Introduction

The discovery of ferromagnetism at a finite temperature in atomically thin van der Waals (vdW) monolayers (MLs)1,2,3 has spurred a surge of experimental and theoretical interests in understanding the two-dimensional (2D) magnetism and furthermore in producing emergent functionalities in 2D vdW heterostructures4,5,6,7,8,9. Fundamentally, the well-known Mermin–Wagner theorem based on the isotropic Heisenberg exchange model10 suggested the absence of either FM or antiferromagnetic (AFM) order in 2D systems at nonzero temperature, and hence the early findings of FM order in CrI3 ML1 and Cr2Ge2Te6 bilayer11 were rather surprising. Recent studies indicated that magnetic anisotropies play a major role in the establishment of their long-range magnetic ordering. The main advantage of these 2D magnetic vdW materials is their integrability with other vdW functional materials. Through the magnetic proximity effect, many spintronic, valleytronic, and optoelectronic properties can be achieved in heterostructures by stacking diverse 2D vdW MLs or ultrathin films5,7,8. For example, the quantum anomalous Hall effect (QAHE) and axion insulator phase can be realized by integrating 2D FM semiconductors with thin films of topological insulators8,12,13,14,15. When transition metal dichalcogenide (TMDC) MLs are in contact with 2D FM semiconductors, a valley splitting can be produced for valleytronic and optoelectronic manipulations7, as recently observed in WSe2/CrI316. Obviously, it is beneficial to have large spin polarization in the outer anions of 2D FM MLs to maximize the magnetic proximity effect.

Recently, Janus 2D materials have attracted increasing attention17,18 since TMDC Janus ML MoSSe was successfully fabricated by controlling the reaction conditions in experiments19. Due to the feasibility of selecting a suitable pair of anions, Janus 2D materials add an extra dimension for the rational design of 2D vdW MLs with desired properties. For example, because the out-of-plane symmetry is broken, 2D Janus CrGe(Se,Te)3, CrXTe (X = S, Se) and manganese dichalcogenide MLs may possess large Dzyaloshinskii–Moriya interaction (DMI) and thus can host magnetic skyrmions20,21,22,23. Besides, Janus structure as electrodes in Li-ion batteries may have good performance due to its structural asymmetry24. Several theoretical studies25,26,27,28 predicted that Janus MLs, such as VSSe27, a Janus structure of the FM VSe22,29, have FM order up to room-temperature. Although 2D Janus magnets’ own properties have been widely investigated, their heterostructures with other vdW functional materials, such as TMDC MLs and three-dimensional (3D) topological insulator thin films, remain underexplored17,18. Moreover, the formation of complex magnetic patterns in 2D heterostructures due to the competition among Heisenberg exchange, magnetic anisotropy, DMI, and external magnetic field is rarely discussed.

In this work, we systematically study the electronic and magnetic properties of vdW Janus ML Cr-based dichalcogenide halides CrYX (Y = S, Se, Te; X = Cl, Br, I) using first-principles calculations. This is partially inspired by the experimental observation of high-temperature (~200 K) ferromagnetism in 1T-CrTe2 ML30,31,32,33,34. We identify that CrSX (X = Cl, Br, I) are the very attractive out-of-plane FM semiconductors with high Curie temperatures (~176 K) and large magnetic moments on S2− anions. Excitingly, through the magnetic proximity effect, the sought-after large-gap QAHE can be achieved in CrSBr/Bi2Se3/CrSBr. For the same reason, a sizable valley splitting of 37.9 meV, corresponding to a magnetic field of 379 T35, can be generated in MoTe2/CrSBr. Furthermore, we find that large DMI leads to magnetic skyrmion states in CrTeX (X = Cl, Br, I) under an appropriate external magnetic field by virtue of Monte Carlo (MC) simulations. Our work highlights the remarkable multifunctionalities of these 2D vdW Janus ML magnets that are promising for applications in the next-generation topotronic and valleytronic devices.

Results

Electronic and magnetic properties of CrYX ML

Figure 1a shows the crystal structure of Janus ML CrYX (Y = S, Se, Te; X = Cl, Br, I). Magnetic Cr3+ cations form a triangular lattice and are sandwiched by Y2− and X− anions. Similar to CrI3 and Cr2Ge2Te6 MLs1,11, Cr3+ cations in CrYX are surrounded by the distorted edge-shared octahedrons formed by Y2− and X− anions, which implies FM nearest-neighbor (NN) exchange interactions. As a direct result of different sizes of Y2− and X− anions, CrSCl and CrTeI have the smallest and largest in-plane lattice constants (Supplementary Table 1), respectively. Since no imaginary frequency is found in the calculated phonon spectra of all CrYX MLs (Supplementary Fig. 1), they should be dynamically stable.

