Covalent Mixing in the 2D Ferromagnet CrSiTe3 Evidenced by Magnetic X‐Ray Circular Dichroism

The low‐temperature electronic structure of the van der Waals ferromagnet CrSiTe 3 is investigated. This ferromagnetic semiconductor has a magnetic bulk transition temperature of 33 K, which can reach up to 80 K in single‐ and few‐layer flakes. X‐ray absorption spectroscopy (XAS) and X‐ray magnetic circular dichroism (XMCD) measurements, carried out at the Cr L 2,3 and Te M 5 edges in vacuo‐cleaved single crystals, give strong evidence for hybridization‐mediated superexchange between the Cr atoms. The observed chemical shift in the XAS, as well as the comparison of XMCD with the calculated Cr L 2,3 multiplet spectra, confirms a strong covalent bond between the Cr 3 d ( e g ) and Te 5 p states. Application of the XMCD sum rules gives a nonvanishing orbital moment, supporting a partial occupation of the e g states, apart from t 2 g . Also, the presence of a nonzero XMCD signal at the Te M 5 edge confirms a Te 5 p spin polarization due to mixing with the Cr e g bonding states. The results strongly suggest that superexchange, instead of the previously suggested single‐ion anisotropy, is responsible for the low‐temperature ferromagnetic ordering of 2D materials such as CrSiTe 3 and CrGeTe 3 . This demonstrates the interplay between electron correlation and ferromagnetism in insulating 2D materials.


Introduction
2D van der Waals materials [1] and their heterostructures have been the focus of materials research ever since the field started off with the discovery of grapheme. [2] Among the 2D materials, magnetically ordered films have caught the attention of the magnetism community as they promise the possibility of further device scaling. Despite being in principle "forbidden" at The low-temperature electronic structure of the van der Waals ferromagnet CrSiTe 3 is investigated. This ferromagnetic semiconductor has a magnetic bulk transition temperature of 33 K, which can reach up to 80 K in single-and few-layer flakes. X-ray absorption spectroscopy (XAS) and X-ray magnetic circular dichroism (XMCD) measurements, carried out at the Cr L 2,3 and Te M 5 edges in vacuo-cleaved single crystals, give strong evidence for hybridization-mediated superexchange between the Cr atoms. The observed chemical shift in the XAS, as well as the comparison of XMCD with the calculated Cr L 2,3 multiplet spectra, confirms a strong covalent bond between the Cr 3d(e g ) and Te 5p states. Application of the XMCD sum rules gives a nonvanishing orbital moment, supporting a partial occupation of the e g states, apart from t 2g . Also, the presence of a nonzero XMCD signal at the Te M 5 edge confirms a Te 5p spin polarization due to mixing with the Cr e g bonding states. The results strongly suggest that superexchange, instead of the previously suggested single-ion anisotropy, is responsible for the low-temperature ferromagnetic ordering of 2D materials such as CrSiTe 3 and CrGeTe 3 . This demonstrates the interplay between electron correlation and ferromagnetism in insulating 2D materials.
monolayer flakes, has been investigated via Hall measurements. [10] From the observed change in resistivity at 80À120 K, the Curie temperature of those flakes was estimated to be %80 K. [10] This remarkable increase from the bulk value of 33 K [6,7,11] is in stark contrast to the behavior of other 2D ferromagnets and has been proposed to stem from the increased intralayer superexchange interaction via Te in the few-layer limit. [9,12] Recently, in the ultrathin layer limit, the thicknessdependent magnetic transition from 3D (Heisenberg) to 2D Ising behavior has been observed for a CrSiTe 3 thickness of %7 nm, which goes hand in hand with a drop in Curie temperature from 33 to 17 K. [13] This behavior is often tied to the strong dependence of the electronic structure on the reduced dimensionality in the ultrathin layer limit, as it has been experimentally observed for CrI 3 . [1] CrSiTe 3 crystallizes in the space group R3. Its reported effective moment μ eff ¼ 3.88ð2Þ μ B (Hkc) is in good agreement with the moment expected for Cr 3þ , [7] and so is the saturation moment at 2 K of 3.08 μ B (compared with 3 μ B for Cr 3þ with three unpaired spins). CrSiTe 3 shows almost no hysteresis with very small remanent magnetization of 0.001 μ B (Hkc). [7] From a detailed analysis of the critical behavior of the magnetic phase transition, it was concluded that CrSiTe 3 can be described with a 2D Ising model coupled with long-range interaction. [14] The bulk T C is also very sensitive to the applied pressure, and an increase from 33 to 138 K has been reported, also changing the soft magnetic normal behavior to a hard magnetic one. [15] Therefore, the exploration of the mechanism behind the magnetic ordering of 2D CrSiTe 3 is an important yet challenging task.
