Fig. 5: The DFT calculations.
a–c Refer to the \(\sqrt{5}\times \sqrt{5}\) R26.6° structure and d-f refer to the c(4 x 2) structure. a, d show the surface unit cells, where the open red circles indicate the locations of the oxygen vacancies in the unit cell. All calculations were done with a structure having 5 TiO2 planes thick. b, e show the DOS for the SR-STO structure with U = 2 eV in comparison with the total DOS to show the onset of the spin-polarized in-gap peaks for the surface Ti atoms. The shaded region in each plot shows the energy range used in calculating the spin densities. Finally, c, f show the net spin densities for the surface of our SR-STO unit cells, directly correlating with the net magnetic moment due to states in the energy range shaded in b, e. The color bar represents the values of local magnetic moment calculated from DFT. The regions indicated by the green circles are referencing the Ti sites neighboring the vacancies, as in the surface unit cells in a, d. By expanding the visible area to 2 × 2 unit cells in the x and y directions, we can see that the presence of periodic, patterned oxygen vacancies leads to the appearance of a spin density wave.
