Observation of quantum Griffiths singularity and ferromagnetism at the superconducting $\mathrm{LaAl}{\mathrm{O}}_3/\mathrm{SrTi}{\mathrm{O}}_3\left(110\right)$ interface

Diverse phenomena emerge at the interface between band insulators $\mathrm{LaAl}{\mathrm{O}}_3$ and $\mathrm{SrTi}{\mathrm{O}}_3$, such as superconductivity and ferromagnetism, showing an opportunity for potential applications as well as contributing to fundamental research interests. Here, we report the superconductor-metal transition driven by a perpendicular magnetic field in superconducting two-dimensional electron gas formed at the $\mathrm{LaAl}{\mathrm{O}}_3/\mathrm{SrTi}{\mathrm{O}}_3\left(110\right)$ interface, which offers an appealing platform for quantum phase transition from a superconductor to a weakly localized metal. Interestingly, when approaching the quantum critical point, the dynamic critical exponent is not a constant but a diverging value, which is direct evidence of a quantum Griffiths singularity arising from quenched disorder at ultralow temperatures. Furthermore, the hysteretic property of magnetoresistance is observed at the $\mathrm{LaAl}{\mathrm{O}}_3/\mathrm{SrTi}{\mathrm{O}}_3\left(110\right)$ interface, which suggests the potential coexistence of superconductivity and ferromagnetism.

Figure 1

The magnetic-field-driven superconductor-metal transition. (a) The temperature dependence of resistance at zero magnetic field. $T_c^{\mathrm{zero}}$ and $T_c^{\mathrm{onset}}$, marked by black arrow, are 0.123 K and 0.711 K, respectively. The inset shows the determination of $T_c^{\mathrm{onset}}$. (b) Isomagnetic $R\left(T\right)$ curves measured at different $B$. (c) Isotherm $R\left(B\right)$ curves measured at different $T$, where the inset shows the zoom-in view of the crossing region.

Figure 2

The isotherms of magnetoresistance $R\left(B\right)$ from 0.020 K to 0.650 K. The sweep directions and rates are the same for all the curves. The inset shows the $T$ dependence of corresponding $B_c$ for crossing points (blue dots) of every two adjacent $R\left(B\right)$ curves, and the resistance plateaus (green squares) extracted from $R\left(T\right)$ curves.

Figure 3

Finite-size scaling analysis for one representative group. (a) The isotherms $R\left(B\right)$ close to the critical point in the lowest temperature region (0.020–0.035 K). The crossing region formed by four adjacent $R$(B) curves are denoted as one critical point $(B_c=0.427\mathrm{T},R_c=877.50\mathrm{\Omega })$. (b) Normalized $R$ as a function of $t|B_c-B|$, where $t={\left(T/T_0\right)}^{-1/zv}$. The insets show the power-law plot $T$ dependence of scaling parameter $t$. The $zv$ value is obtained from the slope of the fitting line.

Figure 4

The $B$ dependence of critical exponent $zv$: activated scaling behavior. Magenta dots are $zv$ values extracted from FSS analysis in different temperature regions. Blue line is the fitting by $zv=C{\left(B_c^{*}-B\right)}^{-0.6}.$ Two red dash lines represent the constant value with $B_c^{*}=0.428\mathrm{T}$ and $zv=1$, respectively.

Figure 5

The quantum Griffiths singularity for $V_G=20\mathrm{V}$. (a) $R\left(T\right)$ at zero magnetic field with $T_c^{\mathrm{zero}}=0.109\mathrm{K}$. The inset shows the definition of $T_c^{\mathrm{onset}}$, with a value of 0.696 K. (b) Isotherms $R\left(B\right)$ measured at different $T$. Zoom-in view of cross region is shown in the inset. (c) Isotherms $R\left(B\right)$ measured at different $T$ ranging from 0.020 K to 0.300 K. The inset provides the crossing points $B_c$ as a function of $T$, which were determined from the cross point of every two adjacent $R\left(B\right)$ curves. (d) The $B$ dependence of $zv$ values reveals the activated scaling behavior.

