Hole‐Mediated RKKY Interaction in 2D Ferromagnetic CrTe2 Ultra‐Thin Films

The rapid development of 2D magnetic materials has opened new possibilities in the field of spintronics. CrTe2, a 2D material with perpendicular magnetic anisotropy (PMA) and ferromagnetic transient temperature near room temperature, holds promise for various applications. However, the underlying mechanism responsible for its global magnetism remains unclear. This work focuses on investigating the magneto‐transport properties of ultra‐thin CrTe2 Field Effect Transistor (FET) under the influence of top gate biases. The application of gate voltage ranging from 25 to −15 V tunes its coercivity (HC) and Curie temperature (TC) (from 152 to 191 K). Notably, a linear correlation is observed between the TC and the hole concentration ( np1/3$n_{\mathrm{p}}^{1/3}$ ) in the CrTe2 film, indicating the involvement of the Ruderman–Kittel–Kasuya–Yosida interaction. This experimental analysis sheds light on the mechanism of the CrTe2’s ferromagnetism and paves the way for future advancements and applications in this material.

In theory, it is generally believed that long-range ferromagnetic ordering is typically generated through two mechanisms.The van-Vleck mechanism relies on the large spin magnetic susceptibility of valence electrons to acquire global magnetism, [23] thus it is independent of the carriers.On the other hand, the Ruderman-Kittel-Kasuya-Yosida (RKKY) mechanism describes the interaction between adjacent magnetic ions through free electrons or holes, resulting in long-range ferromagnetic ordering that depends on the density of the free carriers. [24]he key to determining the dominant mechanism lies in verifying whether charge carriers actively contribute to the generation of global magnetism.
In this study, we have successfully grown high-quality epitaxial CrTe 2 thin films consisting of ten layers using molecular beam epitaxy (MBE).The thin film is then fabricated into a field effect transistor (FET) device.By applying gate voltages, the carrier concentrations in the conducting channel are adjusted according to the capacitive coupling effect. [25]As a result, the T C of the CrTe 2 film increased from 152 to 191 K when the gate voltage was tuned from 25 to −15 V, exhibiting a positive correlation with the hole densities.This result fits perfectly with the holemediated RKKY interaction. [26]The understanding of the ferromagnetic mechanism in CrTe 2 provides valuable insights for future voltage-controlled spintronic devices based on 2D magnetic materials.

Experimental Section
After performing surface cleaning of the GaAs (111)B substrate by sulfuric acid and acetone, it was placed inside the molecular beam epitaxy (MBE) chamber with a vacuum level below 2 × 10 −10 Torr.High-purity Chromium (Cr) and Tellurium (Te) elements were evaporated onto the substrate with a flux ratio of 1:20, at temperatures of 1200 and 260 °C, respectively, and the substrate temperature was kept at 600 °C.Real-time monitoring of the surface morphology was performed using reflection highenergy electron diffraction (RHEED).As depicted in Figure 1a, a flat GaAs (111)B surface was revealed before growth.After the This was consistent with previous reports. [27]Meanwhile, X-ray diffraction (using a single-crystal diffraction instrument with a wavelength of 1.5406 Å) exhibited the presence of the rhombohedral crystal structure with a space group of P3_mL.The outof-plane lattice constant c was also determined to be 6.11Å, which was consistent with the reported works. [28]As illustrated in Figure 1b, no other phases were detected.These comprehensive analyses verified the high quality of the CrTe 2 films.More detailed investigations concerning CrTe 2 films, focusing on thickness dependence and heterojunction devices, could be found in previous works. [9,29]fter the growth, a top-gated FET device was fabricated using standard photolithography techniques.An eight-terminal Hall bar structure of CrTe 2 material (length: 10/20 μm, width: 10 μm) was created using argon iron.The Field effect coupling involved the use of an insulating material to protect the ferromagnetic layer, forming an electric double coupling between the gate electrode and the magnetic layer.The electrode was made from the Ti/Au process.Figure 1c demonstrates the optical image of the CrTe 2 FET device, clearly indicating the source, the drain, and the gate regions, along with other contacts used for the transport measurements.The stereoscopic model of the FET is depicted in Figure 1d, providing further insight into the testing principle.In addition, all magnetic transport analyses conducted in this study were performed using the Oxford Instruments low-temperature system (Teslatron PT) and Probe station (PDA Pxle-FS380).
The field effect coupling involved the use of an insulating material to protect the ferromagnetic layer, forming an electric double coupling between a gate electrode and the magnetic layer.In the case of the 2D CrTe 2 FET microstructure, the fabrication process involved several steps.First, an eight-terminal Hall bar structure of CrTe 2 material was created using ion beam etching (IBE).Next, a high-quality MgO (20 nm) insulating layer was deposited on the top of the Hall bar by electron-beam evaporation (EBE), serving as the area for applying voltage.Finally, ten gold electrodes (Ti/Au 20 nm/50 nm) were connected to pins and the top gate with two additional electrodes acting as the gate electrode, and the source and drain electrodes positioned at both ends of the Hall bar.
The testing process provided a source-drain current (I AC ) of 100 μA with a frequency of 17 Hz.The voltage (V g ) was used to adjust the CrTe 2 material on the top gate.According to the test results displayed in Figure S1 (Supporting Information), the gate leakage current (I gs ) was significantly lower than the I AC at voltages below 25 V. Therefore, a gate voltage below 25 V was employed to ensure that the insulation layer remained intact and had not experienced breakdown.

