Interior and Edge Magnetization in Thin Exfoliated CrGeTe3 Films.

CrGeTe3 (CGT) is a semiconducting vdW ferromagnet shown to possess magnetism down to a two-layer thick sample. Although CGT is one of the leading candidates for spintronics devices, a comprehensive analysis of CGT thickness dependent magnetization is currently lacking. In this work, we employ scanning SQUID-on-tip (SOT) microscopy to resolve the magnetic properties of exfoliated CGT flakes at 4.2 K. Combining transport measurements of CGT/NbSe2 samples with SOT images, we present the magnetic texture and hysteretic magnetism of CGT, thereby matching the global behavior of CGT to the domain structure extracted from local SOT magnetic imaging. Using this method, we provide a thickness dependent magnetization state diagram of bare CGT films. No zero-field magnetic memory was found for films thicker than 10 nm, and hard ferromagnetism was found below that critical thickness. Using scanning SOT microscopy, we identify a unique edge magnetism, contrasting the results attained in the CGT interior.

Introduction

Layered van der Waals (vdW) ferromagnets have recently been the focus of intensive research due to the easily accessible broad thickness range they offer, from the bulk material all the way to atomically thin two-dimensional (2D) crystals, enabled by exfoliation. While the revolution triggered by the vdW materials is well underway,[1−4] the emerging field of 2D vdW spintronics is still in its infancy.[5−7] The need for compatible materials with long-range ferromagnetic order and precise analysis of such materials are at the core of this new emerging field. The evolution of the magnetic properties from bulk material to thin exfoliated layers may offer additional insight into the origin of ferromagnetism in vdW materials, where anisotropy was suggested[8] to originate from distinct interlayer and intralayer exchange interactions. Exfoliating bulk vdW ferromagnets, either conducting such as Fe3GeTe2 (FGT)[9] or semiconducting such as CrGeTe3 (CGT)[8] and CrI3[10] has revealed that ferromagnetism can survive down to the few layers regime where the Mermin–Wagner theorem asserts long-range ordering should be suppressed by thermal fluctuations in the absence of magnetic anisotropy.[11] Such anisotropy is manifested as out-of-plane (OOP) easy axis magnetization for both FGT[12] and CGT.[13,14] Ferromagnetism in those materials was mostly characterized using Anomalous Hall effect (AHE) measurements (that cannot be applied to the insulating CGT)[9,15−17] and SQUID (superconducting quantum interference device) magnetometry,[12,13,18] which average over the whole sample, or by local probes such as Kerr rotation,[8] low-temperature magnetic force microscopy (MFM),[12] X-ray magnetic circular dichroism (XMCD),[18] and NV-centers.[19] The local probe methods are highly effective for investigating edge magnetization in vdW materials, an issue that has recently attracted considerable interest.

In our present work we utilize scanning SQUID-on-tip (SOT), with high spatial resolution[20−22] and single-electron magnetic moment sensitivity,[23,24] in combination with transport measurements of CGT/NbSe2 bilayers, to provide an accurate thickness dependence of the magnetic properties of CGT flakes. Our results show that the magnetic characteristics at the flake’s edges is different from its interior. The thickness dependence of the film’s magnetic behavior can offer a control mechanism that could be used in giant magnetoresistance-like devices.

Results

CGT/NbSe2 Bilayer

Probing the magnetic properties of ferromagnetic materials using electrical measurements such as AHE is a powerful method to study samples that are too small to be characterized by bulk magnetization techniques. However, insulating materials such as CGT are not compatible with electrical measurements. Hence, so far the magnetism of CGT was characterized only indirectly by carrying out transport measurements on a conducting layer coupled to CGT, including induced AHE in proximitized Pt,[16] topological insulator (TI),[17] and through magnetoresistance hysteresis in a ferromagnet/superconductor CGT/NbSe2 bilayer.[25]

The CGT/NbSe2 sample presented in Figure consists of ∼30 nm CGT flake placed on a ∼30 nm NbSe2 exfoliated on top of prepatterned Au contacts (see Figure S6). Figure a presents the longitudinal resistance (R) of the NbSe2 flake with constant current I = 250 μA as a function of the out-of-plane (OOP) magnetic field μ0H at 4.2 K. In this magnetoresistance measurement, μ0H was ramped up from 0 to 130 mT (blue curve) and ramped down back to 0 (red curve). A clear hysteresis is evident between μ0H = 40 mT and μ0H = 80 mT, where a switching between the dissipationless and resistive states occurs, consistent with previous measurements reported in ref (25), yet its origin was not explained.

