One of the current research interests in two-dimensional (2D) materials focuses on magnetic van der Waals (vdW) materials, due to the intriguing physical properties for both fundamental research and potential applications in optoelectronics, spintronics, and valleytronics. A number of potentially magnetic single-layer vdW materials have recently been proposed, including V-based dichalcogenides, CrGeTe₃ ternary tritellurides, and CrX₃ trihalides. Studies on CrI₃ reveal that it has a stable ferromagnetic (FM) ordering in 2D form and a little change of layer-number dependence of Curie temperatures.^[1–5] This has attracted a lot of attention in other magnetic vdW crystals that are similar to CrI₃.^[6–12]

Recently, many studies have focused on the magnetic van der Waals crystals MPX₃, which resemble similar lattice structure and chemical composition.^[13–16] MPX₃ is a family of 2D vdW layered crystals that have been prepared and studied for two decades. The structure of bulk MPS₃ is similar to CrI₃ which adopts the monoclinic AlCl₃ structure (point group C_2h). The layer structure is anchored by (P₂X₆)⁴⁻ bipyramids in a triangular lattice which provide enclosures for transition metal (TM) atoms arranged in a hexagonal array.^[17–23] The monolayer MPS₃ has a perfect honeycomb lattice similar to graphene. For magnetism in MPS₃, the intralayer magnetic structures are antiferromagnetic (AF). However, depending on the variety of TM atoms, magnetic structures possess very rich types. For MnPS₃ material, the AF phase transition temperature T_N is 78 K. The magnetic moment is 3.5 ** _B^[23] and the spin lies in the ab plane with inclined angle. The magnetic structure of MnPS₃ in the ab plane is Néel AF in which the spin of the two adjacent magnetic ions is reversed and the magnetism along the c-axis is FM ordering. For FePS₃, its T_N is 120 K and the spin moment is along the c-axis. In the ab plane, the magnetic structure is zigzag-type AF ordering in which the two adjacent magnetic ions are the same and are opposite to the third neighbor. Along the c-axis, the magnetic order is AF type. For NiPS₃, its T_N is 150 K and the angle between the spin and the c-axis is less than 30°. The intralayer magnetic structure of NiPS₃ is zigzag-type which is the same as FePS₃, while the interlayer magnetic order is FM type.^[10]

Raman is a useful tool to study the structure and magnetic properties of ultrathin vdW single crystals. Meanwhile, there are several spectroscopic studies in FePS₃ and NiPS₃. In the previous studies of thin layer FePS₃ and NiPS₃, two different point groups, C_2h and D_3d, have been proposed when discussing the phonon modes and the lattice structure.^[13,14] However, no consensus has yet been reached. The information on MnPS₃ is still lacking. A comparative study of the phonon spectra in MPS₃ (M=Mn, Fe, Ni) is important for the clarification of this issue. Moreover, the temperature dependence behaviors of magnetism in MPS₃ have not been studied or discussed in detail. Therefore, this calls for a systematic research of the phonon spectra and magnetic properties in MPS₃ materials with different transition metals.

In this paper, we present temperature-dependent and polarization-resolved Raman spectroscopy study on layered MPS₃ (M=Mn, Fe, Ni) single crystals. Almost all of the Raman active phonons are observed, and the phonon mode assignments are made by symmetry analysis and comparison with first principle calculations. In particular, we conduct a comparative study of Raman spectra in MnPS₃, FePS₃, and NiPS₃, which share identical lattice structure but exhibit distinct magnetic order, and their temperature evolution crosses the magnetic transition. Consequently, we provide comprehensive information on the relation of the lattice dynamics and magnetism in the MPS₃ system.

