Nanoscale Electrostatic Manipulation of Magnetic Flux Quanta in Ferroelectric/Superconductor ${\mathrm{BiFeO}}_3/{\mathrm{YBa}}_2{\mathrm{Cu}}_3{\mathrm{O}}_{7-\delta }$ Heterostructures

Using heterostructures that combine a large-polarization ferroelectric (${\mathrm{BiFeO}}_3$) and a high-temperature superconductor (${\mathrm{YBa}}_2{\mathrm{Cu}}_3{\mathrm{O}}_{7-\delta }$), we demonstrate the modulation of the superconducting condensate at the nanoscale via ferroelectric field effects. Through this mechanism, a nanoscale pattern of normal regions that mimics the ferroelectric domain structure can be created in the superconductor. This yields an energy landscape for magnetic flux quanta and, in turn, couples the local ferroelectric polarization to the local magnetic induction. We show that this form of magnetoelectric coupling, together with the possibility to reversibly design the ferroelectric domain structure, allows the electrostatic manipulation of magnetic flux quanta.

Figure 1

(a) AFM of the multiprobe measurement bridge. (b) HRTEM of a $\mathrm{BFO}(30\mathrm{nm})/\mathrm{YBCO}(5\mathrm{u}.\mathrm{c}.)//\mathrm{STO}$ heterostructure. (c) Local out-of-plane piezoresponse phase hysteresis loop. (d) PFM phase image in the pristine state (prior to poling). (e) PFM phase image after the area in between the voltage probes has been poled up, for a sample with $t_{\mathrm{YBCO}}=3\mathrm{u}.\mathrm{c}.$

Figure 2

(a) $R(T)$ normalized to the resistance at $T=150\mathrm{K}$ of a heterostructure with $t_{\mathrm{YBCO}}=3\mathrm{u}.\mathrm{c}.$ measured with $J=1.7\mathrm{kA}·{\mathrm{cm}}^{-2}$ for two neighboring areas in which the BFO polarization points down [left-hand (blue) curve] and up [right-hand (red) curve]. The inset shows schematics of the charge carrier depletion or accumulation induced in the YBCO by the ferroelectric polarization (white arrows). (b) $T_C$ vs charge carrier density $n$ for samples with different $t_{\mathrm{YBCO}}$ (see legend in u.c.), for the “depleted” (hollow symbols) and “doped” (solid symbols) states. Inset: modulation of the $T_C$ vs carrier density modulation $\Delta n$. The labels indicate $t_{\mathrm{YBCO}}$ in u.c.

Figure 3

(a) PFM phase image of the ferroelectric nanodomain array A, defined in the BFO layer of a heterostructure with $t_{\mathrm{YBCO}}=3\mathrm{u}.\mathrm{c}.$ The array plaquette is a parallelogram with $b=157\pm 3\mathrm{nm}$, $a=195\pm 3\mathrm{nm}$, and base angle $\alpha =104.0°\pm 0.5°$. (b) Same for array B in a heterostructure with $t_{\mathrm{YBCO}}=4\mathrm{u}.\mathrm{c}.$, with $b=143\pm 3\mathrm{nm}$, $a=113\pm 3\mathrm{nm}$, and $\alpha =106.0°\pm 0.5°$. (c) Resistance (normalized to the zero-field one) vs applied field at $T=1.05T_C$ and with injected current density $J=8.7\mathrm{kA}·{\mathrm{cm}}^{-2}$ for a heterostructure with $t_{\mathrm{YBCO}}=3\mathrm{u}.\mathrm{c}.$, in the case in which the periodic ferroelectric array A is present [dark (black) curve] and after this has been erased [light (red) curve] at $T=0.94T_C$. (d) Resistance (normalized to the zero-field resistance) vs field applied perpendicular to the film plane for a heterostructure with $t_{\mathrm{YBCO}}=4\mathrm{u}.\mathrm{c}.$, at a $T=0.99T_C$ and with $J=3.3\mathrm{kA}·{\mathrm{cm}}^{-2}$, in the case in which the periodic ferroelectric array B is present [dark (black) curve]. The vertical lines point out the matching fields. (e) $R(H)$ in the presence of the periodic array A, with $H$ applied at different angles $\theta =0°$, $30°$, $45°$, $60°$, and $70°$ (top to bottom) with respect to the $c$ axis (see sketch). The vertical lines point out the matching fields for the different $\theta$. (f) Matching field $H_1$ as a function of $1/\cos (\theta )$ for the array A (squares) and B (circles). The straight line is the best linear fit. Inset: schematics of the periodic charge carrier depletion/accumulation and $T_C$ modulation induced by the structure of ferroelectric domains.