Ferromagnetism and structure of epitaxial Cr-doped anatase ${\mathrm{TiO}}_2$ thin films

The materials and magnetic properties of Cr-doped anatase ${\mathrm{TiO}}_2$ thin films deposited on ${\mathrm{LaAlO}}_3\left(001\right)$ and ${\mathrm{SrTiO}}_3\left(001\right)$ substrates by oxygen-plasma-assisted molecular beam epitaxy have been studied in detail to elucidate the origin of ferromagnetic ordering. Cr substitution for Ti in the anatase lattice, with no evidence of Cr interstitials, segregation, or secondary phases, was independently confirmed by transmission electron microscopy with energy dispersive x-ray spectroscopy, extended x-ray absorption fine structure, and Rutherford backscattering spectrometry in the channeling geometry. Epitaxial films deposited at $\sim 0.1\mathrm{\AA }∕\mathrm{s}$ were found to have a highly defected crystalline structure, as quantified by high-resolution x-ray diffraction (XRD). These films were also ferromagnetic at room temperature with a moment of $\sim 0.5{\mu }_B∕\mathrm{Cr}$, Curie temperatures in the range of $400\text{–}700°\mathrm{C}$, and exhibited shape and in-plane magnetocrystalline anisotropy. However, no free carrier spin polarization was observed by Hall effect measurements, raising questions about the mechanism of magnetism. Films deposited slowly $(\sim 0.015\mathrm{\AA }∕\mathrm{s})$ possessed a nearly perfect crystalline structure as characterized by XRD. Contrary to expectations, these films exhibited negligible ferromagnetism at all Cr concentrations. Annealing in vacuum to generate additional oxygen defects and free carrier electrons did not significantly increase the ferromagnetic ordering in either fast- or slow-grown films. These results contradict both oxygen-vacancy-derived free-carrier-mediated exchange and F-center-mediated bound magnetic polaron exchange mechanisms, and instead indicate the primary role of extended structural defects in mediating the ferromagnetic ordering in doped anatase films.

Figure 1

(Color online) RHEED (00) intensity oscillations along the [100] azimuth of anatase and final RHEED patterns along the [100] and [110] azimuths for slow-grown 7% $\mathrm{Cr}:{\mathrm{TiO}}_2$ deposited on LAO at $\sim 0.015\mathrm{\AA }∕\mathrm{s}$ (top), and fast-grown 14% $\mathrm{Cr}:{\mathrm{TiO}}_2$ deposited on LAO at $\sim 0.1\mathrm{\AA }∕\mathrm{s}$ (bottom). For the fast-grown film (bottom), the arrow indicates when the Cr source shutter was opened to begin deposition of $\mathrm{Cr}:{\mathrm{TiO}}_2$; the Cr shutter was already open when the oscillations for the slow-grown material (top) were collected.

Figure 2

(Color online) RBS random (solid lines) and channeling (dotted lines) measurements with the $2\mathrm{MeV}$ ${\mathrm{He}}^{+}$ incident beam normal to the surface. (a) Channeling minimum yields for $825\mathrm{\AA }$ of fast-grown 6% $\mathrm{Cr}:{\mathrm{TiO}}_2∕\mathrm{LAO}$ were 38% for Ti and 59% for Cr. (b) Minimum yields for $465\mathrm{\AA }$ of slow-grown 7% $\mathrm{Cr}:{\mathrm{TiO}}_2∕\mathrm{LAO}$ were 8% for Ti and 9% for Cr. (c) Channeling rocking curve of slow-grown sample. Coincidence of minima for Ti (circles) and Cr (triangles) indicates Cr occupies the same cation position as Ti in the anatase lattice.

Figure 3

(Color online) (a) $\mathrm{Cr}K$-edge XANES spectra for fast-grown 9% $\mathrm{Cr}:{\mathrm{TiO}}_2∕\mathrm{LAO}$ and slow-grown 8% $\mathrm{Cr}:{\mathrm{TiO}}_2∕\mathrm{STO}$, as well as standards of Cr metal (thin solid line), ${\mathrm{Cr}}_2{\mathrm{O}}_3$ (dashed), and ${\mathrm{CrO}}_2$ (dashed-dotted). The inflection point energies of both $\mathrm{Cr}:{\mathrm{TiO}}_2$ spectra match that for ${\mathrm{Cr}}_2{\mathrm{O}}_3$, indicating Cr is present as $\mathrm{Cr}\left(\mathrm{III}\right)$ in $\mathrm{Cr}:{\mathrm{TiO}}_2$. (b) $k^2$-weighted $\mathrm{Cr}K$-edge EXAFS data for the slow-grown sample (circles) and fit to the data by FEFF calculations assuming Cr is substitutional in anatase (solid line).