Fig. 1: Crystal structure and magnetic properties of CrYX.
figure 1

a Top and side views of the crystal structure. Green, black and red dashed lines show the NN, second-NN and third-NN exchange paths, respectively. b Heisenberg exchange parameters Ji (i = 1, 2, 3). c |D1| of the NN DM interaction vector D1 (red dots) and \(\left| {{{{\bf{D}}}}_{1,//}} \right|/\left| {J_1} \right|\) (blue dots). d SIA parameter A. e MC simulated magnetic ground states of CrYX.

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To explore the magnetic ground states of CrYX MLs, we consider a spin Hamiltonian consisting of Heisenberg exchange interactions, DMI and single ion anisotropy (SIA). This spin Hamiltonian is in the form of21,22

$$\begin{array}{l}H = J_1\mathop {\sum}\limits_{\left\langle {ij} \right\rangle } {{{{\bf{S}}}}_i \cdot {{{\bf{S}}}}_j} + J_2\mathop {\sum}\limits_{\left\langle {\left\langle {ij} \right\rangle } \right\rangle } {{{{\bf{S}}}}_i \cdot {{{\bf{S}}}}_j}\\\qquad +\, J_3\mathop {\sum}\limits_{\left\langle {\left\langle {\left\langle {ij} \right\rangle } \right\rangle } \right\rangle } {{{{\bf{S}}}}_i \cdot {{{\bf{S}}}}_j} + \mathop {\sum}\limits_{\left\langle {ij} \right\rangle } {{{{\bf{D}}}}_{ij} \cdot \left( {{{{\bf{S}}}}_i \times {{{\bf{S}}}}_j} \right)} - A\mathop {\sum}\limits_i {\left( {S_i^z} \right)^2} .\end{array}$$
(1)

Here, Si is the normalized spin vector at site i; J1, J2, and J3 are NN, second-NN, and third-NN Heisenberg exchange parameters, respectively; Dij = (Dx, Dy, Dz) is the NN DMI vector and A is the SIA parameter. The Heisenberg exchange parameters Ji (i = 1, 2, 3), NN DM vector D1 and SIA parameter A from DFT calculations are tabulated in Supplementary Table 2. As expected, the NN J1 is FM and dominates over the second-NN J2 and third-NN J3 for all CrYX (Fig. 1b). Since DMI is directly related to the spin–orbit coupling (SOC)36, the magnitude of the NN DMI vector, \(\left| {{{{\bf{D}}}}_1} \right| = \sqrt {D_x^2 + D_y^2 + D_z^2}\), increases when Y (X) goes from S (Cl) to Te (I), as shown in Fig. 1c. It is interesting that \(\left| {{{{\bf{D}}}}_{1,//}} \right|/\left| {J_1} \right|\) (D1,//, the inplane component of D1) has a similar trend to |D1| when Y (X) varies (Fig. 1c). Particularly, \(\left| {{{{\bf{D}}}}_{1,//}} \right|/\left| {J_1} \right|\) of CrTeX (X = Cl, Br, I) is in the typical range of 0.1–0.2 that is known to generate magnetic skyrmions37. Lastly, CrSX (X = Cl, Br, I) and CrSeI have an out-of-plane SIA while the other five of CrYX have an in-plane SIA (Fig. 1d). Note that the present results of NN FM Heisenberg exchange interactions and in-plane SIAs of CrSeBr and CrTeI Janus MLs are consistent with those obtained in a previous theoretical study38.

Owing to the competition between Heisenberg exchange interactions, DMI and SIA, MC simulations reveal that CrYX exhibits very rich magnetic ground configurations (Fig. 1e). It has been reported that magnetic ground state of 2D magnets is mainly determined by a critical dimensionless factor \(\left| A \right|K/{{{\bf{D}}}}_{//}^2\) (K, the stiffness parameter originating from FM Heisenberg exchange interactions)39. A large \(\left| A \right|K/{{{\bf{D}}}}_{//}^2\) yields a FM ground state, while a small one results in a spiral ground state39. First, CrSY (Y = Cl, Br, I) MLs have small DMI, out-of-plane SIA and hence an out-of-plane FM ground state with a Curie temperature up to 176 K (Supplementary Fig. 2). CrSeCl also has a FM ground state, but its magnetization is in plane due to its negative SIA. Second, CrSeBr and CrSeI have medium DMI, small SIA, and hence small \(\left| A \right|K/{{{\bf{D}}}}_{//}^2\). Therefore, they have a spin spiral ground state with a large periodic length. Finally, CrTeX (X = Cl, Br, I) MLs have both large DMI and SIA. Their magnetic ground states have wormlike domains, similar to what was found in the previous studies of 2D Janus manganese dichalcogenides20.

