Evolution of valence- and spin-specific local distortions in La 2 − x Sr x CoO 4

We present x-ray spectral evidence for the evolution of valence- and spin-specific tetragonal distortions in single-layer cobaltates. Measurements of Co ${L}_{3}$-edge resonant inelastic x-ray scattering reveal the ${t}_{2g}$ electronic structure of Co in hole-doped ${\mathrm{La}}_{2\ensuremath{-}x}{\mathrm{Sr}}_{x}{\mathrm{CoO}}_{4}$ ($x=0.5$, 0.7, and 0.8). As the Sr-doping $x$ increases, the tetragonal splitting of the ${t}_{2g}$ states of high-spin ${\mathrm{Co}}^{2+}$ decreases, whereas that of low-spin ${\mathrm{Co}}^{3+}$ increases and the population fraction of high-spin ${\mathrm{Co}}^{3+}$ increases. The results enable us to clarify the origin of the change of magnetic anisotropy and in-plane resistivity in the mixed-valence cobaltates caused by the interplay of spin-orbit coupling and tetragonal distortion.