Ruthenium dioxide RuO$_{2}$: effect of the altermagnetism on the physical properties

Ruthenium oxide with the rutile structure is one of example of altermagnets. These systems are characterized by compensated magnetic moments (typical for antiferromagnets) and strong time reversal symmetry breaking (typical for ferromagnets). However, in such cases, the electronic band structure exhibit strong spin splitting along some directions in the momentum space. Occurrence of the compensated magnetic textures allows for realization of surfaces with specific magnetization, which dependent on the surface orientation and/or its termination. Here, we study interplay between the electronic surface states and the surface magnetization. We show that the spin-resolved spectra strongly depends on a direction in reciprocal space. Such properties can be used for the experimental confirmation of the altermagnetism in RuO$_{2}$ within the spectroscopic techniques. Additionally, we show that the most modified orbitals in the system are $d_{z^{2}}$ and $d_{xy}$ orbitals of Ru. Similarly, the Ru $e_{g}$ states are most sensitive on epitaxial strain, what can suggest some link between altermagnetism and strain.