Magnetism in semiconducting molybdenum dichalcogenides

Abstract

Transition metal dichalcogenides (TMDs) are interesting for understanding the fundamental physics of two-dimensional (2D) materials as well as for applications to many emerging technologies, including spin electronics. Here, we report the discovery of long-range magnetic order below T _M = 40 and 100 K in bulk semiconducting TMDs 2H-MoTe₂ and 2H-MoSe₂, respectively, by means of muon spin rotation (μSR), scanning tunneling microscopy (STM), and density functional theory (DFT) calculations. The μSR measurements show the presence of large and homogeneous internal magnetic fields at low temperatures in both compounds indicative of long-range magnetic order. DFT calculations show that this magnetism is promoted by the presence of defects in the crystal. The STM measurements show that the vast majority of defects in these materials are metal vacancies and chalcogen-metal antisites, which are randomly distributed in the lattice at the subpercent level. DFT indicates that the antisite defects are magnetic with a magnetic moment in the range of 0.9 to 2.8 μ_B. Further, we find that the magnetic order stabilized in 2H-MoTe₂ and 2H-MoSe₂ is highly sensitive to hydrostatic pressure. These observations establish 2H-MoTe₂ and 2H-MoSe₂ as a new class of magnetic semiconductors and open a path to studying the interplay of 2D physics and magnetism in these interesting semiconductors.

Fig. 1. ZF μSR time spectra and temperature-dependent ZF μSR parameters for MoTe₂.

ZF μSR time spectra for the single-crystal (A) and polycrystalline (B) samples of MoTe₂ recorded at various temperatures up to 450 K. (C) Temperature dependence of the internal field μ₀H_int of 2H-MoTe₂ as a function of temperature. (D) Temperature dependence of the magnetic fractions V_M and V* of the precession and strongly damped signals, respectively (see text). The total signal is also shown.

Fig. 2. Temperature-dependent weak-TF μSR parameters and weak-TF μSR spectra for MoTe₂.

(A) WTF μSR time spectra for MoTe₂ recorded at T = 5 and 300 K. The solid gray lines represent fits to the data by means of Eq. 2. Temperature dependence of the oscillating fraction (B) and the paramagnetic relaxation rate λ (C) of the single-crystalline and polycrystalline samples of MoTe₂ obtained from the weak-TF μSR experiments. The solid arrows mark the magnetic transition temperatures T_M and T*. The solid gray lines represent fits to the data by means of phenomenological function (see Eq. 3 in Materials and Method).

Fig. 3. Temperature- and field-dependent magnetization data for MoTe₂ and MoSe₂.

The temperature dependence of ZFC and FC magnetic moments of MoTe₂ (A) and MoSe₂ (C), recorded in an applied field of μ₀H = 10 mT. The arrows mark the onset of the difference between ZFC and FC moment as well as the anomalies seen at low temperatures. The field dependence of magnetic moment of MoTe₂ (B) and MoSe₂ (D), recorded at various temperatures.

Fig. 4. Observation of intrinsic defects in 2H-MoTe₂ through STM and sample characterizations.

(A) Large-scale atomic-resolution STM topography (20 nm) of the MoTe₂ surface. The image reveals an approximately uniform density of two types of defects over the entire surface. The STM topography was taken at −1.25 V and −100 pA set point. (B) Small-scale atomic-resolution STM topography (2 nm) shows that these two types of defects are mainly substitutional Mo atoms at Te sites (Mo_sub) and Mo vacancies (Mo_vac). (C and D) Local STM topography (1 nm) and DFT + U–optimized geometry for Mo_sub defect, respectively. The observed atoms in (C) are those at the top layer of tellurium, with an increased topographic height profile at the center of the six brightest spots. We attribute this to a molybdenum replacement of a tellurium atom. (E and F) Local-scale STM topography (1 nm) and DFT + U–optimized geometry of the second type of defects observed, respectively. The image in (E) shows a depression in the topographic height profile, centered between three tellurium atoms. On the basis of the symmetry, we attribute this to a molybdenum vacancy under the layer of tellurium. (G) ESR spectra for 2H-MoTe₂, recorded at various temperatures. (H) PDF average structure refinements for 2H-MoTe₂ at 300 K fitted to the hexagonal 2H-structure model.

Fig. 5. DFT + U and STM.

(A) Spin-polarized density of states, DOS(states/eV), of Mo_sub defects in the antiferromagnetic (AFM) phase. Fermi level, E_Fermi, is set to zero. Both the spin-up and spin-down DOS reveal an in-gap state due to the defect. (B) Magnetization density (±0.001 electrons/Bohr³) on the top surface of bulk 2H-MoTe₂ in AFM configuration. Spin-up and spin-down states are shown in faint blue and orange isosurfaces, respectively. Note that spins also couple antiferromagnetically at the local level between the Mo impurity and the nearest Mo atoms. (C) Scanning tunneling spectroscopy dI/dVs taken on the two types of defect as well as far from any defect.

Fig. 6. Pressure evolution of various quantities.

(A) Magnetic transition temperature T_M and magnetic volume fraction V_M as a function of pressure. (B) Pressure dependence of the magnetic fractions V_M and V*, corresponding to the precession μSR signal and the strongly damped μSR signal, respectively. The total magnetic signal is also shown. The dashed lines are guides to the eyes.