Anomalous thickness dependence of Curie temperature in air-stable two-dimensional ferromagnetic 1T-CrTe2 grown by chemical vapor deposition

The discovery of ferromagnetic two-dimensional van der Waals materials has opened up opportunities to explore intriguing physics and to develop innovative spintronic devices. However, controllable synthesis of these 2D ferromagnets and enhancing their stability under ambient conditions remain challenging. Here, we report chemical vapor deposition growth of air-stable 2D metallic 1T-CrTe2 ultrathin crystals with controlled thickness. Their long-range ferromagnetic ordering is confirmed by a robust anomalous Hall effect, which has seldom been observed in other layered 2D materials grown by chemical vapor deposition. With reducing the thickness of 1T-CrTe2 from tens of nanometers to several nanometers, the easy axis changes from in-plane to out-of-plane. Monotonic increase of Curie temperature with the thickness decreasing from ~130.0 to ~7.6 nm is observed. Theoretical calculations indicate that the weakening of the Coulomb screening in the two-dimensional limit plays a crucial role in the change of magnetic properties.

We selected CrCl2 as the Cr source due to its lower melting point compared to that of CrCl3 and Cr2O3, that can lower the growth temperature. The uniform optical contrast from OM images indicates high uniformity of the synthesized crystals (Supplementary Figure 1). The thickness of the resulting sample is very sensitive to the growth temperature. Similar observations were previously reported in the growth of NiTe2 1 .

Supplementary Figure 2. OM images of CVD grown 1T-CrTe 2 under different atmospheric conditions. (a)
The growth temperature was set at 983 K with 200 sccm pure argon as reaction atmosphere. (b -d) Grown under the same reaction condition as "a" but with additional hydrogen of 1 sccm, 5 sccm and 10 sccm, respectively. H2 is used to reduce sample thickness via slow-etching. As shown, the optical contrast is reduced when the hydrogen concentration increases. When the hydrogen concentration is higher than 10 %, no sample was synthesized. The thickness data from AFM can not only be mutually verified with that from crosssectional STEM-HAADF, but also be used to confirm the layered nature of 1T-CrTe2. In order to give a clear evidence, we found some samples with the top layer not completely covered, which has also been observed in the growth of other 2D materials 2,3 . The origin of multiple pits with trigonal symmetry may probably due to the layer by layer growth mechanism. The height profile extracted from AFM is about 0.62 nm which is comparable to that from cross-sectional STEM-HAADF and is in good accordance with the thickness of the unit cell of the 1T-CrTe2 crystal 4 .

Supplementary Figure 5. XPS characterization of as-grown 1T-CrTe 2 .
According to the XPS measurements, the binding energies for the Te 3d5/2 and 3d3/2 doublets are 574.4 eV and 582.8 eV, and those for the Cr 3p3/2 and 3p1/2 are 577.0 and 586.9 eV, respectively. The elemental analysis gives the empirical formula of CrTe2.

Supplementary Figure 6. Thickness-dependent Raman spectrum of 1T-CrTe 2 flakes in ambient atmosphere.
The Raman spectrum shows that there are two main characteristic peaks for 1T-CrTe2, each at 123.6 cm -1 (E2g) and 143.6 cm -1 (A1g) 5 . Thickness-dependent Raman measurement suggests that both modes show no obvious shift with increasing thickness, which is similar to that of VTe2 6 . Additionally, the Raman intensity is monotonically decreasing with increasing thickness from 2.0 nm to 20.0 nm, providing an intuitive method for qualitative evaluation of sample thickness.

