Dominant orbital magnetization in the prototypical altermagnet MnTe

TL;DR

This work investigates the prototypical altermagnet α-MnTe using density functional theory to quantify both spin and orbital magnetizations. The authors demonstrate that, despite a large intrinsic band gap, a substantial orbital magnetization of about $-0.176$ μ_B per unit cell dominates the net magnetization, while the spin contribution is minuscule with $M^{spin}_z o 0.002$ μ_B per unit cell and a minute spin canting angle of about $0.01^ ext{°}$. The orbital magnetization remains robust over a wide energy window and is largely insensitive to hole doping, highlighting the importance of orbital effects in altermagnets and pointing toward orbital-based phenomena and orbitronics in these materials. The findings also emphasize that the experimentally observed net magnetization can be reduced by domain compensation, underscoring the need to include orbital contributions for a complete description of altermagnetic systems and their potential device applications.

Abstract

Altermagnetism is an unconventional form of antiferromagnetism characterized by momentum-dependent spin polarization of electronic states and zero net magnetization, arising from specific crystalline symmetries. In the presence of spin-orbit coupling (SOC) and broken time-reversal symmetry, altermagnets can exhibit finite net magnetization and anomalous Hall effect (AHE), phenomena typically associated with ferromagnets. Due to the dependence of AHE on magnetization, understanding the interplay between spin and orbital contributions to magnetization is essential for interpreting experiments and designing altermagnetic devices. In this work, we use density functional theory to investigate the intrinsic spin and orbital magnetization of the magnetic ground state of the prototypical altermagnet α-MnTe. We find that SOC induces weak ferromagnetism through spin canting, accompanied by a slight in-plane rotation of the Néel vector. Notably, we identify a significant net orbital magnetization of 0.176 μB per unit cell oriented along the z-axis, while the spin magnetization in the same direction is much smaller at 0.002 μB. By varying the chemical potential, we show that the spin magnetization is tunable through hole doping, whereas the orbital magnetization remains robust against carrier density changes. These results highlight the important role of orbital magnetization and establish its relevance for orbital-based phenomena in altermagnets.

Figures (6)

• Figure 1: Structure and charge density of MnTe.(a) Crystal structure with the magnetic moment orientation along the $y$-axis. (b) The corresponding hexagonal Brillouin zone. (c) Difference between the charge densities of the Néel vector along the $y$-axis and $x$-axis for the isosurface $1.5\cdot 10^{-6} \; e/$Å$^3$. The blue and yellow colors indicate the positive and negative values of the charge differences, respectively. The breaking of $\qty{6^{\pm}_{001}\vert 0,0,\frac{1}{2}}$ and $\qty{3^{\pm}_{001}\vert 0}$ symmetries is observed, while the inversion $\qty{\bar{1}\vert0}$ and $\qty{2_{001}\vert 0,0,\frac{1}{2}}$ symmetries are preserved.
• Figure 2: Relativistic spin density of states in the valence bands for MnTe with Néel vector along the $y$-axis (N $||$ y).(a)$S_x$ is the component responsible for the slight rotation of the Néel vector in the $xy$-plane. (b)$S_y$ is the main component of the Néel vector. (c)$S_z$ component is responsible for the weak ferromagnetism along the $z$-axis. Positive and negative spin contributions are shown in red and blue, respectively. The total DOS is overlaid in green in all panels.
• Figure 3: Relativistic band structure with the $S_z$ component of the spin texture indicated by the color scale on the side. We plot the band structure along the $k$-path (a)$\rm{\Gamma-A-K-H-A}$ and (b)$\rm{L_1-\Gamma-L_2-\Gamma-L'_2}$. The Fermi energy is set at the VBM.
• Figure 4: Spin-projected isosurfaces with the Fermi level in the valence band. Isosurface $E-E_{F} \approx -0.10$ eV colored by the component of the spin texture (a)$S_x$, (b)$S_y$ and (c)$S_z$. (d) The isoenergy contours for the $k_z = 0$ plane together with the overlaid spin texture component $S_z$.
• Figure 5: Calculated k-resolved orbital magnetization $M^{orb}_z (\vb{k})$ for the Fermi level in the valence band. Orbital magnetization $M^{orb}_z (\vb{k})$ along $k$-paths for $E_F = E_{VBM} -0.23$ eV, that is for the Fermi level shifted to the valence band. Note that $M^{orb}_x (\vb{k})$ and $M^{orb}_y (\vb{k})$ are negligible compared to $M^{orb}_z (\vb{k})$, as shown in the Supplementary Material.