Results and Discussion
According to the testing scheme described in Figure 1d, the longitudinal resistance (R xx ) and the Hall resistance (R xy ) are obtained with an out-of-plane field.Figure 1e is the raw data of the original R xx and R xy at 20 K while the magnetic field cycles between −2 and 2 T. The butterfly-like R xx and the square-like R xy indicate that CrTe 2 possesses strong magnetism with PMA, and the value of H C is also annotated.The positive slope of R xy observed at high magnetic fields suggests that the majority of carriers in the film are holes. [30,31]he relationship between R xy and the magnetic field can be described by the empirical equation R xy = R 0 H + R a M, where the first term represents the ordinary Hall effect, and the second term represents the Anomalous Hall effect (AHE).The empirical formula is used to study the formation mechanism of the Anomalous Hall resistance ( R AHE = R xy − R 0 H = R a M). [32,33]he formula is as follows: The first term in the equation represents the non-intrinsic contribution, where  represents the skew scattering mechanism and  represents the side jump mechanism.The second term, denoted by the coefficient b, corresponds to the intrinsic contribution related to Berry curvature.Normally, in strong 2D magnetic materials, such as Na 3 VAs 2 , and CrI 3 , the non-intrinsic magnetic contribution is often neglected. [34,35]As a result, the expression for R AHE can be simplified as R AHE ∼ bR 2 xx M. In addition, the magnetic resistance (MR) is calculated according to the formula MR =  xx (B)/ xx (0) − 1. MR quantifies the rate of variation in R xx with respect to the magnetic field.Both the R AHE and MR are utilized to characterize the ferromagnetic properties of CrTe 2 and display significant responses to the gate voltages and the temperatures in Figure S2a-d  Figure 2a illustrates the square hysteresis loops of R AHE with an out-of-plane field at various gate voltages at 20 K.The sat-urated R AHE decreases with the voltage decrease as indicated by the dash arrows.This can be understood by the equation of R AHE ∼ bR 2 xx M. At a specific temperature, the ferromagnetism (M) stays constant.Thus, the saturated R AHE is linearly proportional to R 2 xx illustrated in Figure S4 (Supporting Information). [36]Additionally, a sign change of the saturated R AHE is observed at 150 K.This is associated with the hysteresis loops transitioning from counter-clockwise to clockwise as indicated by the solid black arrows.Here, we suspect that the inverse sign has occurred in the intrinsic term that is associated with the Berry curvature.This has been evidenced by the slops changing from positive to negative in Figure S4 (Supporting Information).
In the inset of Figure 2a, the H C exhibits an increase from 6740 to 7700 Oe along with the voltage decreases from 25 to −15 V.This change is accompanied by a shift in the peak position of the MR data, as shown in Figure 2e.The trend of H C , under the influence of voltage, remains consistent with increasing temperatures, as shown in Figure 2e-h.
One crucial parameter of ferromagnetic materials is the Curie temperature (T C ), which refers to the temperature at which the spontaneous magnetization in the magnetic material drops to zero.Here we extracted the T C of the device under different gate voltages using two methods.First, the temperature at which H C reaches zero is defined as the T C1 (Curie temperature) for the specific voltage.As depicted in Figure 3a, the H C decreases with increasing temperature and eventually vanishes at 180 K without a gate voltage.Applying a positive voltage leads to a decrease in T C1 , whereas a negative voltage leads to an increase in T C1 .The extracted T C1 values, as shown in the inset of Figure 3a  Simultaneously, the carrier concentrations are determined through the linear fitting of R xy at high magnetic fields for different gate voltages.The hole concentration (n p ) is calculated using the formula n p = 1/(e*R 0 ), where R 0 represents the normal Hall coefficient at high fields (1.6-2 T).Δn p is close to 8 × 10 13 cm −2 , which is consistent to the theoretical value in the Note S1 (Supporting Information).It is observed that the carrier concentration shows a linear increase with the voltage decreases.This is accompanied by the decreases of R xx , as depicted in Figure S5 (Supporting Information), indicating that CrTe 2 is hole-dominated. [37]This observation is consistent with the p-type behavior of CrTe 2 , as illustrated in Figures 1e and 4a.As this increases by gate tuning, the T C exhibits a linear increase.This relationship between T C and the carrier density can be explained by the RKKY interaction model.In magnetic samples, ferromagnetism is mediated by itinerant carriers through the RKKY mechanism, where T C is reduced at low carrier densities and enhanced at higher carrier densities.The relevant formula is expressed as follows: [38] T Where k B is the Boltzmann constant, x is the concentration of the magnetic ions, a 0 is the lattice constant, n 0 is the carrier concentration, S is the spin polarization of the magnetic ions, and J is the coupling coefficient that characterizes the strength of the magnetic interaction.Here, we have observed that the gate voltage solely affects the n 0 without causing alterations in other parameters.Consequently, the variation in T C is only attributed to changes in the charge carrier density.This significant finding serves as evidence supporting the existence of the RKKY mechanism in the overall generation of magnetism in 2D CrTe 2 .

