Giant anisotropic magnetoresistance in oxygen-vacancy-ordered epitaxial ${\mathrm{La}}_{0.5}{\mathrm{Sr}}_{0.5}\mathrm{Co}{\mathrm{O}}_{3-\delta }$ films

Recent advances in complex oxide heterostructures have realized extraordinary control over oxygen vacancies ($V_{\mathrm{O}}$), including strain-tuned $V_{\mathrm{O}}$ order, and electric-field-controlled transformations between perovskite and $V_{\mathrm{O}}$-ordered structures. Perovskite cobaltites such as ${\mathrm{La}}_{1-x}\mathrm{S}{\mathrm{r}}_x\mathrm{Co}{\mathrm{O}}_{3-\delta }$ provide a prime example, recent work demonstrating that strain engineering of $V_{\mathrm{O}}$ ordering induces large ($\sim {10}^7\mathrm{erg}/\mathrm{c}{\mathrm{m}}^3$) perpendicular magnetic anisotropy. Here we show that $V_{\mathrm{O}}$-ordered epitaxial ${\mathrm{La}}_{0.5}{\mathrm{Sr}}_{0.5}\mathrm{Co}{\mathrm{O}}_{3-\delta }$ films exhibit not only strong magnetic anisotropy, but also a giant form of anisotropic magnetoresistance (AMR). This has magnetic field, temperature, and angular dependencies in quantitative accord with conventional AMR, but with AMR ratios up to an extraordinary 40.3%, 20 times enhanced over bulk cobaltites, and ∼10–100 times larger than typical transition metals. This giant AMR has no strong dependence on heteroepitaxial strain (between −2.1% and +1.8%) or thickness, and is instead ascribed to symmetry lowering associated with $V_{\mathrm{O}}$ ordering. The AMR ratios thus obtained are among the largest reported in the over 160-year history of this phenomenon, despite the absence of heavy elements.

Figure 1

(a)–(e) High-resolution specular wide-angle x-ray diffraction, i.e., intensity (arbitrary units, log scale) vs out-of-plane scattering vector magnitude ($Q$), around the 002 reflections of representative 195-Å-thick ${\mathrm{La}}_{0.5}{\mathrm{Sr}}_{0.5}\mathrm{Co}{\mathrm{O}}_{3-\delta }$ (LSCO) films on (001)-oriented (a) SLAO (green), (b) LAO (red), (c) SLGO (yellow), (d) LSAT (blue), and (e) STO (purple). In-plane strains (${\varepsilon }_{\mathrm{xx}}$) are labeled. (f) Out-of-plane strain (${\varepsilon }_{\mathrm{zz}}$) vs ${\varepsilon }_{\mathrm{xx}}$ for the films in (a)–(e), using a bulk LSCO lattice parameter of 3.833 Å. The red dashed line corresponds to Poisson ratio $\nu =1/3$. (g),(h) High-resolution cross-sectional high-angle annular dark field (HAADF) images of representative ∼100-Å-thick LSCO films on LAO and STO. The insets show Fourier transforms of areas around the boxed regions, red arrows and circles marking O-deficient planes and half-integer spots.

Figure 2

(a)–(e) Transverse (Hall) resistivity (${\rho }_{\mathrm{xy}}$) vs perpendicular magnetic field (${\mu }_{0}H$) for 195-Å-thick ${\mathrm{La}}_{0.5}{\mathrm{Sr}}_{0.5}\mathrm{Co}{\mathrm{O}}_{3-\delta }$ (LSCO) films on (001)-oriented (a) SLAO (green), (b) LAO (red), (c) SLGO (yellow), (d) LSAT (blue), and (e) STO (purple) substrates. All data are at temperature ($T$) of 5 K, and are normalized to the 9-T value. The lattice mismatch [and thus in-plane strain (${\varepsilon }_{\mathrm{xx}}$) in these pseudomorphic films] is shown on each substrate. (f)–(j) Corresponding 5-K magnetoresistivity for in-plane magnetic fields (${\mu }_{0}H$) parallel ($\mathrm{\Delta }{\rho }_{//}$, solid lines) and perpendicular ($\mathrm{\Delta }{\rho }_{\perp }$, dashed lines) to the current [42]. The anisotropic magnetoresistance ratio ($\mathrm{AMR}=\left[({\rho }_{\parallel }-{\rho }_{\perp })/{\rho }_0\right]\times 100\%$, where ${\rho }_0$ is the zero-field resistivity), is shown in each case, evaluated at 9 T [42].

Figure 3

Temperature ($T$)-dependent (magneto)transport properties of 195-Å-thick ${\mathrm{La}}_{0.5}{\mathrm{Sr}}_{0.5}\mathrm{Co}{\mathrm{O}}_{3-\delta }$ (LSCO) films on (001)-oriented SLAO (green), LAO (red), SLGO (yellow), LSAT (blue), and STO (purple) substrates. The lattice mismatch [and thus in-plane strain (${\varepsilon }_{\mathrm{xx}}$) in these pseudomorphic films] is shown on each substrate. Plotted are (a)–(e) the zero-field resistivity (${\rho }_0$), (f)–(j) parallel and perpendicular magnetoresistivities ($\mathrm{\Delta }{\rho }_{//}, \mathrm{\Delta }{\rho }_{\perp }$) in 9-T in-plane magnetic field (${\mu }_{0}H$), and (k)–(o) the 9-T anisotropic magnetoresistance ratio ($\mathrm{AMR}=\left[({\rho }_{\parallel }-{\rho }_{\perp })/{\rho }_0\right]\times 100\%$). Vertical dashed lines mark the Curie temperature of each film.

Figure 4

(a) Schematic showing polar and azimuthal angles (θ, ϕ) between the applied magnetic field ($\mathit{H}$) and current ($\mathit{I}$) for a ${\mathrm{La}}_{0.5}{\mathrm{Sr}}_{0.5}\mathrm{Co}{\mathrm{O}}_{3-\delta }$ (LSCO) film on a LAO substrate. (b) ϕ dependence of the resistivity (ρ) of a 195-Å-thick LSCO film on LAO with ${\mu }_{0}H=9\mathrm{T}$ applied in the film plane ($\theta ={90}^{\circ }$) at temperatures ($T$) of 5, 100, 180, 220, 240, and 300 K. (c) θ dependence of ρ at 9 T,$\varphi =0^{\circ }$, and the same $T$. Open circles in (b) and (c) are data; solid lines are fits to $\rho =\left(\mathrm{\Delta }\rho \right)\mathrm{co}{\mathrm{s}}^2\left(\varphi ,\theta \right)+{\rho }_{\perp }$. (d)–(f) Thickness ($t$) dependence of the (d) 5-K zero-field resistivity (${\rho }_0$), (e) 5-K transverse (Hall) conductivity (${\sigma }_{\mathrm{xy}}$) at 9 T (perpendicular-to-plane), and (f) 5-K anisotropic magnetoresistance ratio ($\mathrm{AMR}=\left[({\rho }_{\parallel }-{\rho }_{\perp })/{\rho }_0\right]\times 100\%$) at 9 T for LSCO films on LAO. Solid red lines in (d)–(f) are guides to the eye. Green horizontal dashed lines are bulk single-crystal values [for ${\mathrm{La}}_{0.7}{\mathrm{Sr}}_{0.3}\mathrm{Co}{\mathrm{O}}_3$ in (d) and (e) [43, 44] and $\mathrm{SrCo}{\mathrm{O}}_3$ in (f) 34].