Determination of the resistivity anisotropy of $\mathrm{Sr}\mathrm{Ru}{\mathrm{O}}_3$ by measuring the planar Hall effect

We have measured the planar Hall effect in epitaxial thin films of the itinerant ferromagnet $\mathrm{Sr}\mathrm{Ru}{\mathrm{O}}_3$ patterned with their current paths at different angles relative to the crystallographic axes. Based on the results, we have determined that $\mathrm{Sr}\mathrm{Ru}{\mathrm{O}}_3$ exhibits small resistivity anisotropy in the entire temperature range of our measurements (between 2 and $300\mathrm{K}$); namely, both above and below its Curie temperature $\left(150\mathrm{K}\right)$. Our results indicate that in addition to anisotropy related to the spontaneous magnetization, the resistivity anisotropy of $\mathrm{Sr}\mathrm{Ru}{\mathrm{O}}_3$ has an intrinsic, nonmagnetic source. We have found that the two sources of anisotropy have competing effects.

Figure 1

Photo of the measured sample which consists of eight patterns at different orientations. Inset: a scheme of an individual pattern.

Figure 2

(a) $R_{\mathrm{FD}}$ as a function of temperature for the eight patterns. In decreasing order of $R_{\mathrm{FD}}$ value at $300\mathrm{K}$, the curves correspond to patterns at angles of 45°, 30°, 15°, 0°, 75°, 90°, and $-45°$. (b) The antisymmetric contribution to $R_{\mathrm{FD}}$. (c) PHE contribution to $R_{\mathrm{FD}}$. In decreasing order of their value at $300\mathrm{K}$, the curves correspond to patterns at angles of 45°, 60°, 30°, 15°, 75°, 0°, 90°, and $-45°$.

Figure 3

(Color online) (a) Refined PHE (see text) vs temperature. The number near the curve indicates the pattern orientation. (b) The PHE in patterns oriented at various angels vs the PHE in the pattern oriented at 45°. The lines are linear fits. Inset: the slope of the linear fits $\alpha$ as a function of $\theta$. The line is the expected $\sin \theta \cos \theta$ dependence.

Figure 4

The anisotropy ${\rho }_0-{\rho }_{90}$ as determined by PHE measurements (continues) and from subtraction of longitudinal resistivities (dashed).

Figure 5

The PHE for the pattern oriented at 45° at $155\mathrm{K}$ as a function of $\theta$, the angle between an in-plane $8\mathrm{T}$ field and $\left[1\overline{1}0\right]$. The dashed line is the zero field value of the PHE.

Figure 6

The PHE for the 45° oriented pattern vs $H$ applied along the $b$ axis at 155, 160, and $165\mathrm{K}$. Inset: PHE normalized by its zero-field value as a function of $H^2$ at 155, 160, and $165\mathrm{K}$. At each temperature, the data for all the patterns are presented; however, due to scaling, the data points are undistinguishable.