Fig. 2: The temperature and field dependence of ρ and ρ_xy in SRO thin films.

a An illustration of the measurement geometry for ρ and ρ_xy with respect to the SRO crystalline axes. b The T dependent ρ in SRO(t)/STO (001) with thicknesses ts ranging from about 7.7–35.3 nm. The kink at T ≈ 150 K corresponds to the onset of the ferromagnetism. The upper panel and lower panel of c show the MR and ρ_xy, respectively, as a function of field at T = 2.5 K, and they share the same color codes as that in (b). Pronounced quantum oscillations were observed for μ₀H ≥ 3.5 T in all five SRO films with different t values. d The θ dependent MR for t ≈ 13.7 and 18.7 nm are shown in the upper panel and lower panel, respectively. The inset cartoon shows the definition of the θ angle. For the field perpendicular to the film surface plane (θ = 0^o), a large and positive MR was observed, which is practically linear with the field strength up to 35 T without saturation. The magnitude of the positive MR drops with increasing θ, and it becomes a negative MR when the field is applied along the current direction (θ = 90^o).