Betancourt et al., 2024). Experimentally, MnTe thin films exhibit strong $D_{6h}$08, $D_{6h}$09, and $D_{6h}$10 harmonics in longitudinal ADMR, an odd $D_{6h}$11 transverse component, a spin-flop scale near $D_{6h}$12 T, and a positive isotropic magnetoresistance of $D_{6h}$13 at 14 T (Betancourt et al., 2024).

The anomalous Hall effect in MnTe is now understood as multi-regime rather than single-mechanism. In high-quality MnTe/InP films, ARPES finds that the top bulk valence band lies $D_{6h}$14 meV below $D_{6h}$15 while surface states cross $D_{6h}$16, and transport shows a robust AHE down to 2 K with a sign reversal near 175 K. First-principles calculations attribute the measured two-dimensional $D_{6h}$17 scale, roughly $D_{6h}$18, to Berry curvature of two surface channels with opposite signs, $D_{6h}$19 at the top Te/MnTe interface and $D_{6h}$20 at the bottom MnTe/InP interface (Zhou et al., 10 Feb 2026). A separate wafer-scale growth study likewise observed hysteretic AHE with net magnetic moment approaching zero and attributed the response to Berry curvature in phase-pure $D_{6h}$21-MnTe (Shao et al., 12 Feb 2026). By contrast, Mn-rich films show AHE that tracks the weak ferromagnetic component introduced by stoichiometry deviation (Chilcote et al., 2024). The literature therefore distinguishes intrinsic Berry-curvature-driven AHE, surface-state-driven AHE, and defect-dominated AHE.

The intrinsic Hall and spin-current responses are naturally written in Berry-curvature form. For the charge Hall effect,

$D_{6h}$22

and for the spin current $D_{6h}$23, fully relativistic first-principles calculations identify a large magnetic spin Hall effect in MnTe (Zhou et al., 10 Feb 2026, Hirakida et al., 24 Sep 2025). In the multipole framework, $D_{6h}$24 and $D_{6h}$25 correspond to distinct order parameters: $D_{6h}$26 plus octupoles for the former, and a pure octupole $D_{6h}$27 for the latter. The $D_{6h}$28 state allows anomalous Hall conductivity and reaches $D_{6h}$29 S/cm at $D_{6h}$30 eV, whereas the $D_{6h}$31 state forbids AHE by symmetry (Hirakida et al., 24 Sep 2025). The magnetic spin Hall angle peaks at $D_{6h}$32 for $D_{6h}$33 and $D_{6h}$34 for $D_{6h}$35, placing MnTe in the range usually associated with heavy-metal spin-current sources (Hirakida et al., 24 Sep 2025).

Finite-frequency magneto-optical response is another consequence of altermagnetism in MnTe. First-principles calculations for detwinned samples predict that $D_{6h}$36 is the only nonzero off-diagonal optical conductivity for in-plane spins and scales as $D_{6h}$37, where $D_{6h}$38 is the angle of the spin axis relative to a Mn–Mn bond; the response turns on at the direct optical gap of $D_{6h}$39 eV (Mazin, 2023). This optical selection rule directly parallels the symmetry restrictions seen in transport.

6. Lattice excitations, inhomogeneity, and tunability

Raman spectroscopy has established a detailed phononic fingerprint of epitaxial α-MnTe. In MBE-grown $D_{6h}$40-MnTe/GaAs(111)B, three prominent peaks are observed: $D_{6h}$41 cm$D_{6h}$42 and $D_{6h}$43 cm$D_{6h}$44 from MnTe, and $D_{6h}$45 cm$D_{6h}$46 from the GaAs substrate. The MnTe features are assigned as $D_{6h}$47 at $D_{6h}$48 cm$D_{6h}$49 and $D_{6h}$50 at $D_{6h}$51 cm$D_{6h}$52, with the appearance of both modes interpreted as a consequence of symmetry lowering relative to bulk $D_{6h}$53. Converting Raman shifts to energy gives $D_{6h}$54 meV and $D_{6h}$55 meV, a window relevant for coupling to low-energy electronic and magnetic excitations (Sheokand et al., 25 May 2026). Time-resolved Kerr measurements add a dynamical counterpart: a field-dependent magnon near $D_{6h}$56 GHz, likely excited by inverse stimulated Raman scattering, persists up to at least $D_{6h}$57 K, and two optical phonons at $D_{6h}$58 THz and $D_{6h}$59 THz broaden and redshift with increasing temperature (Gray et al., 2024).

Strain strongly reshapes the transport-active valence structure. Calculations for $D_{6h}$60-MnTe show that the competition between valence-band maxima along $D_{6h}$61-K and at $D_{6h}$62 can be switched by $D_{6h}$63 strain along $D_{6h}$64. At $D_{6h}$65, unstrained films give $D_{6h}$66 for $D_{6h}$67 and $D_{6h}$68 for $D_{6h}$69, compressive strain $D_{6h}$70 raises these to $D_{6h}$71 and $D_{6h}$72, and tensile strain $D_{6h}$73 suppresses $D_{6h}$74 to very small values (Chen et al., 22 Jul 2025). In the $D_{6h}$75-top regime the computed AMR ratio approaches $D_{6h}$76 and the maximum Hall angle reaches $D_{6h}$77, whereas the $D_{6h}$78-top regime gives negligible AMR and planar Hall response (Chen et al., 22 Jul 2025). Chemical substitution provides an additional symmetry knob: single Te-site substitutions by Se, Sb, or I preserve g-wave altermagnetism, while pair dopants generate a broader space of altermagnetic and quasi-altermagnetic configurations with symmetry-selected anomalous Hall tensor components (Devaraj et al., 27 Aug 2025).

At the same time, MnTe is electronically non-uniform on the nanometer scale. Low-temperature STM/STS on cleaved single crystals resolves two distinct regions: Region A has a gap of approximately $D_{6h}$79 eV, chemical potential near the valence-band edge, and $D_{6h}$80 meV nanoscale chemical-potential variations; Region B has a gap of approximately $D_{6h}$81 eV and chemical potential near mid-gap (Ma et al., 16 Mar 2026). Region A alone hosts an incommensurate charge modulation with periodicity $D_{6h}$82 and coherence length of order $D_{6h}$83 nm (Ma et al., 16 Mar 2026). This heterogeneity provides a concrete explanation for why nominally similar MnTe samples can show different transport responses: local doping, local strain, and interface chemistry all shift the balance among altermagnetic splitting, weak magnetization, and Berry-curvature transport.

Taken together, the current literature portrays altermagnetic MnTe as both a canonical symmetry platform and a materially rich system. Ideal hexagonal symmetry yields a clean altermagnetic prototype; epitaxy, interfaces, stoichiometry, strain, and local polar distortions then reshape that prototype into experimentally distinct regimes that can emphasize bulk compensated order, interfacial magnetization, surface-state Hall transport, or defect-driven ferromagnetism. That coexistence of rigorous spin-group constraints with unusually strong materials tunability is the defining characteristic of MnTe in the contemporary altermagnetism literature (Rooj et al., 5 Feb 2025, Ren et al., 26 May 2026).