Considering the needed semiconducting nature of vdW ferromagnets for engineering emergent physical properties via the magnetic proximity effect in heterostructures7,13,16, we first analyze the electronic properties of CrSX (X = Cl, Br, I) MLs which have a FM ground state and out-of-plane magnetic anisotropy. Band structures in Fig. 2a–c show that all CrSX MLs are indirect-gap semiconductors. As the electronegativity weakens from Cl to Br and to I, the band gaps of CrSX decrease from 2.17 eV (CrSCl) to 1.77 eV (CrSBr) and to 0.81 eV (CrSI). The curves of density of state (Supplementary Fig. 3) suggest that the conduction bands mainly come from the d states of Cr while the valence bands have mixtures of Cr, S, and X states. Besides, the d–p hybridization between Cr and S atoms is stronger than that between Cr and X atoms near the Fermi level.

Fig. 2: DFT + U + SOC calculated band structures.
figure 2

a CrSCl, b CrSBr and c CrSI. d A summary of the DFT calculated induced magnetic moments (M) on the ligand anions of CrSX and other eight representative FM semiconductors. The value of M on S2− ion in CrSBr is highlighted by the green dashed line.

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As the magnetic ions are mostly covered by nonmagnetic anions in vdW FM semiconductors, the spin polarization of the outer layer is typically very small. The magnetic proximity effect is hence weak in most vdW heterostructures. Interestingly, the magnetic moments on S2− anion are about 0.14 μB/S in CrSX MLs, the largest for 2D FM semiconductors reported so far (Fig. 3c)1,11,40,41,42,43,44,45. Especially, this magnetic moment is much larger than that of I2− anions in CrI37,13,16,46,47,48,49, suggesting that CrSX may have a significant magnetic proximity effect on other vdW functional materials.

Fig. 3: Electronic and topological properties of CrSBr/BS/CrSBr.
figure 3

a Side view of the stable stacking configuration at the CrSBr/BS interface. b The spin polarization at the CrSBr/BS interface. Spin-up and spin-down densities are indicated by the yellow and cyan isosurfaces, respectively. The isovalue surface level of spin density is 6 × 10−6 e Å−3. c DFT + U+ SOC calculated band structure. The inset shows the sketch of the magnetizations (represented by blue arrows) of CrSBr MLs. d The four bands near the Fermi level. e The band structure and the chiral edge state (highlighted by the black arrow) of the one-dimensional CrSBr/BS/CrSBr nanoribbon.

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Large-gap QAHE in CrSBr/Bi2Se3/CrSBr vdW heterostructure

We first examine the effect of CrSX MLs on magnetizing topological surface states (TSSs) of 3D topological insulators for the realization of QAHE8. We construct an vdW heterostructure with two CrSBr MLs and a six quintuple-layer Bi2Se3 (BS) thin film (CrSBr/BS/CrSBr). The calculated binding energies of different stacking configurations suggest that Cr3+ cations of CrSBr prefer to align with Bi and the S2− side contacts BS thin film (Fig. 3a and more details in Supplementary Fig. 4). Our ab initio molecular dynamics simulations show that this CrSBr/BS/CrSBr heterostructure is thermodynamically stable (Supplementary Fig. 5). The induced spin polarization on BS penetrates through the film (Fig. 3b), with a strength twice as large as that in CrI3/BS/CrI313. Figure 3c shows the band structure of CrSBr/BS/CrSBr when the magnetizations of top and bottom CrSBr MLs are ferromagnetically ordered. As a result of the strong magnetization in CrSBr, the system has a large band gap up to 19 meV at the Γ point, indicating its efficient magnetic proximity effect on the TSSs of BS thin film. By examining the spin components of the four bands near the Fermi level (Fig. 3d), we find that the two bands below (above) the Fermi level have the same spin-down (spin-up) components. These features clearly suggest the TSSs of the BS thin film are strongly magnetized by CrSBr.