Figure 1

CrGeTe3/NbSe2 magnetoresistance and corresponding SOT images at 4.2K. (a) R measurements of the NbSe2 layer as a function of out-of-plane (OOP) magnetic field μ0H while applying current I = 250 μA and sweeping the field up/down (blue/red). Left inset: Schematic illustration of the bilayer below the demagnetization field Hd = 40 mT in the enhanced vortex pinning state. Stationary vortices are depicted in orange. Right inset: Same as left but above Hd in the vortex flow (finite R) state. (b–g) Sequence of magnetic images of the OOP component of the local magnetic field B(x,y) of different states of CGT at distinct values of μ0H acquired simultaneously with transport data in (a) (labeled black dots). (b–d) B (x,y) images acquired sweeping up the field at μ0H values of (b) 0, (c) 85, and (d) 130 mT. (e–g) B(x, y) images acquired sweeping the field down μ0H = (e) 50, (f) 40, and (g) 0 mT. All images are 1 × 1 μm2 in size (pixel size = 20 nm); acquisition time 5 min/image. The blue to red color scale represents lower and higher magnetic fields, respectively, with a shared scale of B = (b, g) 1 mT and (c–f) 5 mT. See Supplementary Movie 1.

To gain better insight into the origin of this hysteretic behavior, we conduct local magnetic field imaging B(x,y) using a scanning SOT, aiming to correlate the local magnetic structure of the CGT flake and the magnetoresistance hysteresis of the bilayer. The SOT measurements were simultaneously carrying out with the transport using SOT with loop diameter ranging from 155 to 180 nm (see Methods and Supplementary Note 1). Figure b presents a SOT image of the CGT sample measured at a distance of ∼100 nm above the sample for μ0H = 0. The image resolves magnetic domain features sized lower than the tip diameter (155 nm), yielding a magnetic contrast of ∼1 mT. With increasing OOP field, domains parallel to the field grow at the expense of the antiparallel domains (Figure b–d and Supplementary Movie 1). Above the saturation field, μ0Hs ∼ 100 mT, the magnetic landscape becomes smooth with a weaker contrast. These results are consistent with the transport and global magnetization measurements of Pt/CGT(65 nm) bilayers[16] as well as with the general behavior of bulk CGT.[13,26] By decreasing the field, the sample’s magnetic images remain featureless down to μ0H = 40 mT (Figure d,e and 1a, right inset), where magnetic domains reappear (Figure f and 1a, left inset).

A clear correlation emerges between the transport measurement and the magnetic images. The magnetic texture of the CGT flake (Figure b) is expected to provide local pinning potentials, inhibiting flux flow, which is manifested as the zero-voltage state (Figure a, blue curve prior to point c). Upon saturating the CGT magnetization (Figure c), the pinning potential flattens, allowing flux flow that generates dissipation and hence a finite voltage. Once CGT is fully magnetized (Figure a, right inset), the pinning potential is sufficiently uniform to yield uninhibited flux flow manifested in a linear magnetoresistance.[27] When reducing the field back from the saturation field, the linear magnetoresistance persists (Figure a, red curve), in agreement with the featureless images (Figure d,e). An abrupt formation of magnetic domains takes place at a demagnetization field, μ0Hd = 40 mT. Importantly, CGT’s demagnetization (Figure f) occurs simultaneously with the switching of the transport measurements back to the dissipationless state where vortices are pinned by the magnetic structure (Figure , left inset).

Our SOT images thus provide a clear evidence for the magnetic texture of CGT causing the hysteretic magnetoresistance observed on the CGT/NbSe2 bilayer (Figure a). Furthermore, due to the exact correlation between the transport measurements and the magnetic imaging, we demonstrate how the magnetoresistance of the CGT/NbSe2 bilayer could be used to globally probe the magnetic properties of the CGT flake.

