Coexistence of Superconductivity and Ferromagnetism in Two Dimensions

Ferromagnetism is usually considered to be incompatible with conventional superconductivity, as it destroys the singlet correlations responsible for the pairing interaction. Superconductivity and ferromagnetism are known to coexist in only a few bulk rare-earth materials. Here we report evidence for their coexistence in a two-dimensional system: the interface between two bulk insulators, ${\mathrm{LaAlO}}_3$ (LAO) and ${\mathrm{SrTiO}}_3$ (STO), a system that has been studied intensively recently. Magnetoresistance, Hall, and electric-field dependence measurements suggest that there are two distinct bands of charge carriers that contribute to the interface conductivity. The sensitivity of properties of the interface to an electric field makes this a fascinating system for the study of the interplay between superconductivity and magnetism.

Figure 1

(a) Superconducting transition at different gate voltages $V_g$. (b) Current-voltage characteristics of the sample at 15 mK. (c) Transition temperature $T_c$ (defined as the midpoint of the resistive transition) and critical current (defined as the current at which the sample switches to the resistive state on ramping the current up from zero) as a function of $V_g$. Both measures indicate that the maximal superconducting properties are obtained for $V_g\simeq 80\mathrm{V}$. Error bars indicate the difference in $T_c$ measured between cooling and warming traces.

Figure 2

(a) Superconducting transition for $V_g=80\mathrm{V}$, at a few different magnetic fields. Inset: $T_c$ vs $H$ obtained from these data. $T_c$ is defined by the midpoint of the resistive transition. The line represents a linear fit to the data points, with a slope of $1.6\mathrm{mK}/\mathrm{mT}$, giving a zero temperature coherence length of ${\xi }_0=64\mathrm{nm}$. (b) Phase diagram, $T_c$ vs $H$, for a gate voltage of $V_g=80\mathrm{V}$, where the superconducting properties are maximal. The three curves represent different resistance bias points along the superconducting transition, with the normal state resistance per square being $704\Omega$. The arrows mark the direction of the magnetic field ramp. (c) Phase diagrams at a bias point of $R_S=83\Omega$, at the foot of the resistive transition, at three different gate voltages. Data for $V_g=40\mathrm{V}$ are shifted by 10 mK and data for $V_g=80\mathrm{V}$ by 20 mK for clarity.

Figure 3

(a) Magnetoresistance (MR) at $V_g=-100\mathrm{V}$ at four different temperatures. (b) Expansion of the low-field data of (a) for the three highest temperatures. (c) Simulation of the longitudinal MR assuming weak localization contributions from two parallel conducting channels. The inset shows an expanded view of the zero field region, showing the hysteresis and the nonmonotonic dependence seen in the experimental data. (d) Hall resistance at $V_g=-100\mathrm{V}$ at three different temperatures. Data for 50 mK and 375 mK have been offset by $+5$ and $-5\Omega$, respectively. (e) Hall coefficient and zero field longitudinal resistance at different gate voltages at 270 mK. The longitudinal resistance decreases with increasing gate voltage, but the Hall coefficient, nominally inversely proportional to the electron density, increases.

Figure 4

(a) Magnetoresistance (top curve) and Hall resistance (bottom curve) at $V_g=20\mathrm{V}$ at 50 mK. (b) Same data as in (a), for one direction of the magnetic field sweep, except the background linear component is subtracted from the Hall resistance.