Conclusion
In summary, we have fabricated FET devices using an ultrathin ten-layer CrTe 2 film, and its ferromagnetism can be tuned through gate voltages.The AHE characterization results reveal

Figure 1 .
Figure 1.a) The RHEED patterns of the GaAs (111)B substrate and a ten-layer (6 nm) CrTe 2 thin film.The sharp streaky lines suggest the flat surface morphology.The double-headed arrows between the two first-order stripes represent the d-spacing, which can be used to extract the in-plane lattice constant of 3.81 Å. b) XRD characterization results of the sample, the rhombohedral crystal geometry phase of CrTe 2 is determined based on the peak position.c) Optical images of the FET device exhibit the conducting channel with a width of 10 μm.d) Schematic diagram of the 2D CrTe 2 FET with the testing principles.e) The magnetic transport measurement results of the device at 20 K.The butterfly-like R xx and the square-like R xy demonstrate the out-of-plane magnetism of the CrTe 2 film.

Figure 2 .
Figure 2. a-d) The R AHE with different gate voltages at various temperatures.At fixed temperature, the H C increases as the gate voltage decreases.The solid black arrows indicate the sweeping direction of the external magnetic field.e-h) The MR with different gate voltages at various temperatures.At fixed temperature, the MR peak position increases according to the HC as the gate voltage decreases.

Figure 3 .
Figure 3. a) The temperature-dependent H C at various gate voltages.The Curie temperature (T C1 ) can be determined when H C reaches 0 as indicated by the arrows in the inset.b) The temperature-dependent intercepts of the Arrott-plots d-g) at various gate voltages.The Curie temperature (T C2 ) can be determined when the intercepts cross Zero as indicated by the arrows.c) The gate voltage-dependent Curie temperatures.As the gate voltage decreases, the T C increases.d-g) Arrott-plot lines near Curie temperature at various gate voltages.

Figure
Figure 4b exhibits the linear relationship between the T C and the n 1∕3 p .As this increases by gate tuning, the T C exhibits a linear increase.This relationship between T C and the carrier density can be explained by the RKKY interaction model.In magnetic samples, ferromagnetism is mediated by itinerant carriers through the RKKY mechanism, where T C is reduced at low carrier densities and enhanced at higher carrier densities.The relevant formula is expressed as follows:[38]

Figure 4 .
Figure 4. a) The carrier concentrations as a function of gate voltages at 160 K. b) The linear dependence between T C and n 1∕3 p , fits perfectly with the RKKY model.
that T C increases from 152 to 191 K with the voltage changing from 25 to −15 V.More importantly, the T C of CrTe 2 exhibits a linear relationship with n 1∕3 p , indicating the influence of carrier density on T C .This observation is direct evidence of the RKKY theory, which explains the origin of the long-range ferromagnetic ordering in the CrTe 2 films.