Supplementary Figure 7. Environmental stability investigations. (a)
Optical images of 1T-CrTe2 samples exposed in the atmosphere for 0 day, 5 days, 7 days, 9 days, 10 days, 12 days, 14 days and 15 days, respectively. (b) AFM image of the sample being tested. (c) The corresponding Raman spectrum from a. (d) Humidity and temperature data during the test.
After 5 days exposure in air, the sample has unchanged color, morphology and the Raman intensity are comparable to that of the fresh one. When the exposure time extends to more than 10 days, the color and morphology of 1T-CrTe2 become lighter and rugged. The corresponding Raman signals decrease in intensity and ultimately vanish. Finally, after 15 days air-exposure, no Raman signals are detected, which indicated that the sample has degenerated. Ambient temperature and humidity conditions may have a significant impact on the stability investigations, thus we have also recorded the data simultaneously. It is worth noting that the VSM test can only obtain the averaged signal, and the thickness of the sample will significantly affect the signal obtained. Before processing the VSM/SQUID test, we statistically analyzed the thickness data of 1T-CrTe2 samples on a large scale, and use the sample thickness with the dominate percentage to name the sample.  Figure 11a, b, c). The calculated Tc for 40.0 nm thick 1T-CrTe2 crystals is ~ 170 K, while it is ~ 189 K in the thickness of 3.0 nm. The Tc increases as the sample thickness decreases (Supplementary Figure 11d) 7 , this trend is different from the recent reports on other two-dimensional ferromagnetic materials 8,9 . For the in-plane magnetic field, the magnetic transition only occurs in the relatively thick samples (Supplementary Figure 11 a, b), with no surviving remanence when the thickness reduces to a few layers. As shown in Supplementary Figure 11d Noting that the magnetic field has significant effect on the criticality and a proper magnetic field is very important for determining the Tc. Thus, we compared the resulted M-T curve under different magnetic fields. Meanwhile, the magnetic moment from inplane and out-of-plane has also been compared. Noting that the magnetic moment is normalized by the area. As shown in Supplementary Figure 12, the magnetic moment increases first and then decreases as the magnetic field increases at the same temperature. The extracted Tc at both in-plane and vertical magnetic field under a weaker magnetic field is slightly lower than that under a higher magnetic field. Thus, by comparing the values of magnetic moment and Tc under the three magnetic fields, we infer that 1300 Oe may be a suitable magnetic field. For all samples, the hysteresis loops shrink as the temperature going up and vanish at the magnetic transition point. The transition temperature from ferromagnetic phase to the paramagnetic state could be estimated from RMCD signal as a function of vertical magnetic field measured at several fixed temperatures. Figure 18. Zero-field remanent RMCD signal as a function of temperature for samples with different thicknesses. The solid lines are the least square fitting results of primary data using the formula: α(1 -T/Tc) β . Zero RMCD signal is indicated by the dotted line.

Supplementary
In order to obtain the critical point stringently, the Tc was extracted from the plots of temperature-dependent remanence of RMCD signal at zero field (Supplementary Figure 18) 12 . Note the criticality fits are only accurate in the vicinity of the critical point, where the correlation length diverges. When we perform the fits, we start by fitting data very close to the Curie temperature and then progressively include more lower temperature data until the dates are all added. This cutoff ends up being 1 -/ c ≲ 0.25. The disappearance of magnetic signal in the 7.6 nm sample appears at around 212 K (Figure 4e in the main text), a prominent increase from the bulk value (d ~ 47.9 nm) of about 167 K (Figure 4f in the main text). This result, consistent with that of the previous SQUID and magneto-transport results, further confirms the anomalous thicknessdependent Tc in this material. Figure 19. The investigation of magnetic performance of 1T-CrTe 2 samples with and without encapsulation by RMCD. (a) OM image of the samples being tested. Samples with and without h-BN encapsulation are highlighted by a blue and light blue hexagon, respectively. (b, c) RMCD signal as a function of the out-ofplane magnetic field at different temperatures obtained in 1T-CrTe2 domains without and with encapsulation. (d) Corresponding zero-field remanent RMCD signal as a function of temperature for samples being tested. The solid lines are the least square fitting results of primary data using the formula: α(1 -T/Tc) β . Zero RMCD signal is indicated by the black dotted line.