Anisotropic magnetotransport in SrTiO${}_3$ surface electron gases generated by Ar${}^{+}$ irradiation

Metallic surface layers are fabricated by doping (100) SrTiO${}_3$ (STO) single crystals with oxygen vacancies generated by bombardment with Ar ions from an rf plasma source. The presence of oxygen vacancies is confirmed by cathodoluminescence and x-ray photoemission spectroscopy. This technique produces a surface electron gas with high values of the sheet carrier density ($n_{2\mathrm{D}}$ $=$ 2.45×10${}^{17}$ cm${}^{-2}$). A strong increase (300%) of the low-temperature magnetoresistance is observed when the magnetic field is rotated away from the surface, characteristic of orbital effects of confined electrons. We estimate the width of the confinement region to be in the 200–300 nm range. When a magnetic field is applied in the surface plane and parallel to the current direction, a large negative magnetoresistance is found below the structural transition of the STO, which is discussed in terms of spin-orbit scattering. On further reduction of temperature, there is a change to a positive magnetoresistance regime due to the scattering of charge carriers at the disordered surface region.

Figure 1

(a) Temperature dependence of the sheet resistance in zero applied magnetic field of STO crystals irradiated at a power of 30 W for 5 min. Magnetic field dependence of the 4 probe (van der Pauw) magnetoresistance at 200, 100, 50, 20, 10, 5, 3, 2.5 and 2 K (from bottom to top) (b) and Hall effect at 100, 200, 50, 2, 2.5, 3, 20, 5, and 10 (from bottom to top at 8 T) (c) in magnetic fields applied perpendicular to the crystal surface.

Figure 2

(a) Cathodoluminescence spectrum of Ar${}^{+}$-irradiated STO sample at 220 K recorded with an acceleration voltage of 5 keV. Fit (continuous line) using Gaussian components (dotted lines) with maximum peaks at 2.76 and 3.06 eV. (b) High-resolution XPS Ti 2$p_{3/2}$ spectra. Peaks were fitted to Gaussian-Lorentzian combinations. The peak centered at about 458.3 eV corresponds to Ti${}^{4+}$, and the peak centered at a binding energy 1.4 eV below the Ti${}^{4+}$ peak was ascribed to Ti${}^{3+}$.

Figure 3

(a) Angular dependence of the magnetoresistance when the magnetic field of 8.5 T is rotated around an in-plane axis perpendicular to the current direction. As shown in the sketch for an angle ϕ $=$ 90 ° the magnetic field is perpendicular to the front surface of the crystal and for ϕ $=$ 0 ° it is parallel to the current direction. Different data sets are measurements at different temperatures (3, 4.2, 7, 15, 20, 50, 100, 200, 300 K from top to bottom at 90°) of a crystal irradiated at 30 W. Data are normalized to the zero-field resistance for comparison at different temperatures as $R_{\mathrm{norm}}(\phi )=[R(\phi )-R(H=0)]/R(H=0)$. (b) Amplitude of angular magnetoresistance change according to ${\mathit{MR}}_{\perp }=[R(\phi ={90}^{°})-R(\phi =0^{°})]/R(H=0)$ as a function of temperature.

Figure 4

(a) Angular dependence of the magnetoresistance in an in-plane magnetic field of 8.5 T. As shown in the sketch, for an angle θ $=$ 0 the magnetic field is parallel to the current direction and for θ $=$ 90 ° it is perpendicular. Different data sets are measurements at different temperatures (15, 20, 7, 4.2, 3, 50, 100, 200, 300 K from top to bottom at 90°) of a crystal irradiated at 30 W. Data are normalized to the zero-field resistance $R_{\mathrm{norm}}(\theta )=[R(\theta )-R(H=0)]/R(H=0)$. (b) Amplitude of the angular magnetoresistance change according to $\mathit{MR}=[R(\theta ={90}^{°})-R(\theta =0^{°})]/R(H=0)$ as a function of temperature.

Figure 5

Magnetoresistance with field perpendicular to surface at $T$ $=$ 50 K for various geometries. Square 5×5 mm${}^2$ sample with van der Pauw configuration in the two current geometries (black and red dotted lines), same sample cut into three individual pieces, with in-line 4-contact geometry (green, dark blue, light blue solid lines).

Figure 6

Magnetic field dependence of the magnetoresistance for magnetic fields applied parallel to the current direction. Different data sets correspond to different temperatures (3, 4.2, 7, 200, 300, 50, 100, 20, 15 K from top to bottom at 8 T) of a crystal irradiated at 30 W. Data have been normalized to the zero-field resistance.