It is worth noting that both the magnetic images and the transport measurement indicate magnetic hysteresis between μ0H = 40 mT and μ0H = 80 mT and that CGT demagnetizes at a positive field. Figure b,g shows a very similar domain structure at zero field both before and after the saturation field Hs was attained. However, the magnetic images alone cannot provide a definitive answer as to whether CGT holds any magnetization at zero field or whether CGT loses any magnetic memory in the absence of applied field. To describe the magnetic behavior near zero field, we saturated the sample by applying large opposite fields, μ0H = ±1 T, before changing the field back to zero and carrying out transport measurements and magnetic imaging between μ0H = 0 mT to μ0H = 130 mT (see Figure a). By employing this protocol, any memory that CGT might hold at zero field will be manifested as deviations in the magnetoresistance and magnetic imaging between the two excursions at either μ0H = +1 T or μ0H = −1 T. The two magnetoresistance curves presented in Figure a, taken after negative/positive excursions (blue/red curves) show no measurable difference between them. The magnetic images also appear to be insensitive to the change in initial conditions. Figure c–f show the same type of features as a function of the field as Figure g–j (Supplementary Movie 2). Both local (images) and global (transport) measurements show no measurable memory effect for ∼30 nm thick CGT.

Figure 2

SOT images and transport of bilayer CrGeTe3/NbSe2 showing no magnetic memory at μ0H = 0 at 4.2K. (a) Evolution of R as a function of the out-of-plane (OOP) field H from zero to above the saturation field Hs after an excursion to μ0Hexc = −1 T (blue) and μ0Hexc = 1 T (red). (b) Evolution of R from μ0H = μ0Hmin to μ0H > μ0Hs after applying OOP field μ0Hmax = 130 mT saturating the sample. μ0Hmin = 0, 20, 40, 60, 80, 100 mT. (Inset) History of H during R measurements shown in (b) with color corresponding to the segment color. Gray segments are not shown. (c–j) Sequence of magnetic images of different states of CGT at distinct H values. Evolution from μ0H = 0 mT to μ0H > μ0H after Hexc = −1 T (c–f) and Hexc = 1 T (g–j). μ0H = (c, g) 0, (d, h) 60, (e, i) 80, (f, j) 130 mT. All images are 1 × 1 μm2, pixel size is 20 nm and acquisition time 5 min/image. The blue to red color scale represents lower and higher magnetic fields, respectively, with a shared scale of B = (c, g) 1 and (d–f, h–j) 5 mT. See Supplementary Movie 2.

The measurements shown in Figure show that the ∼30 nm CGT flake retains magnetic memory and therefore is hysteretic only in the field range of μ0H = 40–80 mT. To verify that the sample loses memory at higher fields than zero, we ramped down the field between increasing minimal fields μ0Hmin = 0, 20, 40, 60, 80, and 100 mT while keeping the maximum field constant and above the saturation field μ0Hmax = 130 mT. An illustration of the measurement scheme is presented in the inset of Figure b. By not ramping down the field to zero, it is expected that more domains pointing with the field will act as nucleation centers to change the field at which the sample is fully magnetized.[28,29] The magnetoresistance curves are shown in Figure b. The transport measurements reveal that CGT is hysteretic only when μ0Hmin > 40 mT, i.e., CGT shows no measurable memory effect below μ0H = 40 mT, in excellent agreement with magnetic images that indicate 40 mT to be the demagnetization field.

The data presented in Figures and 2 show two key points: that ∼30 nm CGT does not present a macroscopic finite magnetization below Hd, and that the CGT flake globally demagnetizes abruptly at a field indicated by the local magnetic images (Figure f). Importantly, the magnetic images lend themselves to determine Hs and Hd even without the need of NbSe2 (or any other) metallic layer, as shown in the following.

Thickness Dependence of CGT Magnetization

We now turn to the thickness dependence of the saturation and demagnetization fields. We use the SOT to image areas of distinct thickness d on various CGT flakes (Figure a–l). For areas where d ≳ 10 nm, the magnetic images presented in Figure a–h are used to find the values of Hs and Hd. These values are then plotted in Figure m and connected to each other with a dashed line giving rise to a bowtie hysteresis loop (Figure m, top two sketched curves). Thinner films yield lower values of Hd and Hs. For d ≲ 10 nm, the two hysteretic parts of the loop merge and the sample behaves like a standard ferromagnet with an open hysteresis loop (Figure m, bottom curve). This is seen in Figure i and 3l where the sample stays fully magnetized at zero field, in contrast with thicker area of the flake where the sample demagnetizes (Figure a,d,e,h). A comprehensive thickness dependence on sketched magnetization curves for a broad range of CGT thicknesses is plotted in Figure S3. Transport measurements similar to those shown in Figures and 2 were carried out for a d < 10 nm CGT flake manifesting zero-field magnetization effect (See Supplementary Figure S11 and Note 4).

