Dilution and clustering of Fe in the rutile phases of ${\mathrm{TiO}}_2$ and ${\mathrm{SnO}}_2$

Dilute magnetic semiconductors of Fe-doped ${\mathrm{SnO}}_2$ and ${\mathrm{TiO}}_2$ with the structure of rutile were prepared in forms of powder and thin films using the techniques of sol gel and pulsed-laser deposition. We present the results of measurement of vibrational density of states of Fe impurity dopants in these oxides and demonstrate the cases of dilution and clustering. The oxygen pressure during the film deposition was varied between ${10}^{-1}$ and ${10}^{-8}\mathrm{Torr}$. In ${\mathrm{TiO}}_2$ films made at ${10}^{-1}\mathrm{Torr}$, Fe is diluted, however, in films made at ${10}^{-8}\mathrm{Torr}$ Fe is clustered. The case of true Fe dilution in ${\mathrm{SnO}}_2$ is also shown. In spite of larger mass defect for Fe in ${\mathrm{SnO}}_2$ than that for Fe in ${\mathrm{TiO}}_2$ the dilute Fe species probe the phonon states in ${\mathrm{SnO}}_2$ more faithfully than in ${\mathrm{TiO}}_2$. This result is understood in terms of the combined effect of mass defect and nearest-neighbor force-constant changes. The impurity modes are more pronounced in ${\mathrm{TiO}}_2$ than in ${\mathrm{SnO}}_2$ due to ca. 10% difference of the lattice cell volumes between these two rutile oxides.

Figure 1

(Color online) Characterization of the structure of ${\mathrm{TiO}}_2$ films, geometry of scattering experiments, and film-substrate epitaxial relationship. In (a), the out-of-plane $\omega$-rocking curves of the (101) reflection for the films deposited at the pressures of ${10}^{-1}\mathrm{Torr}$ and ${10}^{-6}\mathrm{Torr}$ exhibit the FWHM of $1°$ and $0.5°$, respectively. (b) Spherical coordinate system represents the general orientation of the grazing incidence radiation wave vector $\vec{s}$ in the frame of rutile lattice axes as described by the zenith angle $\Theta$ and azimuth angle $\phi$. In (c), the film is oriented at $\Theta =90°$, i.e., ${\vec{s}}_{\perp }\left[010\right]$; in this orientation, the structure of epitaxial film is shown projected onto the rutile plane (010).

Figure 2

(Color online) (a) Partial vibrational DOS of ${}^{57}\mathrm{Fe}$ in ${\mathrm{Sn}}_{0.9}{\mathrm{Fe}}_{0.1}{\mathrm{O}}_2$ powder compared to original and (b) rescaled by factor 1.07 partial VDOS of ${}^{119}\mathrm{Sn}$ in ${\mathrm{SnO}}_2$.

Figure 3

(Color online) VDOS of $\alpha \text{−}\mathrm{Fe}$ calculated from the fifth-neighbor general force constant model $g\left(E\right)$ (Ref. 14), its convolution with the resolution-limiting Gaussian [Eq. (6)] and $G\left(E\right)$ for quality factor $Q=11.4$ in Eq. (1), fitted to the experimental partial ${}^{57}\mathrm{Fe}$ DOS of ${\mathrm{TiO}}_2$ DMS PLD thin films deposited at ${10}^{-8}\mathrm{Torr}$.

Figure 4

(Color online) (a) Partial DOS of ${}^{57}\mathrm{Fe}$ impurity in the pulsed-laser-deposited film of rutile ${\mathrm{TiO}}_2$ prepared at the oxygen pressure of ${10}^{-1}\mathrm{Torr}$ in comparison with (b) the intrinsic Ti direction-projected and plane-projected Ti DOS. The direction-projected DOS are calculated for the in-plane directions $\left[010\right]$ $g\left(E\right)=g_{xy}\left(E\right)$ and $\left[10\overline{1}\right]$ $g\left(E\right)=\frac{1}{2}{g}_{xy}\left(E\right){\cos }^2\vartheta +\frac{1}{2}{g}_z\left(E\right){\sin }^2\vartheta$. The (101)-plane-projected DOS is the plane-averaged $g_{\left(101\right)}\left(E\right)=\frac{1}{2}{g}_{xy}\left(E\right)(1+{\cos }^2\vartheta )+\frac{1}{2}{g}_z\left(E\right){\sin }^2\vartheta$. According to Ref. 27, the areas under each of the PDOS curves in (a) and (b) are normalized to unity; cf. a different way of the area normalization adopted for $g_{xy}$ and $g_z$ in calculations (Ref. 26): $\int g_{xy}\left(E\right)dE=2∕3$ and $\int g_z\left(E\right)dE=1∕3$.