  Altermagnetic (AM) materials exhibit non-relativistic, momentum-dependent
spin-split states, ushering in new opportunities for spin electronic devices.
While the characteristics of spin-splitting have been documented within the
framework of the non-relativistic spin group symmetry, there has been limited
exploration of the inclusion of relativistic symmetry and its impact on the
emergence of a novel spin-splitting in the band structure. This study delves
into the intricate relativistic electronic structure of an AM material,
alpha-MnTe. Employing temperature-dependent angle-resolved photoelectron
spectroscopy across the AM phase transition, we elucidate the emergence of a
relativistic valence band splitting concurrent with the establishment of
magnetic order. This discovery is validated through disordered local moment
calculations, modeling the influence of magnetic order on the electronic
structure and confirming the magnetic origin of the observed splitting. The
temperature-dependent splitting is ascribed to the advent of relativistic
spin-splitting resulting from the strengthening of AM order in alpha-MnTe as
the temperature decreases. This sheds light on a previously unexplored facet of
this intriguing material.
