Anomalous Magnetic Ground State in an ${\mathrm{LaAlO}}_3/{\mathrm{SrTiO}}_3$ Interface Probed by Transport through Nanowires

Resistance as a function of temperature down to 20 mK and magnetic fields up to 18 T for various carrier concentrations is measured for nanowires made from the ${\mathrm{SrTiO}}_3/{\mathrm{LaAlO}}_3$ interface using a hard mask shadow deposition technique. The narrow width of the wires (of the order of 50 nm) allows us to separate out the magnetic effects from the dominant superconducting ones at low magnetic fields. At this regime hysteresis loops are observed along with the superconducting transition. From our data analysis, we find that the magnetic order probed by the giant magnetoresistance effect vanishes at $T_{\text{Curie}}=954\pm 20\mathrm{mK}$. This order is not a simple ferromagnetic state but consists of domains with opposite magnetization having a preferred in-plane orientation.

Figure 1

Left: Fabrication method of the nanowires. On top of the ${\mathrm{TiO}}_2$ terminated ${\mathrm{SrTiO}}_3$ substrate an amorphous oxide layer number 1 with a thickness $d$ was deposited and patterned with standard optical lithography process. The substrate is then tilted to an angle $\theta$ and a second amorphous oxide layer is deposited. This results in a nanotrench with a width $w=d\tan (\theta )$. Finally, an epitaxial ${\mathrm{LaAlO}}_3$ layer is deposited as described in the text, resulting in a conducting ${\mathrm{LaAlO}}_3/{\mathrm{SrTiO}}_3$ nanowire. Right: Scanning electron microscope image of such a nanowire designed with $w=70\mathrm{nm}$, consistent with the dimensions measured by the microscope.

Figure 2

(a) Resistance as function of temperature at zero magnetic field and $V_g=0\mathrm{V}$ (as grown). (b) Resistance as a function of magnetic field at 20 mK and $V_g=0\mathrm{V}$ (as grown). (c) Focus on the Shubnikov–de Haas (SdH) oscillations plotted as function of inverse field after application of a low pass filter to reduce measurement noise. Periodic oscillations are observed. (d) A fast Fourier transform of the SdH oscillations yielding a sharp peak at 77.05 T. (e) Resistance versus magnetic field for various gate voltages. The gate voltage is decreased from 31.2 (bottom magenta curve ) to 22.8 V (top black curve)

Figure 3

Resistance as function of magnetic fields for the low fields region at 20 mK. Reproducible magnetic hysteresis curves are observed in (a) perpendicular, (b) transverse, and (c) parallel field orientations. Solid blue lines correspond to the curve plotted while increasing the field and the dashed red lines for decreasing the field. Inset: The magnetic effect shown in (a) after subtraction of the superconducting background, a function of the form $a|H|+b$. (d) Schematic illustration of adjacent domain orientation in the various resistance states. The data are taken from (b).

Figure 4

(a) Resistance versus magnetic field for various angles between the perpendicular to the interface and the applied magnetic field 90 deg corresponds to the parallel field direction. (b) Saturation field for various angles. For the circles (triangles) 90 deg corresponds to the parallel (transverse) field orientation.

Figure 5

Inset: Resistance versus magnetic field for various temperatures for parallel field orientation. (a) Saturation field $H_s$ as a function of temperature for parallel and perpendicular field orientations. The solid lines are fits to $H_s(0)(1-T/T_0{)}^{1/2}$. (b) Normalized saturation field $H_s(T)/H_s(0)$ for both parallel and perpendicular orientations. $H_s(0)$ is determined from the fit in (a). Black solid line is a fit to $(1-T/T_{\text{Curie}}{)}^{1/2}$ yielding $T_{\text{Curie}}=954\pm 20\mathrm{mK}$.