To investigate the topological property of CrSBr/BS/CrSBr, we fit its band structure using an effective four-band model. With the bases of \(\left\{ {\left| {t, \uparrow } \right\rangle ,\left| {t, \downarrow } \right\rangle ,\left| {b, \uparrow } \right\rangle ,\left| {b, \downarrow } \right\rangle } \right\}\), the model Hamiltonian of inversion symmetric heterostructures is written as50

$$\begin{array}{ll}H\left( {k_x,k_y} \right) = Ak^2 + \left[ {\begin{array}{*{20}{c}} {v_{\mathrm {F}}\left( {k_y\sigma _x - k_x\sigma _y} \right)} & {M_k\sigma _0} \\ {M_k\sigma _0} & { - v_{\mathrm {F}}\left( {k_y\sigma _x - k_x\sigma _y} \right)} \end{array}} \right] \\\qquad\qquad\quad+ \left[ {\begin{array}{*{20}{c}} {\Delta \sigma _z} & 0 \\ 0 & {\Delta \sigma _z} \end{array}} \right].\end{array}$$
(2)

In Eq. (2), ↑ (↓) denotes spin-up (spin-down) states; vF, \(k^2 = k_x^2 + k_y^2\) and \(\sigma _{x,y,z}\) are the Fermi velocity, in-plane wave vector and Pauli matrices, respectively. The coupling between the top and bottom TSSs of BS thin film is described by \(M_k = \Delta _h + Bk^2\) and \(\Delta _h\) is the coupling induced gap. By fitting the DFT calculated band structure with Eq. (2) (Supplementary Fig. 6), we obtain \(\Delta _h\) and Δ are 1.0 and 10.4 meV, respectively. According to the general rule proposed in ref. 13, CrSBr/BS/CrSBr is a Chern insulator with Chern number CN = 1. This topological nature is further confirmed by the presence of one chiral edge state that connects the valence and conduction bands in the band structure of the one-dimensional CrSBr/BS/CrSBr nanoribbon (Fig. 3e). Taking together TC (176 K) of the FM semiconductor CrSBr ML and the large nontrivial band gap (19 meV, corresponding to 220 K), it is conceivable that QAHE with a high temperature can be achieved in CrSBr/BS/CrSBr.

Sizable valley splitting in CrSBr/MoTe2 vdW heterostructure

We further explore the valley splitting of TMDC MLs in contact with CrSBr. To this end, we study the vdW heterostructure of CrSBr and MoTe2 MLs (CrSBr/MoTe2). Again, the calculated binding energies (Supplementary Fig. 7) indicate that the S2− side of CrSBr binds to MoTe2 (Fig. 4a). Cr3+ cations and S2− anions sit on the top of Mo4+ cations and the hollow sites, respectively. The fat band representation in Fig. 4b shows two important features: (i) conduction bands of CrSBr locate in the gap of MoTe2; (ii) valence and conduction bands of MoTe2 are not much affected by CrSBr, suggesting a weak hybridization between CrSBr and MoTe2. The Berry curvature map in the 2D Brillouin zone (Fig. 4c) shows opposite Berry curvatures in the vicinity of K+ and K− valleys. These illustrate that the coupled spin and valley physics is remained in CrSBr/MoTe2.

Fig. 4: Electronic and topological properties of CrSBr/MoTe2.
figure 4

a Top and side views of the stable stacking configuration. b MoTe2-projected (colored lines) band structure. Color bar indicates the spin projections. c Distribution of Berry curvature (in unit of Å2) over 2D Brillouin zone. d Dependence of \(\sigma _{xy}\) on the Fermi level. The shaded area denotes the energy window between the two valence-band valley extrema.

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To quantitatively determine the valley splitting in CrSBr/MoTe2, we adopt an energy scale35, \(\Delta _{{\mathrm {val}}}^{c/v,\tau } = E_ \uparrow ^{c/v,\tau } - E_ \downarrow ^{c/v, - \tau }\). Here, v (c) denotes valence (conduction) bands; \(K_ \pm\) are distinguished by index \(\tau = \pm\). According to this definition, \(\Delta _{{\mathrm {val}}}^{v, + }\), \(\Delta _{{\mathrm {val}}}^{v, - }\), \(\Delta _{{\mathrm {val}}}^{c, + }\), and \(\Delta _{{\mathrm {val}}}^{c, - }\) are estimated as −37.9, −8.8, 8.6, and 8.7 meV, respectively. We sees that \(\Delta _{{\mathrm {val}}}^{v, + }\) in CrSBr/MoTe2 is sizable, corresponding to the valley splitting generated by a magnetic field of 379 T35. It is worth noting that this value is much larger than the counterparts in CrI3/WSe216,46,47 and CrI3/MoTe249. More remarkably, the smallest energy for the band edge vertical optical transition without spin flip in two valleys reaches a giant value of 46.5 meV. Thanks to the time reversal symmetry breaking and the nonvanishing Berry curvature, CrSBr/MoTe2 has a nonzero anomalous Hall conductivity, \(\sigma _{xy}\), when Fermi level lies between the valence band maxima of K+ and K- valleys (Fig. 4d). Taking together the anomalous Hall conductivity and sizable valley splitting, it is conceivable that a spin- and valley-polarized Hall current can be generated in CrSBr/MoTe2 when applying an in-plane electric field51, thus providing applications in valleytronics.