Single crystals of MPS₃ (M=Mn, Fe, Ni) were grown by chemical vapor transport (CVT) method. The crystal naturally cleaves along the (001) surface, forming MnPS₃ flakes weakly bonded by van der Waals force. In this experiment, the MnPS₃ flakes were cleaved from bulk single crystals, transferred on to silicon substrates, and capped with 90 nm silicon oxide (SiO₂) because of the transparent characteristic. The SiO₂ capping layer does not induce any extra signal in the energy range we are interested in and can enhance Raman scattering signal intensity from the sample. The FePS₃ and NiPS₃ single crystals were tested on the copper holder directly. The temperature-dependent and polarization-resolved Raman spectra were collected in a backscattering configuration using an HR800 spectrometer (Jobin Yvon) equipped with a liquid-nitrogen-cooled charge-coupled device (CCD) and volume Bragg gratings. The samples were placed in an ultra high vacuum (UHV) cryostat with a vacuum of ** mbar. A ** laser was focused to a spot on the ab surface of the sample. The scattered signal was collected through a 50×long focus-length objective, and dispersed with a 600 grooves/mm grating. The laser power was kept at approximately ** 1.4 mW. We define X and Y axes inside the crystallographic ab plane. X is perpendicular to the b axis and Y is along the b axis. Z is perpendicular to X and Y.

First-principles calculations were employed to work out the Brillouin zone-center (Gamma point) phonon modes of MnPS₃. The projector augmented wave (PAW) method implemented in the Vienna ab initio simulation package (VASP) package was used to describe core electrons.^[24–28] For the exchange–correlation potential, the generalized gradient approximation (GGA) of Perdew–Burke–Ernzerhof formula was adopted.^[29] To describe the van der Waals interaction in layered systems not included in the conventional density functional theory, the vdW-optB86b functional was chosen.^[30] The on-site Coulomb repulsion among the localized Mn 3d electrons was also included by using the formalism (GGA+U) of Dudarev et al.^[31] with an effective U = 5 eV. The kinetic energy cutoff of the plane-wave basis was set to be 300 eV. The simulations were carried out with a triclinic cell containing two Mn atoms, two P atoms, and six S atoms, in which two Mn atoms took the antiferromagnetic order. An 8×8×8 k-point mesh for the Brillouin zone sampling and the Gaussian smearing with a width of 0.05 eV around the Fermi surface were employed. In structure optimization, both cell parameters and internal atomic positions were allowed to relax until all forces were smaller than 0.01 eV/Å. When the equilibrium structure was obtained, the phonon modes at Brillouin zone center were calculated by using the dynamic matrix method. The calculations with a 10-atom cell gave 27 optical modes. However, to illustrate the displacement patterns of phonon modes, we show our results in a 20-atom supercell deduced from the real-space translational invariance of the 10-atom cell; as in ^[32].

The MPS₃ crystal has a monoclinic structure with C_2h point group (space group C2/m). With 10 atoms in a primitive unit cell, we have a total of 30 phonon modes. At the ** point, there are 8A_g+7B_g Raman active modes. The corresponding Raman tensors are

In Figs. 1(a) and 1(b), we show Raman spectra of MnPS₃ at room temperature. The peak at 520.7 cm⁻¹ is from the Si substrate. All the remaining peaks are the phonons of MnPS₃. We assign the three MnPS₃ phonons that only appear in XX polarization to A_g mode. However, no phonon modes only appear in the XY scattering geometry. In Figs. 1(c) and 1(d), we track the angular dependence of the phonon intensity under parallel and cross polarizations. Surprisingly, we do not observe any mode that reduces to zero intensity at ** .

Fig. 1.

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Fig. 1. (a) Unpolarized Raman spectrum of MnPS3 collected at room temperature. (b) Polarized Raman spectra of MnPS3 at room temperature under (red line) and (blue line) scattering geometry. Inset: the XYZ/abc coordinates. (c) Intensity map of Raman spectra of MnPS3 under parallel polarization scattering geometry as a function of Raman shift and angle. (d) Same as (c), but under cross polarization geometry.

