Broken Kramers Degeneracy in Altermagnetic MnTe

Altermagnetism is a newly identified fundamental class of magnetism with vanishing net magnetization and time-reversal symmetry broken electronic structure. Probing the unusual electronic structure with nonrelativistic spin splitting would be a direct experimental verification of an altermagnetic phase. By combining high-quality film growth and in situ angle-resolved photoemission spectroscopy, we report the electronic structure of an altermagnetic candidate, $\alpha \text{−}\mathrm{MnTe}$. Temperature-dependent study reveals the lifting of Kramers degeneracy accompanied by a magnetic phase transition at $T_N=267\mathrm{K}$ with spin splitting of up to 370 meV, providing direct spectroscopic evidence for altermagnetism in MnTe.

Figure 1

(a),(b) Crystal structure of MnTe with two opposite-spin sublattices (${\mathrm{Mn}}_{\mathrm{A}}$ and ${\mathrm{Mn}}_{\mathrm{B}}$) and possible sublattice-transposing transformations containing a real-space mirror or sixfold rotation. (c) Schematic constant-energy contour on a $k_x-k_y$ plane with $k_z\ne n\pi /c$ corresponding to a spin group $[C_2\parallel C_{6z}]$. (d) Schematic band dispersion plotted along two momenta $k$ and $k^{\prime }$ marked in (c), showing spin-split electronic structure with alternating spin polarizations. (e),(f) 3D Brillouin zone and spin-degenerate nodal planes protected by (e) $[C_2\parallel M_z]$ and (f) $[C_2\parallel C_{6z}]$. (g),(h) DFT calculated spin-resolved electronic structures of MnTe plotted on (g) nodal ($k_z=0$) and (h) off-nodal ($k_z=0.3\pi /c$) planes. Here, the red and blue colors correspond to spin-up and spin-down, respectively. The spin splitting is clearly realized along the off-nodal $\mathsf{D}\text{−}\mathsf{U}$ line.

Figure 2

Physical properties of MnTe films. (a) Temperature-dependent longitudinal resistivity ${\rho }_{xx}$ for $T$ between 20 and 400 K. (b) Magnetization for a magnetic field direction $H//[01\overline{1}0]$ measured at $T=50$ and 300 K, showing absence of net magnetization at $H=0$. The linear slope at a low magnetic field, mainly contributed from diamagnetism of the substrate, is subtracted from the raw data. (c),(d) Surface Brillouin zones of (c) $k_x-k_y$ and (d) $k_x-k_z$ planes. The curve highlighted in (d) corresponds to the momentum space where ARPES is measured with photon energy $h\nu =21.2\mathrm{eV}$. (e) Constant-energy ARPES map taken at $E-E_F=-100\mathrm{meV}$. Dotted lines mark the surface Brillouin zone. (f) ARPES $E-k$ cut along the high-symmetry lines in the surface Brillouin zone highlighted in (e).

Figure 3

Temperature-dependent evolution of MnTe electronic structure. DMFT results in the (a) paramagnetic ($T=2321\mathrm{K}$) and (b) altermagnetic ($T=116\mathrm{K}$) states. Here, the red and blue lines correspond to spin-up and spin-down states, respectively. ARPES cut (left) and its second derivative (right) taken along the $\mathsf{D}\text{−}\mathsf{U}$ direction in the (c) paramagnetic and (d) altermagnetic states taken at $T=300$ and 6 K, respectively.

Figure 4

(a),(b) ARPES cuts taken along the $\mathsf{D}\text{−}\mathsf{U}$ line at temperatures (a) above and (b) below the $T_N$. (c),(d) Detailed temperature-dependent evolution of the ARPES spectral function taken at (c) $\mathsf{D}$ and (d) $0.1{\AA }^{-1}$ away from $\mathsf{D}$. The fitted positions of the peaks are marked with black circles, red crosses, and blue diamonds, denoting spin-degenerate nodes and spin-up and spin-down states, respectively. The spin splitting at $k_x=-0.175{\AA }^{-1}$ is marked with the black arrow. (e) Temperature-dependent energy splitting between the spin-up and spin-down bands. Error bars are obtained from the standard errors of the fitted peak positions. Energy splittings in the shaded area near the $T_N$ ($210\le T\le 260\mathrm{K}$) could not be reliably determined due to the uncertainty in the peak fitting at this temperature range.