Figure 6

The hysteretic behavior of $R\left(B\right)$ at different temperatures plotted for $V_G=0\mathrm{V}$. The peaks that emerge in the magnetoresistance weaken with increasing temperature, while the corresponding magnetic field value remains unchanged. The arrows indicate the sweep directions of the magnetic field.

Figure 7

(a) Typical resistance versus temperature curve measured for a low-temperature system (4–180 K). The inset shows the configuration of the electrodes for standard four-terminal measurements. (b) Atomic force microscopy surface topography of the 5 unit-cell LAO film. Atomically flat terraces were preserved after the film deposition.

Figure 8

Finite-size scaling analysis (0.020–0.0.95 K). (a), (c), (e), (g) Isotherms $R\left(B\right)$ close to the critical points at different temperature regions. The crossing region formed by four adjacent $R\left(B\right)$ curves is denoted as one critical point. (b), (d), (f), (h) Normalized $R$ as a function of $t|B_c-B|$, where $t={\left(T/T_0\right)}^{-1/zv}$. The insets show the power-law plot $T$ dependence of scaling parameter $t$. The linear fitting gives the $zv$ values.

Figure 9

Finite-size scaling analysis (0.100–0.0.175 K). (a), (c), (e), (g) Isotherms $R\left(B\right)$ close to the critical points at different temperature regions. (b), (d), (f), (h) Normalized $R$ as a function of $t|B_c-B|$, where $t={\left(T/T_0\right)}^{-1/zv}$. The insets show the power-law plot $T$ dependence of scaling parameter $t$. The $zv$ values are obtained from the slope of the fitting line.

Figure 10

The quantum Griffiths singularity for $V_G=60\mathrm{V}$. (a) $R\left(T\right)$ at zero magnetic field gives $T_c^{\mathrm{zero}}\approx 0.098\mathrm{K}$, and the inset shows the definition of $T_c^{\mathrm{onset}}$, with a value of 0.696 K. The temperature where the $R\left(T\right)$ first deviates from its linear dependence at high temperature is defined as $T_c^{\mathrm{onset}}$. (b) Isotherms $R\left(B\right)$ measured at different $T$. Close-up view of cross region is shown in the inset. (c) Isotherms $R\left(B\right)$ measured in detail at different $T$ ranging from 0.020 K to 0.650 K. The inset gives the crossing points $B_c$ as a function of $T$, which are formed by every two adjacent $R\left(B\right)$ curves. (d) The $B$ dependence of $zv$ values gives the activated scaling behavior. As we can see, the critical exponent diverges at low temperatures. Thus, the quantum Griffiths singularity is also observed for $V_G=60\mathrm{V}$.

Figure 11

The measurements of the 12-unit-cell LAO/STO(110) sample prepared under the same conditions as the 5-unit-cell sample (the main text). (a) $R\left(T\right)$ at zero magnetic field with $T_c^{\mathrm{onset}}\approx 0.560\mathrm{K}$. (b) Isotherms $R\left(B\right)$ measured at different $T$. The crossing region around 0.530 T is formed instead of one crossing point, which is analogous to data from the 5-unit-cell sample. The periodic oscillation of the normal state resistance is somewhat puzzling. We speculate that it may be due to the accidental formation of conducting loops at the interface. The magnetoresistance peaks also appear at around $-0.056\mathrm{T}$, as marked by the dashed line. The magnetic field sweeps from positive to negative.

Figure 12

The hysteretic behavior of $R\left(B\right)$ with different sweep rate of the magnetic field at $T=0.030\mathrm{K}$ for $V_G=60\mathrm{V}$. The amplitude of the peak increases when the field sweep rate increases. The arrows indicate the sweep direction of the magnetic field. The arrow pointing left indicates the magnetic field sweeps from positive to negative, while the arrow pointing right shows the opposite. Similar results have been reported at LAO/STO(001) interfaces [47]. The property of the $R\left(B\right)$ curves suggests the coexistence of superconductivity and ferromagnetism at the LAO/STO(110) interfaces.