To find the origin of the remaining four phonon modes, we consider a change of the lattice symmetry in the 2D van der Waals materials. For monolayer MnPS₃, the lattice point group is D_3d. At the ** point, there are 3A_1g+5E_g Raman active modes. The corresponding Raman tensors are

The bulk crystals consist of ABC-stacked single layer assemblies that are held together by van der Waals forces. Thus, for bulk crystals, the C₃ symmetry along the c axis has broken compared to the monolayer crystals. Because of the symmetry breaking, the E_g mode in D_3d symmetry will degenerate into A_g and B_g modes which have similar energies in C_2h symmetry. Based on the discussion above, for MnPS₃, the observed phonons are: 115.5 cm⁻¹ ( , ), 153.8 cm⁻¹ ( , ), 245.0 cm⁻¹ ( ), 270.0 cm⁻¹ ( , ), 383.2 cm⁻¹ ( ), 567.5 cm⁻¹ ( , ), and 580.3 cm⁻¹ ).

To relate the observed modes at certain frequencies to the specific atomic displacements, we conduct the first-principles calculations. The experimental and calculated mode frequencies are summarized in Table 1. The calculated phonon frequencies are in good agreement with the experimental data. In Fig. 2, we show the atomic displacements of all of the Raman active modes.

Fig. 2.

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	Fig. 2. Vibration patterns of all Raman modes observed in MnPS3. The mode symmetry, optical activity, and experimental (calculated) phonon frequency (the unit is cm−1) are also listed below each pattern.

Table 1.

Table 1.

Table 1. Calculated and experimental optical phonon modes (in cm−1) for MnPS3. The atomic motions of the modes are also given (see Fig. 4). R and IR denote Raman and infrared activities, respectively. . Symmetry Calculated/cm−1 Experimental/cm−1 Activity 59.7 R 116.5 115.5 R 121.2 115.5 R 147.7 IR 151.1 153.8 R 152.5 153.8 R 154.4 IR 154.8 IR 183.0 IR 190.1 IR 194.0 IR 202.6 R 221.4 R 224.7 R 242.9 245.0 R 244.5 IR 248.0 IR 263.9 270.0 R 266.2 270.0 R 304.0 IR 360.0 383.2 R 425.2 IR 538.8 567.5 R 539.8 567.5 R 539.9 IR 542.2 IR 543.9 580.3 R

Table 1. Calculated and experimental optical phonon modes (in cm−1) for MnPS3. The atomic motions of the modes are also given (see Fig. 4). R and IR denote Raman and infrared activities, respectively. .

Using the same analysis method for MnPS₃, we determine the phonon modes for FePS₃ and NiPS₃. As shown in Fig. 3(a), for FePS₃, the observed phonons are: 94.9 cm⁻¹ ( , ), 156.9 cm⁻¹ ( , ), 223.3 cm⁻¹ ( , ), 245.8 cm⁻¹( , 275.2 cm⁻¹ ( , ), 380.9 cm⁻¹ ( ), and 582.9 cm⁻¹ ( ). Near 275.2 cm⁻¹, the peak energies are slightly different under and scattering geometry, which suggests that there are two different modes at very close energy. The splitting of the peak is found at low temperatures, indicating that the symmetry of bulk crystals is C_2h. The obvious difference between the two channels of FePS₃ at room temperature may be due to the different evolution of different phonon peaks with temperature. The NiPS₃ Raman spectra are shown in Fig. 4, where the observed phonon modes are: 132.2 cm⁻¹ (¹A , ), 177.4 cm⁻¹ ( , ), 234.8 cm⁻¹ ( , ), 255.1 cm⁻¹ (⁴A ), 280.7 cm⁻¹ ( , ), 384.8 cm⁻¹ ( ), and 589.2 cm⁻¹ ( ). The experimental results of FePS₃ and NiPS₃ are in good agreement with the theoretical calculations.^[6]

Fig. 3.

