From weak antilocalization to Kondo scattering in a magnetic complex oxide interface

Quantum corrections to electrical resistance can serve as sensitive probes of the magnetic landscape of a material. For example, interference between time-reversed electron paths gives rise to weak localization effects, which can provide information about the coupling between spins and orbital motion, while the Kondo effect is sensitive to the presence of spin impurities. Here, we use low-temperature magnetotransport measurements to reveal a gradual transition from weak antilocalization (WAL) to Kondo scattering in the quasi-two-dimensional electron gas formed at the interface between $\mathrm{Sr}\mathrm{Ti}{\mathrm{O}}_3$ and the Mott insulator $\mathrm{Nd}\mathrm{Ti}{\mathrm{O}}_3$. This transition occurs as the thickness of the $\mathrm{Nd}\mathrm{Ti}{\mathrm{O}}_3$ layer is increased. Analysis of the Kondo scattering and WAL points to the presence of atomic-scale magnetic impurities coexisting with nanoscale magnetic regions that affect transport via a strong magnetic exchange interaction. This leads to distinct magnetoresistance behaviors that can serve as a sensitive probe of magnetic properties in two dimensions.

Figure 1

(a) Top: a schematic of the $\mathrm{STO}(8\mathrm{u}.\mathrm{c}.)/\mathrm{N}\mathrm{T}\mathrm{O}(x\mathrm{u}.\mathrm{c}.)/\mathrm{STO}(8\mathrm{u}.\mathrm{c}.)/\mathrm{LSAT}\left(001\right)$ heterostructure, where $x=2$, 4, 10, 20. The directions of applied fields are indicated with respect to the heterointerface. Bottom: false-color optical image of a typical Hall-bar sample prepared on the heterostructure. The etched regions are indicated in blue. (b) The temperature dependence of the Hall mobility $\mu$. (c) Magnetoresistance as a function of the perpendicular magnetic field $B_{\perp }$ measured at $T=2\mathrm{K}$. The $x=2$ data in (b) and (c) are reproduced from Ref. [8] to allow direct comparison with the $x=4$, 10, and 20 samples.

Figure 2

Sample resistance $R$ (dots) at $B=0$ as a function of temperature $T$ on a logarithmic scale, normalized to its value at $T=300\mathrm{K}$, for the $\mathrm{STO}(8\mathrm{u}.\mathrm{c}.)/\mathrm{N}\mathrm{T}\mathrm{O}(x\mathrm{u}.\mathrm{c}.)/\mathrm{STO}(8\mathrm{u}.\mathrm{c}.)/\mathrm{LSAT}\left(001\right)$ heterostructures, with $x=2$, 4, 10, and 20, respectively, for (a), (b), (c), and (d). Dashed lines show the low-temperature logarithmic dependencies and solid lines correspond to the theoretical fits using Eqs. (1) and (2). The data in (a) are reproduced from Ref. [8] and rescaled in the same way as (b)–(d) for direct comparison.

Figure 3

Magnetoresistance as a function of the parallel field $B_{\parallel }$ at various temperatures for samples with different NTO thicknesses, $x=2$ (a), 4 (b), 10 (c), 20 u.c. (d). Experimental data (dots) and theoretical fits (solid lines). (e) The magnetic field scale $B_K$ of the Kondo contribution extracted from the fits in (c) and (d) for the 10 and 20 u.c. samples, respectively. (f) The inverse of the apparent local moment $1/{\mu }_m$ as function of $1/T$ (dots) and the associated linear fits (solid lines) for the samples in (a), (c), and (d). The vertical bars in (e) and (f) represent the standard errors of the data obtained from the fits. The data on the $x=2$ sample in (a) and (f) are replotted here based on Ref. [8] for direct comparison.

Figure 4

Magnetoresistance as a function of the perpendicular magnetic field $B_{\perp }$ at various temperatures for samples with different NTO thicknesses, $x=2$ (a), 4 (b), 10 (c), 20 u.c. (d): experimental data (open circles) and theoretical fits (solid lines). The extracted values of the fit parameters $B_1$ and $B_2$ are plotted as a function of temperature for each sample. The vertical bars represent the standard errors of the data points obtained from the fittings.

Figure 5

The saturation exchange field $\lambda {\mu }_0{M}_s$ as a function of temperature $T$, extracted from the fits in Figs. 3 and 3 for the 10 and 20 u.c. samples, respectively. Standard errors of the fits are included.