Discussion

Finally, we find that CrTeX (X = Cl, Br, I) MLs can host magnetic skyrmion states in an external magnetic field, because of the strong SOC of Te and the symmetry reduction. This is a very attractive feature for diverse applications as discussed in the literatures for the studies of other magnetic systems52,53,54. To characterize the presence of magnetic skyrmions in MC simulations, we calculate the topological charge Q which is defined as55:

$$Q = \frac{1}{{4\pi }}{\int} {{{{\bf{m}}}} \cdot \left( {\frac{{\partial {{{\bf{m}}}}}}{{\partial x}} \times \frac{{\partial {{{\bf{m}}}}}}{{\partial y}}} \right){\mathrm {d}}x{\mathrm {d}}y} .$$
(3)

In Eq. (3), m is a normalized magnetization vector; x and y are in plane coordinates. On a discrete spin lattice, Eq. (3) is evaluated by summing over the solid angle Ω of three spins according to the Berg formula56,57. Supplementary Fig. 8 shows the topological charge Q of CrTeI as a function of temperature (T) and out-of-plane external magnetic field (B). Through examining the spin textures under different T and B, we find that the red area with large negative value of Q corresponds to the formation of magnetic skyrmion lattices in CrTeI. Because of the strong DMI, magnetic skyrmion lattices may exist in a large T–B parameter space, with T up to 80 K and B from 1 to 8 T. CrTeCl and CrTeBr also form magnetic skyrmion lattices but in a smaller T–B region (Supplementary Fig. 9). Hence, we recommend CrTeI ML as the most promising 2D platform for the realization of magnetic skyrmions.

In summary, based on systematical first-principles studies on vdW Janus ML CrYX (Y = S, Se, Te; X = Cl, Br, I), we find that CrSX (X = Cl, Br, I) are useful FM semiconductors with high Curie temperatures up to 176 K and large induced magnetic moments on the ligand S2− anions. Remarkably, the long-sought QAHE with a large gap of 19 meV and a sizable valley splitting of 37.9 meV are achieved through the magnetic proximity effect in vdW heterostructures CrSBr/Bi2Se3/CrSBr and MoTe2/CrSBr, respectively. Furthermore, CrTeX (X = Cl, Br, I) may host magnetic skyrmion states under external magnetic fields. Our work unveils the promising multifunctionalities of 2D vdW Janus magnet Cr-based dichalcogenide halides and reveals their potential for diverse applications in topotronic and valleytronic devices.

Methods

First-principles calculations

Our first-principles calculations based on the density functional theory (DFT) are performed using the Vienna Ab initio Simulation Package with the generalized gradient approximation58,59. Core-valence interactions are described by projector-augmented wave pseudopotentials60,61. We utilize an energy cutoff of 350 eV for the plane-wave expansion and fully relax lattice constants and atomic positions until the force acting on each atom is smaller than 0.01 eV Å−1. To take into consideration the strong correlation effect among Cr 3d electrons, we adopt U = 3.0 eV and JH = 0.9 eV15. As discussed in Supplementary Note 8, we obtain similar results when different U values are employed. In building vdW heterostructures, we use an inplane lattice constant aBS = 4.16 Å of the relaxed bulk BS for CrSBr/BS/CrSBr and aMT = 3.55 Å of MoTe2 (MT) ML62 for MoTe2/CrSBr. When relaxing structures, the first Brillouin zone is sampled by 12 × 12 × 1, 6 × 6 × 1, and 12 × 12 × 1 Γ-centered Monkhorst–Pack k meshes for CrYX, CrSBr/BS/CrSBr, and MoTe2/CrSBr, respectively. We add a vacuum space of 12 Å between slabs along the normal axis to eliminate the spurious interactions. To obtain the accurate magnetic anisotropy energies of CrYX that arise from SIA, a very dense Γ-centered Monkhorst–Pack k mesh of 24 × 24 × 1 is used to sample the first Brillouin zone and the total energy convergence criterion is set to be 10−7 eV. Magnetic anisotropy energies are determined by computing the total energy difference with magnetic moments of Cr3+ ions being parallel and perpendicular to the plane of the CrYX ML. When calculating magnetic anisotropy energies, SOC is explicitly included in self-consistent loops. To correctly describe the weak interaction across the vdW gap in these heterostructures, we employ the nonlocal vdW functional (optB86b-vdW)63,64. Berry curvatures and chiral edge states are calculated by the wannier9065 and WannierTools66.