Magnetic texture modulated superconductivity in superconductor/ferromagnet shells of semiconductor nanowires

TL;DR

The study addresses how magnetic texture in a ferromagnet–superconductor shell modulates superconductivity in semiconductor nanowires. By combining scanning SQUID magnetometry imaging of the EuS shell with low-temperature transport in fully coated InAs/EuS/Al nanowires, the authors map when superconductivity in the Al shell appears as a function of field magnitude and orientation. They find superconductivity arises only in multi-domain EuS states near coercivity, compatible with both domain-wall superconductivity (DWS) and multi-domain-averaged superconductivity (MDAS), with micromagnetic simulations supporting the coercivity–superconductivity link though a single mechanism cannot be singled out. The work demonstrates magnetic-texture–tunable superconductivity and suggests reconfigurable phase control via movable domain walls, with potential applications in topological qubits, Andreev spin qubits, and superconducting logic.

Abstract

In a one-dimensional ferromagnet-superconductor nanowire, magnetism can suppress superconductivity except where the Zeeman field is suppressed, for example domain wall superconductivity (DWS) near magnetic domain walls or multi-domain-averaged superconductivity (MDAS) in multi-domain states where the net magnetization over the coherence length averages to nearly zero. Here we study full-shell InAs/EuS/Al nanowires using scanning SQUID magnetometry and transport, and find superconductivity in the Al shell only when the EuS is in a multi-domain state, consistent with both DWS and MDAS, and absent in the saturated single-domain state. Scanning SQUID magnetometry further shows that the EuS magnetic texture is position dependent and reconfigurable by small changes in external magnetic field, including moving a well-defined domain wall at $\approx$5.5 $μ$m/mT with sub-mT fields, implying that any associated localized superconducting region would likewise be movable. Such magnetic texture controlled superconductivity along a nanowire may be useful for topological qubits, Andreev spin qubits, superconducting logic, and memory devices.

Figures (6)

• Figure 1: Domain wall superconductivity in a full-shell InAs/EuS/Al nanowire. Schematic of a hexagonal nanowire with an InAs core, EuS ferromagnetic layer, and outer Al shell. The two offset planes show two plausible EuS magnetic textures in which superconductivity can survive in the Al, with the color scale indicating the EuS magnetization component along the nanowire axis, $M_z$. The lower plane has two oppositely magnetized domains ($M_z = \pm 1$) separated by a single magnetic domain wall (MDW), while the upper plane illustrates a multi-domain EuS state with many small $+M_z$ and $-M_z$ domains. A blue surface plot overlaid on the upper plane represents the superconducting order-parameter magnitude $|\Psi|$ in the Al, which is finite only where the Zeeman field from the EuS vanishes or averages to near zero over the Al coherence length, either locally at an MDW or in a multi-domain-averaged superconducting (MDAS) region, where many small EuS domains produce a near-zero net magnetization and is suppressed in regions of nearly uniform magnetization.
• Figure 2: Magnetic texture modulated superconductivity and SQUID magnetometry of domain formation in the EuS shell of an InAs/EuS/Al full-shell nanowire NW1.a Schematic of a nanowire, shown as a thin blue cylinder, with the expected field lines in a fully magnetized, single-domain configuration. The scanning SQUID maps the out-of-plane magnetic flux through its pick-up loop, and the measured flux appears as two lobes of opposite sign at the wire ends. b--j Scanning SQUID magnetometry images as the field along the nanowire is swept from $0 \to +8$ mT, $+8 \to -8$ mT, and then $-8 \to 0$ mT. Next to h, i, and j we show conceptual sketches of plausible magnetization configurations in the EuS shell. The sketches next to h and i illustrate two alternative configurations that could each account for the similar SQUID images in both panels. These schematics are not to scale and represent only the central portion of the nanowire. k Sketch of the corresponding hysteresis loop, showing the nanowire’s normalized axial magnetic moment $\tilde{m}_\text{z}$ versus the applied axial field $H_\mathrm{a}$. The circles are computed from the SQUID images, as described in the End Matter, and the dashed curve is a guide to the eye for the conceptual $\tilde{m}_\text{z}$--$H_\text{a}$ curve. All scans are taken at 4.2 K.
• Figure 3: Bulk transport measurements on an InAs/EuS/Al full-shell nanowire while sweeping a magnetic field $H_\text{a}$ parallel to the wire.a False-color scanning electron micrograph of a nanowire with transport contacts (1--6). b Four-terminal differential resistance $\mathrm{d}V/\mathrm{d}I(I, H_\text{a})$ of segment A after zero-field cooling, for $H_\text{a}$ swept from 0 $\to$ +100 mT. A low-resistance region appears near zero field and vanishes at an annihilation field $H_\text{ann}$, which we interpret as a superconducting phase. c,d$\mathrm{d}V/\mathrm{d}I(I, H_\text{a})$ for field sweeps (c) +70 mT $\to$$-$70 mT and (d) $-$70 mT $\to$ +70 mT. Superconductivity is confined to a narrow field window, nucleating at $H_\text{n}$ and disappearing at $H_\text{ann}$, which we associate with the coercive field. Green and pink arrows indicate sweep directions. Insets in (c) show plausible single-domain magnetization configurations in the EuS shell as $H_\text{a}$ is swept to saturation in either direction. The inset in (d) shows zero-bias $\mathrm{d}V/\mathrm{d}I$ as a function of $H_\text{a}$ for both field-sweep directions. e$\mathrm{d}V/\mathrm{d}I(I)$ line cuts from (d) at $H_\text{a} = 11$, 13, and 17 mT. All data are taken at 30 mK.
• Figure 4: Field angle dependence of the superconducting phase in InAs/EuS/Al full-shell nanowires.a--m SQUID magnetometry images of domain formation in the EuS shell in NW2 at three field angles, $\varphi=0.03\pi$, $0.36\pi$, and $0.5\pi$. $\varphi$ is the angle between the applied field and the nanowire axis. For each $\varphi$, $H_\text{a}$ is swept from $0 \to +8$ mT, $+8 \to -8$ mT, and $-8 \to 0$ mT. These images show how domain nucleation and propagation depend on field angle: as $\varphi$ increases, the coercive field window and the saturation field shift to higher values, and the coercive-field window broadens. These scans are taken at 4.2 K. n Field angle dependence of the differential resistance $\mathrm{d}V/\mathrm{d}I$. Left$\mathrm{d}V/\mathrm{d}I(I,H_\text{a})$ colormaps at different $\varphi$, shown in vertically stacked panels. Two columns correspond to opposite field sweep directions of indicated by pink and green arrows on the bottom plots. With increasing field angle the superconducting region shifts to larger fields and persists over a larger field window. Right Zero-bias $\mathrm{d}V/\mathrm{d}I(\varphi,H_\text{a})$ colormap with the sweep direction indicated on the $H_\text{a}$ axis. The color scale is common to all plots. The red curve overlaid on the measured data is the simulated $H_\mathrm{c} (\varphi)$ of the EuS nanotube shell. All measurements are done on segment B of the transport device (Fig. \ref{['Fig3']}a) at 30 mK.
• Figure 5: Additional transport measurements on InAs/EuS/Al full-shell nanowire devices while sweeping an applied magnetic field and field angle.