Dataset: Dominant orbital magnetization in the prototypical altermagnet 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, while the spin magnetization in the same direction is much smaller at 0.002 {\mu}B. 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.