Intrinsic Magnetic (EuIn)As Nanowire Shells with a Unique Crystal Structure

In the pursuit of magneto-electronic systems nonstoichiometric magnetic elements commonly introduce disorder and enhance magnetic scattering. We demonstrate the growth of (EuIn)As shells, with a unique crystal structure comprised of a dense net of Eu inversion planes, over InAs and InAs1–xSbx core nanowires. This is imaged with atomic and elemental resolution which reveal a prismatic configuration of the Eu planes. The results are supported by molecular dynamics simulations. Local magnetic and susceptibility mappings show magnetic response in all nanowires, while a subset bearing a DC signal points to ferromagnetic order. These provide a mechanism for enhancing Zeeman responses, operational at zero applied magnetic field. Such properties suggest that the obtained structures can serve as a preferred platform for time-reversal symmetry broken one-dimensional states including intrinsic topological superconductivity.

and an inner collection angle of 70.0 mrad. EDS hyperspectral data were obtained with a Super-X G2 four-segment SDD detector with a probe semi-convergence angle of 30 mrad and a beam current of approximately 200 pA. The EDS hyperspectral data was quantified using the Velox software (Thermo Fisher Scientific Electron Microscopy Solutions, Hillsboro, USA), by background subtraction and spectrum deconvolution. Nanobeam electron diffraction data was taken in scanning mode on an EMPAD hybrid-pixel detector with a beam semiconvergence angle of 0.19 mrad.
To examine a core/shell cross-sectional structure of NWs, lamella preparation was done using a thick lift-out procedure (Helios 600 FIB/SEM Dual Beam Microscope, Thermo Fisher Scientific). The lamella (~50 nm thick) was placed on a TEM grid and analyzed by EDS mapping in order to obtain the radial composition across the NWs diameter.
To understand why the shell with Eu ions forms much better on the ZB core structures than on WZ, the Lammps Molecular Dynamics simulation package was used to model Eu incorporation at the side facets of NW.
We used scanning superconducting quantum interference device (SQUID) microscopy to search for magnetic signals from the NWs. A SQUID functions as a magnetic flux to voltage converter, allowing sensitive detection of magnetic fields 4 . The planar SQUID, in scanning configuration, allows mapping of the static magnetic field, and the local susceptibility 5 . The sensitive area of the SQUID used in this work, the pickup loop, has a diameter of 1.5 µm. Local susceptibility is measured using an on-chip coil to apply magnetic field (the field-coil, operated at ~kHz, applies ~Gauss), while the pickup loop records the local response to the applied magnetic field. The positive signal in our data indicates a paramagnetic response. These two measurements were performed simultaneously and plotted in units of Tesla (magnetism, Phi_0 normalized by the sensitive area), and Tesla/Ampere (susceptibility, Phi_0 normalized by the sensitive area and the current in the field-coil).

(EuIn)As on WZ InAs
As discussed in the main text we launched the Europium project by evaporating (EuIn)As on the sides of reclining WZ InAs nanowires (NWs). The coating thus formed is extremely rough.
Slight bending of the wires towards the substrate can be observed. In this section of the supplementary information we present a bird's eye view SEM image of an as grown sample, a TEM image of the side of a single NW and a summary of EDS data collected from an as grown NW as well as a lamella cross section prepared from such a sample. To the best of our knowledge the unique mosaic structure exposed by TEM data, was never before observed in III-V NWs.

(EuIn)As on Stalactite InAs NWs EDS Mapping
As indicated in the main text, the observation of a smooth (EuIn)As coating on vertical <001> oriented stalactite NWs formed at the intersections, was the driving force for switching from WZ to ZB core NWs 2 . This can be observed in both SEM and TEM images of the stalactite NWs, which are predominantly ZB. Yet the same structure which characterizes the (EuIn)As shell grown on WZ NWs is typical of the stalactite ones. This can be noticed even in the low magnification HADAF and TEM images. Two such images are presented in Figure SI

(EuIn)As on ZB InAs 1-x Sb x NWs
To improve the smoothness of the (EuIn)As shell grown on InAs we switched to growth of core NWs of InAs 1-x Sb x with a small concentration of antimony (5-7 atomic percent) 6,7 . This assured the ZB structure of the core NWs and their high aspect ratio and thus the smoothness of the (EuIn)As shell. In this section we add information on the ZB core InAs 1-x Sb x NWs and the shell formed (Figure SI(5)), with typical bending of the NWs away from the substrate.
Respective EDS mappings is shown in Figure SI (6). The effect of the crystal structure of the core on the (EuIn)As is also seen in the 45° SEM image which is taken on several different core NW. This clearly shows the difference in the (EuIn)As morphology over different cores.

