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 Fe 3 GeTe 2 (FGT) 9 or semiconducting such as CrGeTe 3 (CGT) 8 and CrI 3 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/NbSe 2 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/NbSe 2 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/NbSe 2 bilayer. 25 The CGT/NbSe 2 sample presented in Figure 1 consists of ∼30 nm CGT flake placed on a ∼30 nm NbSe 2 exfoliated on top of prepatterned Au contacts (see Figure S6). Figure 1a presents the longitudinal resistance (R xx ) of the NbSe 2 flake with constant current I x = 250 μA as a function of the out-ofplane (OOP) magnetic field μ 0 H z at 4.2 K. In this magnetoresistance measurement, μ 0 H z was ramped up from 0 to 130 mT (blue curve) and ramped down back to 0 (red curve). A clear hysteresis is evident between μ 0 H z = 40 mT and μ 0 H z = 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.
To gain better insight into the origin of this hysteretic behavior, we conduct local magnetic field imaging B z (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 1b presents a SOT image of the CGT sample measured at a distance of ∼100 nm above the sample for μ 0 H z = 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 1b−d and Supplementary Movie 1). Above the saturation field, μ 0 H s ∼ 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 A clear correlation emerges between the transport measurement and the magnetic images. The magnetic texture of the CGT flake (Figure 1b) is expected to provide local pinning potentials, inhibiting flux flow, which is manifested as the zerovoltage state (Figure 1a, blue curve prior to point c). Upon saturating the CGT magnetization (Figure 1c), the pinning potential flattens, allowing flux flow that generates dissipation and hence a finite voltage. Once CGT is fully magnetized (Figure 1a, 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  1a, red curve), in agreement with the featureless images ( Figure 1d,e). An abrupt formation of magnetic domains takes place at a demagnetization field, μ 0 H d = 40 mT. Importantly, CGT's demagnetization ( Figure 1f) occurs simultaneously with the switching of the transport measurements back to the dissipationless state where vortices are pinned by the magnetic structure ( Figure 1, left inset).
Our SOT images thus provide a clear evidence for the magnetic texture of CGT causing the hysteretic magnetoresistance observed on the CGT/NbSe 2 bilayer (Figure 1a). Furthermore, due to the exact correlation between the transport measurements and the magnetic imaging, we demonstrate how the magnetoresistance of the CGT/NbSe 2 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 μ 0 H z = 40 mT and μ 0 H z = 80 mT and that CGT demagnetizes at a positive field. Figure 1b,g shows a very similar domain structure at zero field both before and after the saturation field H s 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, μ 0 H z = ±1 T, before changing Nano Letters pubs.acs.org/NanoLett Letter the field back to zero and carrying out transport measurements and magnetic imaging between μ 0 H z = 0 mT to μ 0 H z = 130 mT (see Figure 2a). 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 μ 0 H z = +1 T or μ 0 H z = −1 T. The two magnetoresistance curves presented in Figure   2a, 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    The measurements shown in Figure 1 show that the ∼30 nm CGT flake retains magnetic memory and therefore is hysteretic only in the field range of μ 0 H z = 40−80 mT. To verify that the sample loses memory at higher fields than zero, we ramped down the field between increasing minimal fields μ 0 H min = 0, 20, 40, 60, 80, and 100 mT while keeping the maximum field constant and above the saturation field μ 0 H max = 130 mT. An illustration of the measurement scheme is presented in the inset of Figure 2b. 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 2b. The transport measurements reveal that CGT is hysteretic only when μ 0 H min > 40 mT, i.e., CGT shows no measurable memory effect below μ 0 H z = 40 mT, in excellent agreement with magnetic images that indicate 40 mT to be the demagnetization field.
The data presented in Figures 1 and 2 show two key points: that ∼30 nm CGT does not present a macroscopic finite magnetization below H d , and that the CGT flake globally demagnetizes abruptly at a field indicated by the local magnetic images (Figure 1f). Importantly, the magnetic images lend themselves to determine H s and H d even without the need of NbSe 2 (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 3a−l). For areas where d ≳ 10 nm, the magnetic images presented in  (Figure 3m, bottom curve). This is seen in Figure 3i and 3l where the sample stays fully magnetized at zero field, in contrast with thicker area of the flake where the sample demagnetizes (Figure 3a,d,e,h). A comprehensive thickness dependence on sketched magnet-ization curves for a broad range of CGT thicknesses is plotted in Figure S3. Transport measurements similar to those shown in Figures 1 and 2 were carried out for a d < 10 nm CGT flake manifesting zero-field magnetization effect (See Supplementary Figure S11 and Note 4).
In Figure 3n, we summarize the values of H d (green dots) and H s (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 xx at μ 0 H z = 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 Bi 2 Te 3 17 or (Bi,Sb) 2 Te 3 . 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 NbSe 2 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 The blue to red color scale represents lower and higher magnetic fields, respectively, with a shared scale for B z = 1 mT. Nano Letters pubs.acs.org/NanoLett Letter 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 H d , its edge retains a magnetic memory. In Figure 4, we present two sets of images measured at μ 0 H z = 0 mT after OOP field excursion to |H exc | > H s ± . 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 4), determined by the polarity of previous excursion H exc , showing only small fluctuations in B z (x, y). The flake thicknesses presented in Figure 4 are 17 nm (Figure 4a,c) and 24 nm (Figure 4b,d). The excursion fields magnetizing the sample were: H exc = ± 1 T (Figure 4a,c) and H exc = 200 mT (Figure 4b,d). For samples below the critical thickness, both edge and interior behave like a hard ferromagnet and no edge magnetization is visible ( Figure S8).
To try to elucidate this surprising effect, we acquired the cross-sectional scanning transmission electron microscopy (STEM) images seen in Figure 4e

■ DISCUSSION
Our work shows that with decreasing thickness, the saturation field H s diminishes as well as the demagnetization field H d . This trend persists down to ∼10 nm, where for thinner flakes H d crosses zero, thus enabling CGT to retain magnetic memory at zero field (Figure 5a,b). We note that the values of H d and H s 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 5b).
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 ⃗ f x ( ), ⃗ g x ( ), and ⃗ h x ( ) 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 4 and 5b). The STEM images in Figure 4e,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 5b). 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 nm 2 . A saturation magnetization of 3 μ B /Cr with a unit cell volume of 0.83 nm 339 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 4e,f. The simulated magnetism then fits well with the measured data, as can be seen by the red lines in Figure 4g,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 z (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 NbSe 2 , 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 NbSe 2 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/NbSe 2 bilayer samples were fabricated using the dry transfer technique, 44 carried out in a glovebox (argon atmosphere). NbSe 2 and CGT flakes were cleaved using the scotch tape method, exfoliated on commercially available Gelfilm from Gelpack. For the transport measurements a NbSe 2 flake was transferred onto prepatterned 50 nm thick Au electrodes fabricated using photolithography on a SiO 2 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.
Additional experimental details and discussion such as SOT images at ZFC and edge of 6 nm CGT flake, magneto-transport measurements of CGT/NbSe 2 with d < 10 nm, movies of protocols present in the manuscript, optical, atomic force microscopy, STEM and EDX measurements of the main CGT flake used for the thickness dependence measurements, and information on the SOT parameters.