Figure 3

Scanning SOT microscopy images of CrGeTe3 for different thickness at 4.2 K. (a–l) Sequence of magnetic images B(x, y) of different states of the sample at distinct values of applied out-of-plane (OOP) field μ0H and sample thickness d. (m) Sketched magnetization curves drawn from B(x, y) measured on film’s parts of different d. Dashed lines are a guide to the eye connecting the two saturated fields. d = 70 nm (light blue), d = 17 nm (blue), d = 6 nm (dark blue). The fields at which the images were taken are marked with black dots. (n) A thickness-dependent magnetization-state diagram of CGT showing three states: domains (purple), hysteretic (orange), and magnetized (blue), Imaging parameters: (a–d) d = 70 nm, area scan 5 × 5 μm2, pixel size 40 nm. μ0H = (a) 0, (b) 115, (c) 175, (d) 0 mT. (e–h) d = 17 nm, area scan 2 × 2 μm2, pixel size 30 nm. μ0H = (e) 0, (f) 70, (g) 120, (h) 0 mT. (i–l) d = 6 nm, area scan 1 × 1 μm2, pixel size 30 nm. μ0H = (i) 0, (j) 20, (k) 120, (l) 0 mT. The blue to red color scale represents lower and higher magnetic fields, respectively, with a shared scale of B = 1 (a, c–e, h–l) and 5 (b, f, g) mT. See Supplementary Movies 3, 4, and 5, corresponding to panels c–f, g–j, and k–n, respectively. The scale bars in c, g and k apply to all images in the respective row. The x-axis labels of panels m and n are the same.

In Figure n, we summarize the values of Hd (green dots) and Hs (red dots) for all the imaged thicknesses. The lines connecting these points constitute borders between distinct magnetic states; the domains state (purple), the hysteretic state (orange), and the fully magnetized state (blue). In the domains state, CGT exhibits small magnetic domains that are insensitive to the excursion field, whereas the opposite holds for the fully magnetized region. In the hysteretic region, the sample can be either in the fully magnetized state or in the domains state depending on the applied magnetic field history.

The thickness dependence of CGT magnetization was measured here for pristine exfoliated single crystals. The recorded critical thickness for holding magnetization in zero field, ∼10 nm, is seemingly not in agreement with a few other AHE works conducted on CGT,[16,17,30] where thicker layers of CGT seem to attain magnetic memory at zero field (finite R at μ0H = 0). This might be because the above works all considered CGT proximitized to large spin orbit materials such as Pt[16] or topological insulators (TIs) such as Bi2Te3[17] or (Bi,Sb)2Te3.[30] Enhanced magnetism due to hybridization of an insulating ferromagnet to a TI was also seen in a EuS/TI bilayer.[31] Moreover, magnetic anisotropy is heavily generated due to the material spin orbit; hence, modifications of that property through proximity can adjust the magnitude of the magnetic anisotropy which, in turn, alters the magnetic properties of the ferromagnet interface.[32] We did not observe any influence on the magnetic structure due to the superconducting proximity effect from NbSe2 probably because of a small spatial gap at the interface (Figure S4) hindering such a proximity effect.

Edge Magnetization

Another possible explanation for the difference between our and previous results is that stronger magnetism is concentrated in small regions of the sample. These ferromagnetic regions might have been overrepresented in the AHE measurements carried out by other groups. With that potential contradiction in mind, we carefully imaged distinct areas of the sample. We discovered that for thick regions that show a bowtie hysteresis loop, i.e., when the flake interior breaks into domains at Hd, its edge retains a magnetic memory. In Figure , we present two sets of images measured at μ0H = 0 mT after OOP field excursion to |Hexc| > Hs±. Under these conditions, domains appear in the CGT interior, but the edge clearly holds the previous magnetization direction (negative or positive, blue or red in Figure ), determined by the polarity of previous excursion Hexc, showing only small fluctuations in B(x, y). The flake thicknesses presented in Figure are 17 nm (Figure a,c) and 24 nm (Figure b,d). The excursion fields magnetizing the sample were: Hexc = ± 1 T (Figure a,c) and Hexc = 200 mT (Figure b,d). For samples below the critical thickness, both edge and interior behave like a hard ferromagnet and no edge magnetization is visible (Figure S8).