Modeling (EuIn)As NW by molecular dynamics simulations
The core of the NW was prepared by setting In and As atoms initially at the sites of the WZ lattice. The NW was oriented in [0001] direction with six { } side surfaces. This WZ stem 1100 was 12 InAs bilayers high. Then, [111] orientated 12 bilayers high ZB NW was positioned on top of the WZ structure. The ZB NW has also six side walls, { } oriented. The results of the 011 simulation presented in the main body of the paper were obtained for this, shown in Figure   SI(7) a, initial structure. Several other initial structures have been considered, e.g., the one with twelve side walls shown in Figure SI  Two layers of As and Eu atoms were added at opposite sides of the NW, moved away from it by 30 interatomic distances. The structure was first minimized, then Lammps program was used for the Molecular Dynamics simulations. Interactions σ of Lennard-Jones 6-12 type were set between atoms. The parameters for σ reflect the length of the interatomic distance in the lattice, for ε the melting temperature. Thus, we have: σ = 2.3A for In-As interaction, 2.7A for Eu-As, and 4.2A for As-Eu, whereas for As-As, In-In and Eu-Eu pairs we used 3.8A. The depth of energy, ε, was set 0.15 eV for InAs, 0.14eV for EuAs and 0.07eV for EuIn, while all other pair interactions have strength 0.1eV. We took velocities from Boltzmann distribution at 600K, and 2•10 6 simulation steps were run at this temperature. Then, the temperature was decreased successively by 100K and in each temperature 2•10 6 simulation steps were run again. The whole simulation was ended at 300K. The results are indeed very interesting. First, an attachment of As atoms to the NW was observed. A reconstruction of the side facets also takes place, and finally in the ZB part of the NW { } surfaces appear between the { } oriented.

110
Next, Eu atoms stick mainly to the side surfaces, but some of them get attached also on top or at the bottom of NW. As shown in Fig. SI(8), in contrast to the WZ ( ) surfaces the ( )-1100 211 oriented ZB surfaces contain {111} terraces, on which the Eu atoms can attach and regular layers of Eu can develop. This is possible only for one surface polarity, which is compatible with the mutual arrangement of In and As layers in the EuIn 2 As 2 crystal 8 . In order to check whether initial orientation of side walls makes a difference, another type of core NW with 12 different side facets (6 { } and 6 { }) was prepared, as shown in Fig.  110 211 SI(7) b. The final effect was very similar (see Fig. SI(9) a). An impact of other conditions was also checked. Starting the simulations with 900 K caused melting of the structure and different geometry after cooling. We decided therefore to set the initial temperature to 600K. Then, several cooling procedures were tried, faster or slower, and they didn't change much the result.
Finally, we checked different initial positions for the free adatoms -either closer or further to the side walls of NW but also on top and at the bottom of the NW. Again we haven't noticed much difference between the simulation results (see Fig. SI(9) b). We note only that at the beginning it was good to keep the Eu and As atoms far apart, because otherwise they tend to create crystal by themselves.  (7) b, i.e., with twelve side facets; (b) the initial positions for the free Eu and As adatoms at the top of the core NW with six side facets, the one shown in Fig. SI(7) a. See Movie 1.
The morphology of the (EuIn)As shell relates to the structure of the core, having a ZB or WZ structure, or single/multiple twin planes.
Figure SI(10): Bird's eye view image of a variety of (EuIn)As core/shell NWs emphasizing the role of the structural properties of the core. The smooth surface coating of (EuIn)As on ZB NWs is evident, as well as the rough coating of the WZ stems. The effect of single twin plane (STP) or a twinning superlattice (TSL) on the shell can be clearly seen as well.