In an ionic picture, the oxidation state of Cr in CrSiTe 3 and CrGeTe 3 is expected to be þ3 with an electronic configuration 3d 3 . In an octahedral environment, these d levels split into a higher energy e g doublet and a lower energy t 2g triplet. Thus, Cr 3þ ions have S ¼ 3/2, with three unpaired electrons in the half-filled t 2g manifold, in compliance with the first Hund rule. This is consistent with the observed saturation magnetization of bulk CrSiTe 3 that yields a magnetic moment of %3 μ B /Cr. [7] The lack of orbital degeneracy of the orbital singlet state 4 A 2 with L ¼ 0 leads to a vanishing magnetocrystalline anisotropy energy E MCA ∝ λ L h i ⋅ S h i, where λ is the 3d spinÀorbit interaction parameter. The slightly distorted octahedral symmetry, with its bond angles deviating from 90 , has point group symmetry D 3d . Under lower symmetry, the t 2g state splits into a 1g þ e π g and the e g state is relabeled as e σ g . Long-range ferromagnetism in CrSiTe 3 arises from the superexchange between the neighboring e π g and e σ g states, consistent with the GoodenoughÀKanamuri rule. [16,17] This model is supported by angular-resolved photoelectron emission spectroscopy (ARPES) results and density functional theory (DFT) þ dynamical mean-field theory (DMFT) calculations on CrSiTe 3 . [18] In magnetic insulators dominated by superexchange, as realized in many transition metal oxide and chalcogenide materials, the superexchange between the spins on neighboring metal sites depends on the electron hopping (charge transfer) between the metal 3d and neighboring ligand p states. [19] Above the Curie temperature, the Coulomb repulsion drives the system into a charge transfer insulator phase. [18] Here we report the X-ray absorption spectroscopy (XAS) and X-ray magnetic circular dichroism (XMCD) of the low-temperature ferromagnetic phase of CrSiTe 3 . These elementspecific techniques offer the most direct way to determine the local electronic and magnetic structure of 3d transition metal atoms due to their valence, site, and symmetry selectivity. [20][21][22][23] Some recent reports in the literature have claimed that their XMCD measurements on CrSiTe 3 [24] and CrGeTe 3 [25] confirm the single-ion anisotropy of the octahedrally distorted Cr 3þ to be responsible for the long-range ferromagnetic ordering. In contrast, here we show that, while single-ion anisotropy may play a role, the main contribution arises from the hybridization-mediated superexchange between the Cr atoms. We show that the calculated Cr L 2,3 multiplet spectrum in the presence of crystal-field and spinÀorbit interaction provides unique information regarding the hybridized ground state. [20] The XMCD sum rule analysis [26,27] establishes a nonvanishing orbital moment, indicating a partial occupation of 3dðe g Þ states. The observation of XMCD at the Te M 5 edge confirms a Te 5p spin polarization aligned with the Cr 3d moment.

Structural and Magnetic Characterization
CrSiTe 3 single crystals were grown using a self-flux method, as described in detail in the study by Suo et al. [28] The resulting plate-like crystals, which measure %8 mm across, were characterized by room-temperature X-ray diffraction (XRD) using a Mo Kα (λ ¼ 0.7107 Å) source in SuperNova single-crystal XRD system. CrSiTe 3 crystallizes in the R3 space group (Figure 1a-c), consistent with the single-crystal XRD data shown in Figure 1d, from which we determined the following lattice parameters: a ¼ 6.7699 Å, b ¼ 6.7699 Å, and c ¼ 20.6825 Å (α ¼ β ¼ 90 and γ ¼ 120 ), in agreement with the study by Ouvrard et al. [29] The layered structure of CrSiTe 3 can be seen in Figure 1b, where the %3.5 Å-thick CrÀSiÀTe quintuple layers with their Te terminations are separated by a %3.3 Å vdW gap. [7,30] The stacking sequence of the CrÀSiÀTe quintuple layers in the unit cell was AÀBÀC. The crystal orientation of the vdW cleavage planes was normal to the c-axis.