Figure 4

Scanning SOT microscopy images of CrGeTe3 flake interior and edge at zero field and STEM images of the edge. (a–d) Sequence of magnetic images acquired on two different regions of the same flake after distinct field excursions. (a, b) Hexc < Hs–, (c, d) Hexc > Hs+. The areas thicknesses are d = 17 (a, c), 24 nm (b, d). (e, f) STEM cross-sectional images measured on the black lines presented in panels c and d, respectively, lines are not to scale. (g, h) Blue lines represent the average of the local magnetic field B(x, y) along the vertical (y) direction of panels c and d, respectively. Red lines represent the simulations of the edge magnetization stemming from magnetized edges with a trapezoid cross section, marked by green lines in panels e and f, respectively. Imaging parameters: μ0H = 0 mT, area scan 3 × 3 μm2 (pixel size (a, c) 31 and (b, d) 24 nm). The blue to red color scale represents lower and higher magnetic fields, respectively, with a shared scale for B = 1 mT.

To try to elucidate this surprising effect, we acquired the cross-sectional scanning transmission electron microscopy (STEM) images seen in Figure e,f. The images reveal both the exact thickness of the measured CGT flakes and the roughness of the edge. Importantly, the edge of the sample has a tapered cross-section, thinning over a lateral distance of 10–20 nm. The average B(x, y) calculated along lines in the vertical (y) direction as a function of x position in Figure c,d are presented as blue lines in Figure g,h, respectively. The average B(x) signal peaks at ∼0.55 and ∼0.38 mT (and similar values are found for opposite excursion fields), while the inner region remains below 0.25 mT.

Discussion

Our work shows that with decreasing thickness, the saturation field Hs diminishes as well as the demagnetization field Hd. This trend persists down to ∼10 nm, where for thinner flakes Hd crosses zero, thus enabling CGT to retain magnetic memory at zero field (Figure a,b). We note that the values of Hd and Hs were consistently observed in different areas of the same thickness irrespective of their lateral dimensions that ranged from a few micrometers to a few tens of micrometers. Finally, we also observe hard magnetism at the edges for samples above 10 nm (Figure b).

Figure 5

Illustration of the local magnetic structure at the edges and in the interior of CrGeTe3 flakes for different thicknesses. (a) Top panel, sketch of the magnetization loop. Bottom panel, local magnetic structure and the resulting out-of-plane magnetic image B(x, y) at zero applied field for samples thinner than 10 nm. (b) Same as in panel a but for a sample thicker than 10 nm. The edges retain their magnetization unlike the sample’s interior. The magnetization direction of the edge at zero field depends on the field history.

The vanishing remnant magnetization in zero field with increasing thickness is a phenomenon common to a number of vdW ferromagnetic materials.[33,34] The Hamiltonian describing thin OOP magnetized ferromagnets can be written as follows:[35]where J is the exchange integral, λ is the effective magnetic anisotropy, Ω is the strength of the dipole interaction, and , , and are the spatial functions of the magnetization. While J and λ correspond to local interactions stabilizing the spin magnetization, Ω is the long-range dipole interaction, making the single domain formation unstable with respect to the creation of stripe domains. Interestingly, when zero field cooling thick CGT flakes, stripe magnetization is observed (Figure S7), in agreement with the theoretical prediction in the limit where the dipolar interaction exceeds the magnetic anisotropy.[35] In the case of strong magnetic anisotropy λ or larger exchange interaction J, the stripe width increases exponentially with these values,[36] initiating an approach to the single domain phase. An accurate calculation of J, λ, and Ω as a function of CGT thickness was not carried out to date, though ab initio calculations of J and λ have shown qualitative agreement with experiments and were seen to change from the 2D to the bulk limit.[37]J, λ, and Ω are predicted to scale differently as a function of thickness,[38] thus inducing a transition from the fragmented domain formation in the thick limit to the hard ferromagnetism in the thin limit. A similar transition was seen for FGT[34] and was accounted for by the same model.[18]

