Supercurrent reversal in ferromagnetic hybrid nanowire Josephson junctions

We report supercurrent transport measurements in hybrid Josephson junctions comprising semiconducting InAs nanowires with epitaxial ferromagnetic insulator EuS and superconducting Al coatings. The wires display a hysteretic superconducting window close to the coercivity, away from zero external magnetic field. Using a multi-interferometer setup, we measure the current-phase relation of multiple magnetic junctions and find an abrupt switch between $\pi$ and 0 phases within the superconducting window. We attribute the $0\text{−}\pi$ transition to the discrete flipping of the EuS domains and provide a qualitative theory showing that a sizable exchange field can polarize the junction and lead to the supercurrent reversal. Both 0 and $\pi$ phases can be realized at zero external field by demagnetizing the wire.

Figure 1

(a) Color-enhanced micrograph of a representative multi-interferometer device comprising ferromagnetic (target) and nonmagnetic (reference) nanowires. The insets show the schematic device layout and wire cross sections. (b) and (c) Differential resistance $R$ as a function of current bias $I$ and parallel external magnetic field $H_{\parallel }$ measured for the $j_2^{\mathrm{F}}$ junction sweeping $H_{\parallel }$ from (b) negative to positive and (c) positive to negative. $R$ is suppressed in a narrow, sweep-direction-dependent window away from $H_{\parallel }=0$. (d) Disorder-averaged induced magnetization ${\langle M\rangle }_{\xi }$ calculated using the random-field Ising model. $h_{\parallel }$ is a model parameter representing an external magnetic field. The junction superconducts only in a narrow hysteretic window (gray) around the coercive field $\pm h_{\mathrm{C}}$ and is otherwise normal.

Figure 2

Left panels: Schematics of the multi-interferometer device in various open and closed junction configurations with highlighted effective loop areas. Right panels: Corresponding current-phase relations represented by differential resistance $R$ measured as a function of current bias $I$ and flux-threading perpendicular magnetic field $H_{\perp }$ for (a) two ferromagnetic, (b) one ferromagnetic and one nonmagnetic, and (c) two nonmagnetic junctions. All junction configurations show effective-area-dependent, periodic switching current modulations in $H_{\perp }$.

Figure 3

(a) Differential resistance $R$ of $j_2^{\mathrm{F}}$ as a function of current bias $I$ and parallel external magnetic field $H_{\parallel }$ showing the superconducting window of the junction centered around $-21$ mT. The data were taken with $j_1^{\mathrm{F}}$, $j_3$, and $j_4$ depleted. (b) Switching current $I_{\mathrm{SW}}$ as a function of flux-threading perpendicular magnetic field $H_{\perp }$ measured for the $j_2^{\mathrm{F}}\text{−}{j}_3$ interferometer at decreasing $H_{\parallel }$ values. The magnetic junction switches abruptly from the $\pi$ to 0 phase around $-18$ mT as $H_{\parallel }$ is lowered. (c) Current-phase relation measured at ${\mu }_0{H}_{\parallel }=-17$ mT exhibits $I_{\mathrm{SW}}$ minimum at $H_{\perp }=0$, suggesting a $\pi$ junction. (d) Similar to (c) but in the 0-junction regime at ${\mu }_0{H}_{\parallel }=-19$ mT. All the data were taken after polarizing the wire at ${\mu }_0{H}_{\parallel }=100$ mT.

Figure 4

(a) Schematic illustration of the modeled junction and the corresponding density of states with the induced superconducting gap in the wire leads $\mathrm{\Delta }$ and a discrete state in the junction at energy $\varepsilon$, both spin split by an exchange field $h$. (b) Calculated supercurrent $I_{\mathrm{S}}$ as a function of the superconducting phase difference across the junction $\phi$ and $h$, showing a $0\text{−}\pi$ transition for $h\lesssim \mathrm{\Delta }$. (c) Energy of Andreev bound states (ABSs) in the junction as a function of $\phi$ in the 0 (left) and the $\pi$ (right) regimes. (d) ABS and continuum contributions to the total $I_{\mathrm{S}}$ as a function of $h$ at $\phi =\pi /2$ and $\varepsilon =0$. The two contributions have opposite signs for $h\lesssim \mathrm{\Delta }$, while the ABS contribution vanishes in the $\pi$ phase. Inset: $I_{\mathrm{S}}$ dependence on $\varepsilon$, where the white line is an analytic expression for the $0\text{−}\pi$ transition given in the Supplemental Material [51].

Figure 5

(a) Differential resistance $R$ as a function of current bias $I$ and flux-threading magnetic field $H_{\perp }$ measured for a $j_2^{\mathrm{F}}\text{−}{j}_3$ interferometer at zero parallel external field ($H_{\parallel }=0$) showing a $\pi$-shifted current-phase relation. The data were taken after polarizing the wire at ${\mu }_0{H}_{\mathrm{S}}=100$ mT and demagnetizing it at ${\mu }_0{H}_{\parallel }^{\mathrm{D}}=-23$ mT. (b) Similar to (a) but taken after demagnetizing the wire at ${\mu }_0{H}_{\parallel }^{\mathrm{D}}=-25$ mT, showing 0-junction behavior. (c) Calculated disorder-averaged induced magnetization ${\langle M\rangle }_{\xi }$ illustrating the experimental demagnetization scheme. After saturating ${\langle M\rangle }_{\xi }$, the parameter representing the external magnetic field $h_{\parallel }$ is swept to the variable demagnetization value $h_{\parallel }^{\mathrm{D}}$, and then back to 0. Depending on $h_{\parallel }^{\mathrm{D}}$, the junction can either relax to the $\pi$ or 0 phase.