The temperature-dependent magnetic properties of the sample were studied using bulk-sensitive superconducting quantum interference device (SQUID) magnetometry (Quantum Design 7T MPMS SQUID VSM). From the temperature dependence of magnetization, shown in Figure 2, a transition temperature of 32.8 K was estimated (defined as the minimum of the derivative; shown as an inset), consistent with previous studies. [6,7,11] In agreement with earlier reports, [7] CrSiTe 3 showed no hysteretic behavior and a negligible remanent magnetization. Detailed magnetic data on our sample can be found in the study by Zhang et al. [18]

XAS and Magnetic Circular Dichroism
XAS and XMCD measurements were carried out using the electromagnet end-station ELMA on beamline I10 at the Diamond Light Source, UK. The sample was cleaved in ultrahigh vacuum in the magnet chamber. For this purpose, a small ceramic cleaving post was glued to the single crystal, which could be hit in a www.advancedsciencenews.com www.pss-rapid.com controlled way using the sample transfer tool. Spectra were measured with 100% left-(LCP) and right-circularly polarized (RCP) light and positive and negative fields H ¼ AE1.4 T using totalelectron yield detection, which probed the top 3-5 nm of the sample, [23] at a temperature of 10 K. The field was along the X-ray beam, at normal incidence to the sample surface.
Adhering to the sign convention, [23] we took the spectra , I sum ¼ I À þ I þ , and I xmcd ¼ I À À I þ . A reference sample of Cr 2 O 3 was used to calibrate the photon energy, as well as to verify whether the measured CrSiTe 3 spectra showed a fraction corresponding to a surface oxide.
The element-specific spin and orbital magnetic moments were obtained from the integrated intensities of the dichroic spectra using the sum rule analysis. [31] Figure 3 shows the integrate of the XMCD spectra, with p and q the integrated intensities over the L 3 and L 2,3 edges, respectively. From the values of p and q, and using the integrated intensity r over the L 2,3 edge of the sum spectrum as the normalization factor accounting for the number of d holes n h ¼ ð10 À n d Þ, we obtained the spin and   Upper part: XAS for I þ (orange curve), I À (black curve), sum spectrum (I À þ I þ ) (blue curve), and the Cr 2 O 3 reference (green curve). Lower part: XMCD spectrum (I À À I þ ) (red curve), shown on a 2Â expanded scale compared with XAS, together with its integrate (dotted curve). The arrows with labels p and q indicate the integrated intensities over the L 3 and L 2,3 edges, respectively. www.advancedsciencenews.com www.pss-rapid.com orbital moments per Cr atom as follows: m L ¼ À L z h i ¼ Àð4=3Þqn h =r and m S ¼ À 2S eff ,z ¼ Àð6p À 4qÞCn h =r. [23] For the lighter 3d metals, the spin sum rule contains the correction factor C, which is equal to 2.0 for Cr, to rectify for the large overlap of 2p 3=2 and 2p 1=2 multiplet structures. [32] As suggested by the Cr 2 O 3 contribution at the high-energy side, we assumed that %10% of the XAS intensity of CrSiTe 3 came from the oxide and corrected the value of r accordingly.

Multiplet calculations
Atomic multiplet calculations were performed to compute the Cr L 2,3 XAS and XMCD spectra for the electricÀdipole transitions, 3d n ! 2p 5 3d nþ1 , with the spinÀorbit and electrostatic interactions treated on an equal footing. [33,34] The wave functions of the initial-and final-state configurations were calculated in intermediate coupling using Cowan's atomic HartreeÀFock (HF) code with relativistic corrections. [20,35] The atomic electrostatic interactions included the 3dÀ3d and 2pÀ3d Coulomb and exchange interactions, which were reduced to 80% and 75%, respectively, of their atomic HF value to account for intraatomic screening. [33] Hybridization was included by mixing the Cr 3d 3 and 3d 4 L wave functions, where L represented a hole on the neighboring atoms in states of appropriate symmetry. For CrSiTe 3 , the charge transfer energies in the initial and final state were taken as Eð3d 4 LÞ À Eð3d 3 Þ ¼ À1 eV and Eð2p 5 3d 5 LÞ À Eð2p 5 3d 4 Þ ¼ À3 eV, respectively, where E stands for the average energy of the configuration in the parentheses. The hybridization parameter was taken as T ¼ Ψðd 3 ÞjHjΨðd 4 LÞ h i ¼ 1.7 eV. The Cr ions were located at the center of a slightly distorted octahedron of Te atoms. [7] An octahedral crystal field of 10Dq ¼ 1.8 eV was included in the calculation. The computed Cr L 3 (L 2 ) line spectra were convoluted by a Lorentzian with a half width of Γ ¼ 0.2 eV (0.4 eV) for intrinsic lifetime broadening and a Gaussian with a standard deviation of σ ¼ 0.15 eV for instrumental broadening.

