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), altermagnets can exhibit finite net magnetization and anomalous Hall effect (AHE), phenomena typically associated with ferromagnets. As AHE is closely linked to weak ferromagnetism, clarifying its microscopic origin in terms of spin and orbital contributions to magnetization is crucial for interpreting experiments and designing altermagnetic devices. In this work, we use density functional theory to explore the intrinsic spin and orbital magnetization of the magnetic ground state of the prototypical altermagnet $\alpha$-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 ${\mu }_B$ per unit cell oriented along the $z$ axis, whereas the spin magnetization in the same direction is much smaller, at only 0.002 ${\mu }_B$. By varying the chemical potential, we show that the spin magnetization can be tuned through hole doping, whereas the orbital magnetization remains robust against carrier concentration changes. These results highlight the important role of orbital magnetization and establish its relevance for orbital-based phenomena in altermagnets.

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• Magnetic order
• Spin-orbit coupling
• Altermagnets
• Density functional theory