Kondo effect and impurity band conduction in $\mathrm{Co}:\mathrm{Ti}{\mathrm{O}}_2$ magnetic semiconductor

The nature of charge carriers and their interaction with local magnetic moments in an oxide magnetic semiconductor is established. For cobalt-doped anatase $\mathrm{Ti}{\mathrm{O}}_2$ films, we demonstrate conduction in a metallic donor-impurity band. Moreover, we observe a clear signature of the Kondo effect in electrical transport data with remarkably high Kondo temperatures of up to $120\mathrm{K}$. This indicates a strong coupling between local Co moments and delocalized electrons in the impurity band.

Figure 1

(Color) Electrical properties of anatase $\mathrm{Ti}{\mathrm{O}}_2$ and $\mathrm{Co}:\mathrm{Ti}{\mathrm{O}}_2$. Shown are resistivity and Hall mobility versus temperature for two undoped $\mathrm{Ti}{\mathrm{O}}_2$ films (pink symbols) and two $\mathrm{Co}:\mathrm{Ti}{\mathrm{O}}_2$ films (blue symbols) grown under the same deposition conditions ($5\mathrm{Hz}$, $7\times {10}^{-5}\mathrm{mbar}$) at target-substrate distances of $48\mathrm{mm}$ (open circles) and $57\mathrm{mm}$ (solid squares). The inset shows the resistivity of these films versus $1∕T$. The triangles show the mobility for films grown under more oxygen deficient conditions: (solid black triangles) pure $\mathrm{Ti}{\mathrm{O}}_2$, $20\mathrm{Hz}$, $7\times {10}^{-5}\mathrm{mbar}$; (▵) $\mathrm{Co}:\mathrm{Ti}{\mathrm{O}}_2$, $5\mathrm{Hz}$, $3\times {10}^{-3}\mathrm{mbar}$; and (▿) $\mathrm{Co}:\mathrm{Ti}{\mathrm{O}}_2$, $5\mathrm{Hz}$, $6\times {10}^{-3}\mathrm{mbar}$. Film thickness is $150–200\mathrm{nm}$.

Figure 2

(Color) Top panel: Hall constant for pure $\mathrm{Ti}{\mathrm{O}}_2$ films grown at $5–20\mathrm{Hz}$ and $7\times {10}^{-5}\mathrm{mbar}$. Inset shows $R_H$ versus $1∕T$ for films grown at $20\mathrm{Hz}$ and $P_{ox}$ of $7\times {10}^{-5}$, $9\times {10}^{-5}$, and $2.5\times {10}^{-4}\mathrm{mbar}$. Bottom panel: Hall constant for $\mathrm{Co}:\mathrm{Ti}{\mathrm{O}}_2$ films grown at $5\mathrm{Hz}$ and different $P_{ox}$: (A) $7\times {10}^{-5}\mathrm{mbar}$, (B) $5\times {10}^{-4}\mathrm{mbar}$, (C) $8\times {10}^{-4}\mathrm{mbar}$, (D) $2\times {10}^{-3}\mathrm{mbar}$, and (E) $6\times {10}^{-3}\mathrm{mbar}$. Inset shows $R_H$ vs $1∕T$ for a film grown at $20\mathrm{Hz}$ and $7\times {10}^{-5}\mathrm{mbar}$, along with fits (see text). Units for insets and main panels are the same.

Figure 3

(Color) Top panel: magnetic moment versus in-plane applied field for $\mathrm{Co}:\mathrm{Ti}{\mathrm{O}}_2$ films grown at different $P_{ox}$. Bottom panels: variation of $T_{\mathit{max}}^{\mathit{\text{Hall}}}$ (left) and $T_{\mathit{\text{max}}}^{\mathit{mob}}$ (right) versus $P_{ox}$, with the laser repetition rate kept constant. Pink symbols are for undoped anatase $\mathrm{Ti}{\mathrm{O}}_2$; blue symbols are for $\mathrm{Co}:\mathrm{Ti}{\mathrm{O}}_2$. Solid lines are a guide to the eyes.

Figure 4

(Color) Kondo effect in $\mathrm{Co}:\mathrm{Ti}{\mathrm{O}}_2$, shown as the inverse of the Hall mobility versus temperature normalized to $T_K$. The vertical scale is normalized to have a value of 0.5 at $T∕T_K=0.2$ for each curve. All films are grown at $9\times {10}^{-5}\mathrm{mbar}$. Target-substrate distance and laser repetition rate are, respectively, $57\mathrm{mm}$ and $10\mathrm{Hz}$ $(T_K=120\mathrm{K})$, $57\mathrm{mm}$ and $5\mathrm{Hz}$ $(T_K=60\mathrm{K})$, $48\mathrm{mm}$ and $5\mathrm{Hz}$ $(T_K=75\mathrm{K})$, and $48\mathrm{mm}$ and $10\mathrm{Hz}$ $(T_K=95\mathrm{K})$. The inset shows data without normalization for the two films grown at $57\mathrm{mm}$.