Results and Discussion
The XAS and XMCD of CrSiTe 3 at the Cr L 2,3 edge measured at 10 K and 1.4 T are shown in Figure 3. As expected, no XMCD was observed above the Curie temperature (not shown). Compared with the Cr 2 O 3 (Cr 3þ , d 3 ) reference sample (green curve), the Cr L 2,3 edge of CrSiTe 3 is shifted to lower photon energy. Qualitatively, this chemical shift implies a higher d-electron count in CrSiTe 3 as compared with Cr 2 O 3 . [21] It appears that at the high-energy side of both the L 3 and L 2 edges in the XAS, there is a small contribution of chromium oxide present, estimated to %10%. Assuming that this oxide is antiferromagnetic, it will not give an XMCD signal. [36] Most likely, this oxide contribution originates from the edges of the cleaved crystal, as the X-ray beam spot (%1 mm horizontally) is on the order of the sample size (%1 Â 2 mm 2 ; thickness: %2À3 μm).
Much information can be gained by comparison of the measured spectra with atomic multiplet calculations. Calculated spectra for the ionic configurations Cr d 3 and Cr d 4 with different values of the octahedral crystal field parameter 10Dq can be found in the study by van der Laan. [20] It becomes clear that none of the calculated spectra for a pure ionic configuration gives a particularly good fit to the CrSiTe 3 spectra. To obtain a better agreement between the measured and calculated spectra requires treating the ground state of Cr as a hybridized state with %50% d 3 and 50% d 4 L character, corresponding to a d electron count of n d % 3.5 (for details and parameter values, see Section 2.3). This reproduces very well the measured XMCD spectrum (Figure 4). The hybridization with the d 4 L state also leads to lowering in photon energy by %1.5 eV compared with the ionic d 3 configuration. This chemical shift has also been reported for other Cr atoms in a tellurium octahedral environment with n d > 3. [32,[37][38][39] It is interesting to compare the spectral shape of the XMCD with that of related compounds. The XMCD spectrum of CrSiTe 3 resembles that of the structurally similar CrGeTe 3 (T C % 63 K) [39] and CrI 3 (T C % 45 K) [40] (see Figure 4). However, the XMCD line shape is very different compared with some of the other CrTe 6 octahedra-hosting compounds, such as Cr-doped Sb 2 Te 3 [38] ; the latter shows a similar XMCD spectral shape as Cr-doped Bi 2 Se 3 . [32,37] In both magnetically doped topological insulators, Cr has 30% d 3 and 70% d 4 L character (n d % 3.7). Compared with Cr:Sb 2 Te 3 , the XMCD spectra of CrSiTe 3 , CrGeTe 3 , and CrI 3 show a much more pronounced multiplet structure with sharp peaks. The energy separation between the two main negative peaks at the L 3 edge is significantly smaller in CrSiTe 3 (0.95 eV) compared with CrGeTe 3 and CrI 3 (1.1 eV). This does not seem to be related to the vdW interlayer gap in the various materials. The vdW spacing Te M 5 Figure 4. Comparison of Cr L 2,3 XMCD spectra for CrSiTe 3 (this work), CrGeTe 3 [39] CrI 3 , [40] Cr 0.32 Sb 1.68 Te 3 , [38] and the theoretical multiplet spectrum [this work]. The black arrow at %573.8 eV marks the position of the Te M 5 peak. The spectra are normalized to maximum peak intensity and vertically shifted for clarity.
