Magnetic Cr doping ofBi2Se3: Evidence for divalent Cr from x-ray spectroscopy

Ferromagnetically doped topological insulators with broken time-reversal symmetry are a prerequisite for observing the quantum anomalous Hall effect. Cr-doped ${(\mathrm{Bi},\mathrm{Sb})}_{2}{(\mathrm{Se},\mathrm{Te})}_{3}$ is the most successful materials system so far, as it combines ferromagnetic ordering with acceptable levels of additional bulk doping. Here, we report a study of the local electronic structure of Cr dopants in epitaxially grown ${\mathrm{Bi}}_{2}{\mathrm{Se}}_{3}$ thin films. Contrary to the established view that the Cr dopant is trivalent because it substitutionally replaces ${\mathrm{Bi}}^{3+}$, we find instead that Cr is divalent. This is evidenced by the energy positions of the Cr $K$ and ${L}_{2,3}$ absorption edges relative to reference samples. The extended x-ray absorption fine structure at the $K$ edge shows that the Cr dopants substitute on octahedral sites with the surrounding Se ions contracted by $\ensuremath{\Delta}d=\ensuremath{-}0.36$ \AA{}, in agreement with recent band structure calculations. Comparison of the Cr ${L}_{2,3}$ x-ray magnetic circular dichroism at $T=5$ K with multiplet calculations gives a spin moment of $3.64 {\ensuremath{\mu}}_{\mathrm{B}}/{\mathrm{Cr}}_{\mathrm{bulk}}$, which is close to the saturation moment for ${\mathrm{Cr}}^{2+} {d}^{4}$. The reduced Cr oxidation state in doped ${\mathrm{Bi}}_{2}{\mathrm{Se}}_{3}$ is ascribed to the formation of a covalent bond between Cr $d({e}_{g})$ and Se $p$ orbitals, which is favored by the contraction of the Cr-Se distances.