Directly probing g-wave altermagnetism below and above the Fermi level

Altermagnetism is the first phase of matter which can be uniquely classified by a spin group. Due to the additional degree of freedom enabled by the orthogonal operations of crystal and spin rotation required to map the unit cell, the altermagnet manifests a spin-split electronic structure which has very appealing spintronic and neuromorphic applications. While initial probes and realizations of altermagnetic materials have been riddled with disorder, here we combine a pair of direct probes of spin polarized electronic structure to characterize a $g$-wave altermagnetic phase within an intercalated transition metal dichalcogenide $\mathrm{CoNb_4Se_8}$. Using spin-resolved photoemission spectroscopy, we uncover a pair of spin split constant energy surfaces in the occupied electronic structure which are mapped to one another through $C_6$ rotation. Importantly, by implementing a newly-developed technique dubbed spin-and angle- resolved electron reflection spectroscopy (sp-ARRES) [1], we unprecedentedly reveal that spin-split constant energy surfaces persist up to 11 eV above $E_\mathrm{F}$, far into the unoccupied regions of the band structure. We explain our results with \textit{ab-initio} calculations and tight-binding models that elucidate the role of symmetry and the crystal field in the spin splitting. As the material crosses its Néel temperature, the spectral weight of half of the spin split bands in the Fermi surface drops precipitously, confirming the observation of an altermagnetic phase transition.