www.advancedsciencenews.com www.pss-rapid.com of CrGeTe 3 is 3.39 Å, [8,41] which is slightly larger than the value of 3.3 Å of CrSiTe 3 . The vdW spacing of CrI 3 is reported to be even as large as 3.488 Å. [42] For the measured Cr L 2,3 spectra of CrSiTe 3 at a temperature of 10 K, the application of the orbital sum rule (for equations, see Section 2.2) using n d ¼ 3.5 gives an orbital moment of m L ¼ ðÀ0.055 AE 0.05Þμ B /Cr. In comparison, m L ¼ À0.045 (out of plane) and À0.052 (in plane) for CrGeTe 3 and m L is À0.051 for CrI 3 at 20 K. [43] Application of the spin sum rule gives an effective spin moment m S ¼ ð2.86 AE 0.25Þ μ B /Cr (i.e., 0.82μ B per 3d electron). When Cr reduces its symmetry from a pure t 3 2g ( 4 A 2 ) configuration in octahedral symmetry to D 3d , or when e g is partially occupied, the effective spin moment contains a finite contribution of the magnetic dipole term T z h i, which can reach up to AE10% of the total spin moment. [44] Thus, the measured spin moment is close to m S %3μ B /Cr that was reported using conventional magnetization measurements. [7] From the calculated spectrum (also shown in Figure 4), we find m L ¼ À0.022 μ B /Cr and m S ¼ 2.81 μ B /Cr (i.e., 0.80 μ B per 3d electron), which is a very similar result as from the experiment. The fact that the full spin polarization of 3.5 μ B /Cr is not reached is due to the spinÀorbital-coupled nature of the multideterminant wave function for less-than-half-filled configuration where the spin and orbital moments form an entangled state. [34,35] According to the third Hund's rule, the spin and orbital moments for the less-than-half-filled Cr band are aligned antiparallel. Indeed, from the sum rule analysis, we find m L =m S ¼ À0.019. Furthermore, this excludes that we are dealing with an ionic configuration Cr 3þ t 3 2g that has m L ¼ 0. This is a further indication of the partial occupation of the e g state due to the hybridization with the Te 5p states. Similar to CrGeTe 3 , [39] the d-count of n d % 3.5 indicates a Cr ionic configuration with three electrons in the t 2g state and %0.5 electron in the e g state, with parallel spins according to the first Hund's rule. While the overlap of t 2g with the Te 5p is small, that of the e g state is large, resulting in covalent bonding. This hybridization (mixing) leads to unoccupied states in the otherwise-filled Te 5p band, giving rise to the appearance of a nonzero XMCD signal at the Te M 5 edge. The size of Te M 5 XMCD is expected to scale with the number of holes in the Te 5p band and hence the hybridization.
However, in Cr-based materials, it is challenging to observe the Te M 5 edge as its energy position is close to that of the Cr L 3 edge, while its cross section is much smaller. [38] Nonetheless, in both the XAS and XMCD spectra, we find a small peak at 573.8 eV (black arrows in Figure 4), which agrees well with the energy position at which the Te M 5 edge is expected (see Figure S9c in the Supplementary Material of the study by Figueroa et al. [45] ). The absence of such a tellurium feature in the XAS/XMCD of CrI 3 as well as in the multiplet calculation for the Cr-mixed configuration (Figure 4) supports that the peak observed at 573.8 eV originates indeed from the Te M 5 edge. The Te M 5 exhibits a negative XMCD signal, with the same sign as the Cr L 3 edge ( Figure 4). As the azimuthal quantum numbers for the orbitals in these two electricÀdipole transitions are opposite (Te 3d ! 5p and Cr 2p ! 3d, respectively), the moments of less-than-half-filled Cr and the nearly filled Te bands are aligned antiparallel, as should be the case for electronic mixing.

Conclusion
In summary, we performed XAS and XMCD on freshly cleaved CrSiTe 3 crystals below the magnetic ordering temperature. The experimental Cr L 2,3 XMCD, present below T C , shows good agreement with the calculated spectrum for a hybridized ground state. Our experimental results suggest that the hybridization between the Cr and Te states is responsible for the magnetic anisotropy that lies behind the 2D magnetic behavior of CrSiTe 3 . The evidence for covalent mixing arises from the comparison of the measured XMCD with multiplet calculations, indicating %3.5 electrons at the Cr 3d side, a large chemical shift to lower photon energy, and the observation of an XMCD signal at the Te M 5 edge that demonstrates a 5p spin polarization on the neighboring Te atoms. The orbital-to-spin moment ratio m L =m S ¼ À0.019 for Cr 3d, extracted from the sum rules, provides additional support for the presence of e g bonding orbitals that hybridize with the Te 5p states, enabling superexchange that gives long-range ferromagnetic order. Comparison with other 2D magnetic vdW materials such as CrGeTe 3 and CrI 3 , which show similar although not quite identical XMCD spectra, suggests that the superexchange model provides a general picture for such types of 2D materials.