Spin and orbital states in single-layered La${}_{2-x}$Ca${}_x$CoO${}_4$ studied by doping- and temperature-dependent near-edge x-ray absorption fine structure

The doping-dependent valence, orbital, and spin-state configurations of single-layered La${}_{2-x}$Ca${}_x$CoO${}_4$ ($x=0$, 0.5, 1, and 1.5) were investigated with temperature-dependent near-edge x-ray absorption fine structure at the Co $L_{2,3}$ and O $K$ edges. The spectra show that in La${}_2$CoO${}_4$, the superexchange between neighboring Co${}^{2+}$ HS states is responsible for the strong antiferromagnetism. With increasing hole doping, the superexchange interactions between Co${}^{2+}$ HS ions are rapidly reduced by interlaced nonmagnetic Co${}^{3+}$ LS. For La${}_{1.5}$Ca${}_{0.5}$CoO${}_4$, the low Néel temperature of the samples together with the 50% Co${}^{2+}$ HS and 50% Co${}^{3+}$ LS configuration suggests a checkerboard arrangement of these ions. The spin blockade resulting from this arrangement naturally explains the high resistivity of La${}_{1.5}$Ca${}_{0.5}$CoO${}_4$. Upon further doping, Co${}^{2+}$ HS ions are replaced by Co${}^{3+}$ HS, and for LaCaCoO${}_4$ a mixture of Co${}^{3+}$ LS and Co${}^{3+}$ HS occurs. Superexchange via configuration fluctuation processes between these two species seems to induce long-range ferromagnetism, while the superexchange between adjacent Co${}^{3+}$ HS neighbors may lead to a competing antiferromagnetic exchange. For a doping content beyond $x=1$, Co${}^{4+}$ HS is introduced to the system at the expense of Co${}^{3+}$ LS, and a $t_{2g}$ double exchange between Co${}^{3+}$ HS and Co${}^{4+}$ HS is established, which further enhances ferromagnetic interactions and reduces resistivity. No indications for a Co${}^{3+}$ IS state are found throughout the La${}_{2-x}$Ca${}_x$CoO${}_4$ doping series.

Figure 1

Rietveld refinement of the room-temperature x-ray diffraction pattern of La${}_{1.5}$Ca${}_{0.5}$CoO${}_4$ (after Ref. 20), shown as a representative example for the series investigated. Measured data are shown as red dots, calculated data as a black curve, and the difference between measured and calculated data as a blue curve that is vertically offset from the zero line. All fundamental reflections can be indexed using space group $I4/mmm$. The expected Bragg positions are indicated as green tick marks. The strong background is due to Co fluorescence induced by the Cu $K{\alpha }_1$ radiation.

Figure 2

Comparison of the Co $L_{2,3}$ NEXAFS spectra of La${}_2$CoO${}_4$, La${}_{1.5}$Ca${}_{0.5}$CoO${}_4$, LaCaCoO${}_4$, and La${}_{0.5}$Ca${}_{1.5}$CoO${}_4$ taken at 300 K. The spectral shape of both edges strongly changes upon doping. For clarity, the spectra are vertically offset.

Figure 3

Co $2p$ XAS multiplet calculations of Co${}^{3+}$ LS, Co${}^{3+}$ HS, Co${}^{3+}$ IS, Co${}^{2+}$ HS, and Co${}^{4+}$ HS. In addition, the simulated spectra of La${}_2$CoO${}_4$, La${}_{1.5}$Ca${}_{0.5}$CoO${}_4$, LaCaCoO${}_4$, and La${}_{0.5}$Ca${}_{1.5}$CoO${}_4$ are also displayed. For clarity, the spectra for the different configurations are vertically offset. The simulated spectra are scaled to their corresponding experimental data in Fig. 2.

Figure 4

O $K$ NEXAFS spectra of La${}_2$CoO${}_4$, La${}_{1.5}$Ca${}_{0.5}$CoO${}_4$, LaCaCoO${}_4$, and La${}_{0.5}$Ca${}_{1.5}$CoO${}_4$ taken at 40 K. The spectral weight for O $2p$ states hybridized with $e_g$ and $t_{2g}$ levels is strongly doping-dependent. Rough estimates for the valence-dependent $t_{2g}$ and $e_g$ regions are indicated in the figure.

Figure 5

Scheme showing the orbital occupation and the relevant hopping process for La${}_{2-x}$Ca${}_x$CoO${}_4$. (a) Virtual hopping processes between the two Co${}^{2+}$ HS neighbors in La${}_2$CoO${}_4$ induce antiferromagnetic ordering. As a representative, only the virtual hopping of an $e_g$ electron is shown. In principle, all electrons in half-filled orbitals can perform such processes. (b) For La${}_{1.5}$Ca${}_{0.5}$CoO${}_4$, the spin blockade inhibits the transfer of an electron from the Co${}^{2+}$ HS to the Co${}^{3+}$ LS site. (c) For LaCaCoO${}_4$, correlated $t_{2g}$ and $e_g$ hopping processes between Co${}^{3+}$ LS and Co${}^{3+}$ HS neighbors lead to a ferromagnetic superexchange. Due to the correlated hopping of $t_{2g}$ and $e_g$ electrons, spin states are interchanged without a net transfer of charge. In the sketch, only the local $t_{2g}$ and $e_g$ hopping processes for the transformation of a Co${}^{3+}$ LS into a Co${}^{3+}$ HS ion are considered (Refs. 62 and 63). (d) For the $t_{2g}$ double exchange in La${}_{0.5}$Ca${}_{1.5}$CoO${}_4$, an electron moves from a Co${}^{3+}$ HS site to a Co${}^{4+}$ HS neighbor.

Figure 6

Temperature-dependent O $K$ NEXAFS spectra of La${}_{2-x}$Ca${}_x$CoO${}_4$ ($x=0.0$, 0.5, 1.0, 1.5). No significant temperature dependence is found for La${}_2$CoO${}_4$, La${}_{0.5}$Ca${}_{1.5}$CoO${}_4$, and La${}_{1.5}$Ca${}_{0.5}$CoO${}_4$ while small changes in the spin-state structure occur for LaCaCoO${}_4$.