We now discuss the edge magnetism (Figures and 5b). The STEM images in Figure e,f reveal a variation of the flake structure on the edge, where its thickness is substantially diminished. Due to the reduced dimensionality of the edge, it is reasonable to postulate that the thinner edge behaves as the thin CGT flake (<10 nm), thereby possessing finite magnetization at zero field (Figure b). On the basis of this conjecture, we carried out magnetostatic simulation of the field profile generated by the thin end of the flake, depicted as a right-angled triangle cross section of area 15 × 12 nm2. A saturation magnetization of 3 μB/Cr with a unit cell volume of 0.83 nm3[39] was assumed.[26] A convolution of the tip size with the generated stray field at the minimal possible working distance of the SOT (∼10 nm) generated an average field of 0.15–0.2 mT, smaller than the 0.38–0.55 mT measured on the edge, yet having the same direction. To better fit the measured data, the saturated section of the flake edge was increased to include a section of the thicker part of the flake as well as the thin edge, constituting trapezoid cross sections shown in Figure e,f. The simulated magnetism then fits well with the measured data, as can be seen by the red lines in Figure g,h. The simulation fitting yielded a distance of ∼100 nm between the SOT and the CGT surface, as expected. Thus, the simulation shows that the edge magnetism has a width of a few tens of nanometers. The fluctuations observed in B(x, y) may be due to local variations in the effective film thickness, owing to deformations associated with the edge roughness.

The magnetization at the edge could be explained by other mechanisms, related to the in-plane dangling bounds. If such mechanisms would be dominant, then one should find magnetism also at step-edges between two terraces above the critical thickness. The absence of magnetism at such step-edges (see Figure S9) suggests that this scenario is less probable. We also did not find any preferential oxidation at the flake edge which could account for magnetization there (Figure S10). The mechanism we propose above thus appears to be a plausible one, although others could also be considered.

In conclusion, the presented study demonstrates a direct relation between the global magnetization reading of CGT by the NbSe2, and the local domain structure. The control of the small size domain structure can be utilized to generate highly packed magnetic memory that can be probed by GMR or superconducting wires. Small changes in thickness and edge effects can enhance the memory complexity and external field tuning ability. This effect can be also used in a double-layered device with different thicknesses of CGT, where the thick layer will act as the soft magnet and the thinner layer as the hard magnet, which may be useful for spintronics applications.

Methods

Sample Fabrication

Bulk NbSe2 was purchased from graphene HQ. We grew CGT crystals using the flux method.[40,41] We introduced a mixture of Cr (99.99%), Ge (99.999%), and Te (99.999%) from Goodfellow in a ratio of 1:1:8 in a Canfield crucible set[42,43] and sealed it in a quartz ampule in an argon atmosphere. We heated it to 930 °C in 12 h and slowly cooled to 500 °C in 4 days. We removed the ampule from the furnace and rapidly spun the crystals to separate the CGT crystals from excess flux. We extracted large crystals, whose size was limited by the size of the crucible. The crystals have shiny surfaces and are plate like. X-ray scattering, magnetization, and resistance versus temperature measurements will be published elsewhere and are very similar to previous reports.[26,39]

CGT and CGT/NbSe2 bilayer samples were fabricated using the dry transfer technique,[44] carried out in a glovebox (argon atmosphere). NbSe2 and CGT flakes were cleaved using the scotch tape method, exfoliated on commercially available Gelfilm from Gelpack. For the transport measurements a NbSe2 flake was transferred onto prepatterned 50 nm thick Au electrodes fabricated using photolithography on a SiO2 substrate, and a CGT flake was subsequently transferred onto it. Both flakes were ∼30 nm thick as determined by atomic force microscopy measurements (Figures S2). The samples did not undergo heating or treatment in any solvents, deeming them pristine (other than naturally occurring oxidation upon removing the samples from the glovebox (see Supplementary Note 3 and Figure S4 and S5).

Transport Measurements

Transport measurements were carried out at 4.2 K inside a liquid helium dewar employing standard four-probe configuration, where the distances between the current (voltage) contacts were 15 μm (5 μm). Unless otherwise mentioned, a current bias of 250 μA was applied along the ab plane. A magnet consists of a standard SC coil was used to apply out-of-plane (OOP) magnetic fields up to ±1 T.

Scanning SQUID-On-Tip Microscopy

The SOT was fabricated using self-aligned three-step thermal deposition of Pb at cryogenic temperatures, as described in ref (23). Figure S1 shows the measured quantum interference pattern of one of the SOTs used for this work with an effective diameter of 155 nm and a maximum critical current of 105 μA. The asymmetric structure of the SOT gives rise to in slight shift of the interference pattern resulting a good sensitivity in zero field. All measurements were carried out at 4.2 K in low-pressure He of 1–10 mbar.