Anisotropic spin-orbit interaction revealed by in-plane magnetoresistance in single-oriented SrRuO${}_3$ thin films

A detailed analysis of the in-plane magnetoresistance anisotropy in single-orientation thin-film SrRuO${}_3$ grown on (001)SrTiO${}_3$ is presented. The resistivity is measured in strips along [001], [$\overline{1}10$], and [$\overline{1}1\overline{1}$] with an in-plane rotating magnetic field. The data show additional details in the transfer from negative to positive magnetoresistance when the field is rotated in the plane. They show that the magnetoresistance is anisotropic with respect to the crystalline directions rather than with respect to the direction of the current. The data suggest an anisotropic spin-orbit interaction and can possibly be a sign of in-plane weak antilocalization.

Figure 1

(a) Schematic of a SrTiO${}_3$ substrate with atomic force microscope height image of a $1\times 1\mu {\text{m}}^2$ area of a TiO${}_2$ substrate. The height difference from right (black) to left (light gray) is approximately 2.8 nm, which corresponds to seven unit-cell-high steps on the SrTiO${}_3$ ($a\sim 3.9$ Å) surface. (b) Schematic of the SrRuO${}_3$ unit cell and (below) its orientation in relation to the atomic steps on the SrTiO${}_3$ surface. The substrate steps are taken to have edges along the [100]${}_{\mathrm{STO}}$ direction.

Figure 2

Top: X-ray 2$\theta /\omega$ diffraction data from the vicinity of the SrTiO${}_3$ 004 reflection. Two film reflections can be seen: 440 and $\overline{4}\overline{4}0$. Bottom: X-ray area scan ($2\theta /\omega -\omega$) around the SrTiO${}_3$ substrate 011 reflection and the SrRuO${}_3$ 112 reflection.

Figure 3

Sketch of the alignment of Hall bars with respect to the SrRuO${}_3$ crystalline directions and the reference direction $\theta$ for the in-plane magnetic field $H$. The in-plane field direction is illustrated with the arrow to the lower right; $\theta =0^{\circ }$ and $\theta ={90}^{\circ }$ correspond to [$\overline{1}10$]${}_{\mathrm{SRO}}$ and [$00\overline{1}$]${}_{\mathrm{SRO}}$, respectively.

Figure 4

Temperature dependence of resistivity of the strips along the [$\overline{1}$10] (red line with circles) and the [001] (black line with triangles) directions. The dashed lines represent linear fits to the resistance data just above the Curie temperature. The upper inset shows the derivative of the resistance. The critical behavior of the spin-polarized resistance $\Delta {\rho }_{\text{sp}}$ (details in the text) is shown in the inset to the lower right.

Figure 5

Resistance at 2 K as a function of applied magnetic field with field applied in the $\left[001\right]$ (open triangles) and $\left[\overline{1}10\right]$ (open circles) directions. Data for the strips aligned along $\left[\overline{1}10\right]$, $\left[001\right]$, and $\left[\overline{1}1\overline{1}\right]$ are shown in (a), (b), and (c), respectively. Solid line up to $\pm 4$ T in (b) represents data with field applied perpendicular to the plane. Solid lines through triangles and circles are curves fitted with the antilocalization model from Ref. 4. The curves in (c) exhibit hysteresis as indicated by the arrows. The angles given in parentheses represent the direction of the applied magnetic field $\theta$ as defined in Fig. 3.

Figure 6

Magnetoresistance $MR=\left[R\right(H)-R(0\left)\right]/R\left(0\right)$, measured with the field in different directions with respect to $\left[\overline{1}10\right]$ ($0^{\circ }$): (a)–(c) at 2 K, (d) and (e) at 80 K, (f)–(h) at 120 K, and (i) and (j) at 190 K. The panels show data when the field was applied in the directions indicated between (d) and (e). Note that due to the curvature of the data lines the order is reversed in the high-field end of (h). The three columns of plots refer to data acquired from strips in the $\left[\overline{1}10\right]$ (left column), $\left[\overline{1}1\overline{1}\right]$ (center column), and $\left[001\right]$ (right column) directions.