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	Fig. 3. (a) Raman spectrum of FePS3 collected at room temperature. (b) Polarized Raman spectrum of FePS3 at room temperature under different polarization configurations. (c) The angle-dependent Raman spectrum of FePS3 in parallel polarization channel. (d) The angle-dependent Raman spectrum of FePS3 in cross polarization channel.

Fig. 4.

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	Fig. 4. (a) Unpolarized Raman spectrum of NiPS3 at room temperature. (b) Polarized Raman spectrum of NiPS3 at room temperature under different polarization configurations. (c) The angle-dependent Raman spectrum of NiPS3 in parallel polarization channel. (d) The angle-dependent Raman spectrum of NiPS3 in cross polarization channel.

In Fig. 5, we show the Raman spectra in MPS₃ (M=Mn, Fe, Ni) at 10 K, T_N, and 300 K. For all of the samples, we observe that the phonon mode (** 260 cm⁻¹ at 300 K) splits into two peaks at the lowest temperature. We attribute this to the narrowing of the phonon linewidth at low temperature. Moreover, we observe two unusual temperature-dependent behaviors for MPS₃ (M=Mn, Fe, Ni). Firstly, for FePS₃, three new phonon modes appear in the magnetic order phase ( , while we do not observe such additional modes in MnPS₃ or NiPS₃. This different behavior in FePS₃ must be related to its special magnetic structure. We attribute this to the AF interlayer magnetic structure in FePS₃, which doubles the lattice unit cell if there is a strong spin–lattice coupling, and, consequently, the zone boundary modes are folded to the ** point. In Mn/NiPS₃, the interlayer magnetic structure is FM, and will not double the lattice unit cell. This explains the non-observation of additional modes in Mn/NiPS₃. Secondly, for MnPS₃ and NiPS₃, they have the same out-of-plane magnetism but different in-plane magnetism. The in-plane magnetism is zig-zag type AF in NiPS₃, while the in-plane magnetism is Néel type AF in MnPS₃. We find that the energy of the 150 cm⁻¹ phonon mode at 10 K is much lower than that at 300 K in MnPS₃, which is unusual for a normal phonon mode. The lower energy of this mode at 10 K indicates its coupling with spins, which modulates the self-energy of this phonon and causes the lower energy of it. This indicates that the in-plane Néel AF in MnPS₃ favors a spin–phonon coupling compared to the in-plane zig-zag AF in NiPS₃ and FePS₃. Comparing the ab in-plane and the c axis out-of-plane magnetic structure of the series, it is found that spin–phonon coupling is general in this family materials and different magnetic structures will have different influences on the phonons and magnons.

Fig. 5.

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	Fig. 5. The temperature dependence of Raman spectra of MnPS3, FePS3, and NiPS3. The dashed line indicates the softened mode in MnPS3 and the arrows indicate the new modes in FePS3 below TN.

We report the experimental and first-principles calculation for the temperature dependent and polarization resolved Raman spectroscopy on the lattice dynamics of MPS₃ (M=Mn, Fe, Ni) single crystals. We identify 7 out of 11 Raman active phonons and the corresponding atomic displacements. In addition, we observe additional phonons appearing in FePS₃ in the magnetic ordered state, while there is no new phonon mode in MnPS₃ and NiPS₃. This magneto-elastic effect is related to unique AF order along the c axis in FePS₃, which doubles the unit cell and folds the zone boundary mode to the ** point. For MnPS₃, part of the phonons are softened below T_N, suggesting spin–phonon coupling in this material. The present study provides the system information on the lattice dynamics and magnetic of MPS₃ (M=Mn, Fe, Ni) and is of significance for the exploration of structural and magnetic properties of the monolayer MPX₃.

Computational resources have been provided by the Physical Laboratory of High Performance Computing at Renmin University of China. The atomic structures and vibrational displacement patterns were prepared with the XCRYSDEN program.^[33]