Figure 4

(Color online) (a) Saturation moment per Cr dopant cation at room temperature for several fast-grown $\mathrm{Cr}:{\mathrm{TiO}}_2$ films of varying thicknesses and dopant concentrations. The dotted line represents the average saturation moment value of $0.5{\mu }_B∕\mathrm{Cr}$. Inset: Room-temperature hysteresis loops by VSM for a bare uncontaminated LAO substrate (dotted line) and after deposition of $560\mathrm{\AA }$ of fast-grown 10% $\mathrm{Cr}:{\mathrm{TiO}}_2$ (solid line). (b) Hysteresis loops for fast-grown 9% $\mathrm{Cr}:{\mathrm{TiO}}_2$. The applied magnetic field was oriented along the crystallographic directions indicated (the $⟨100⟩$ and $⟨110⟩$ directions are in the plane of the film, while the $⟨001⟩$ direction is perpendicular to the film plane). Both in-plane magnetocrystalline anisotropy and out-of-plane shape anisotropy are observed. Inset: Plot of the low-field region which shows hysteresis of the in-plane magnetization directions.

Figure 5

(Color online) (a) Curie temperature measurement by VSM for one-half $(1\mathrm{cm}\times 0.5\mathrm{cm})$ of fast-grown 8% $\mathrm{Cr}:{\mathrm{TiO}}_2∕\mathrm{LAO}$. ZFC data were obtained first; the sample was then cooled in a magnetic field of $1\mathrm{kOe}$, and the measurement repeated. The Curie temperature was found to be $\sim 415°\mathrm{C}$ for both measurements. (b) Curie temperature measurement by VSM for one-half of fast-grown 10% $\mathrm{Cr}:{\mathrm{TiO}}_2∕\mathrm{LAO}$. ZFC and FC data were collected as in (a). The Curie temperature was found to be $\sim 700°\mathrm{C}$.

Figure 6

(Color online) Total measured magnetization by VSM at room temperature for several slow-grown $\mathrm{Cr}:{\mathrm{TiO}}_2$ films of approximately $450\mathrm{\AA }$ thickness and varying dopant concentrations. The total magnetization does not appear to correlate to Cr dopant concentration. The dotted line is the expected magnetization for a $450\mathrm{\AA }$ thick $\mathrm{Cr}:{\mathrm{TiO}}_2$ film assuming a saturation moment of $0.5{\mu }_B∕\mathrm{Cr}$. The $\mathbf{x}$ symbol represents the total measured magnetization of a pure anatase thin film with no Cr dopant. Inset: VSM hysteresis loops for a bare LAO substrate (dotted line) and after deposition of $450\mathrm{\AA }$ 6% $\mathrm{Cr}:{\mathrm{TiO}}_2$ (solid line).

Figure 7

(Color online) Hysteresis loops by SQUID magnetometry as a function of temperature for slow-grown 8% $\mathrm{Cr}:{\mathrm{TiO}}_2∕\mathrm{LAO}$. The diamagnetic background signal from the LAO substrate has been subtracted. A large paramagnetic contribution is evident at temperatures $<50\mathrm{K}$. Shown in the inset is the extracted ferromagnetic saturation moment, defined as the $y$ intercept of the linear portion of the loops shown in the figure.

Figure 8

(Color online) Room-temperature VSM hysteresis loops of $\mathrm{Cr}:{\mathrm{TiO}}_2∕\mathrm{LAO}$ films as deposited (dotted lines) and after annealing (solid lines). Resistivity values determined by four-point probe conductivity. (a) Fast-grown 6% $\mathrm{Cr}:{\mathrm{TiO}}_2$ as deposited and after annealing in UHV at $600°\mathrm{C}$ for several hours, resulting in a resistivity of $\sim 1.5\mathrm{\Omega }\mathrm{cm}$. (b) Fast-grown 16% $\mathrm{Cr}:{\mathrm{TiO}}_2$ as-deposited and after annealing at $600\text{–}650°\mathrm{C}$ in a tube furnace with flowing ${\mathrm{N}}_2$. Resistivity after annealing was still too high to measure with the four-point probe apparatus. (c) Slow-grown 6% $\mathrm{Cr}:{\mathrm{TiO}}_2$ as-deposited and after annealing in UHV at $550°\mathrm{C}$ for several hours, resulting in a resistivity of $\sim 0.08\mathrm{\Omega }\mathrm{cm}$.

Figure 9

(Color online) XRD $\omega \text{−}2\theta$ scans for $\mathrm{Cr}:{\mathrm{TiO}}_2∕\mathrm{LAO}$ films of varying crystalline quality, as well as final [100] azimuth RHEED patterns collected after deposition. (a) $508\mathrm{\AA }$, 12% Cr. (b) $465\mathrm{\AA }$, 7% Cr. (c) $453\mathrm{\AA }$, 8% Cr. The model fit overlaps the data almost exactly in this plot. (d) $497\mathrm{\AA }$, 7% Cr. (e) $567\mathrm{\AA }$, 10% Cr. (a), (c), and (d) were obtained with the $\mathrm{Ge}\left(220\right)$ analyzer; (b) and (e) were obtained with the $0.25°$ slit. (f) Plot of room-temperature saturation moment per Cr dopant versus the fitted roughness value ${\sigma }_{\mathrm{XRD}}$. As the value of ${\sigma }_{\mathrm{XRD}}$ increases, the ferromagnetic saturation moment also increases.

Figure 10

(Color online) Anomalous Hall measurements at $10\mathrm{K}$ on a reduced fast-grown 8% $\mathrm{Cr}:{\mathrm{TiO}}_2$ sample show no anomalous Hall behavior. Inset: Resistivity (solid line) and free-carrier concentration (circles) from Hall measurements as a function of temperature.