Elemental excitations in MoI₃ one-dimensional van der Waals nanowires

A new research field focused on one-dimensional (1D) van der Waals (vdW) quantum materials has emerged from earlier works on low-dimensional systems.^1–4 The 1D vdW materials are based on 1D structural motifs and include transition metal trichalcogenides and halides.^1–5 It is helpful to distinguish true-1D vs quasi-1D vdW systems. We define the material to be true-1D if it contains only covalent bonds in the direction of the atomic chains with all other bonds being of vdW type; the material is quasi-1D if it contains strong covalent bonds along the 1D chain direction while also bonded by weaker covalent bonds in the perpendicular planes. For example, according to this criterion, Nb₂Se₉ is a true-1D material whereas TaSe₃ is a quasi-1D material.^6–8 The number of vdW materials with quasi- or true-1D structures is not known, but machine learning investigations indicate that hundreds of 1D vdW materials are synthetically accessible.^5,9–11 True-1D vdW materials can be exfoliated chemically or mechanically into individual atomic chains or a few-atomic chain bundles.^2,6,12 One can also envision that progress in chemical vapor deposition (CVD) will eventually allow the controlled synthesis of such 1D materials on substrates of choice, thereby enabling their practical applications.^13–15 

Owing to their unique dimensionality and electronic density of states, 1D materials often support unusual quasiparticle excitations, such as separated spin-charge excitations, Luttinger plasmons with quantized velocities,¹⁶ magnetism,¹⁷ charge density waves, and emergent topology.^18–21 Many of such unusual electronic properties also manifest themselves as nontrivial features in the dispersion relation of other collective excitations, such as phonons and magnons, due to their lower spatial dimensionality and stronger electronic correlation in 1D materials. The magnetic properties of 1D materials are of particular interest. The intrinsic ferromagnetic (FM) and antiferromagnetic (AFM) spin orderings are observed in the single atomic layers of some transition-metal dichalcogenides (MX₂) and transition-metal phospho-trichalcogenides (MPX₃) that constitute quasi-two-dimensional (2D) systems.^22,23 In these compositions, “M” is a transition metal, “X” is a chalcogen, and “P” is phosphorous. The possibility of AFM ordering in true-1D vdW materials is interesting from both fundamental science and practical application point of view. The prospect of the helical spin order, i.e., spin-spiral order, in 1D materials is particularly exciting.²⁴ The challenges with the experimental observation of magnetism in the 1D limit are complex owing to the scarcity of stable true-1D vdW material systems, the low signal-to-noise ratio in magnetometry and other related experiments, and difficulties in handling individual atomic chains. As a step in this direction, we use Raman spectroscopy to investigate the elemental excitations in exfoliated van der Waals nanowires of MoI₃, classified as a true-1D vdW material. While practical applications of such materials are in the distant future, one can envision that electrically insulating magnetic materials with the quasi-1D structure can serve as magnonic interconnects conducting pure spin currents in spintronic circuits.²⁵ 

MoI₃ crystals for this study were prepared from the elements using the chemical vapor transport (CVT) technique.^12,26 The inclusion of NH₄I as a transport agent led to a more reliable synthetic procedure, likely due to lower internal ampule pressure and excellent product quality that allowed us to determine the single crystal structure of MoI₃ by x-ray diffraction; details and atomic coordinates are provided in the supplementary material (see Tables S1–S4 and Figs. S1 and S2). Figure 1(a) presents the crystal structure of MoI₃. Although this structure can be refined in both Pmmn and P6₃/mcm with low R values, we ultimately used Pmmn in line with the interpretation of powder x-ray diffraction (PXRD) data by Ströbele and co-workers.²⁶ The Pmmn structure was further confirmed by our high-angle annular dark-field scanning transmission electron microscopy (HAADF-STEM) imaging (vide infra). The space group selection is critical because Pmmn leads to “dimerized” MoI₃ chains showing clear Peierls distortion with alternating Mo–Mo distances of 2.8793(19) and 3.5298(19) Å, whereas P6₃/mcm leads to 1D chains of equidistant Mo atoms. We also validated the space group by PXRD; Fig. 1(b) shows the experimental pattern from MoI₃ crystals with selected hkl indices. (Complete hkl assignment is shown in Fig. S1 of the supplementary material.) Refined lattice parameters from the single crystal study [a = 12.3183(4) Å, b = 6.4091(2) Å, c = 7.1180(3) Å] are similar to those from our PXRD analysis [$a=12.3200(6) Å$⁠, $b=6.4088(6) Å$⁠, $c=7.1225(3) Å]$ as well as literature values.²⁶ Figures 1(c) and 1(d) present the low-magnification HAADF-STEM and atomically resolved image of the exfoliated MoI₃ crystals, respectively. The latter confirms MoI₃ as the Pmmn lattice structure along the (100) projection. Note that the scanning electron microscopy (SEM) image of representative MoI₃ crystals, presented in Fig. 1(e), shows that this material grows preferentially along the b-axis, leading to needlelike structures with high aspect ratios. The energy dispersive spectroscopy (EDS) mapping of the exfoliated samples shows a homogeneous distribution and overlap of Mo and I [Figs. 1(f) and 1(g)]. The EDS analytical results also confirm the expected composition of ∼1:3 Mo:I (see Table S5).

We used temperature- and polarization-dependent Raman spectroscopy to study the elemental excitations, i.e., phonons and magnons, in MoI₃ crystals. The experiments were conducted in the conventional backscattering configuration using a 488 nm laser excitation. In all experiments, the samples were positioned in such a way that the polarization of the incident light was along the “b” crystallographic direction, i.e., along the nanowires. The polarization of the scattered light was selected to be either parallel with or transverse to the incident light. The power of the laser was kept at 400 μW to avoid self-heating effects. The results of the Raman measurements for the parallel and cross-polarization arrangements in the temperature range of 1.6–300 K are presented in Figs. 2(a) and 2(b), respectively. The unit cell of MoI₃ has 16 atoms with 45 optical phonon branches, resulting in a rich Raman response with many peaks in the range of 10–750 cm⁻¹. These Raman features strongly depend on the respective polarization of the incident and scattered light, which is typical for one-dimensional materials.^27,28 As theoretically shown later in this paper, the maximum energy of optical phonons and magnons in MoI₃ at the Brillouin zone (BZ) center is ∼228 and ∼310 cm⁻¹, respectively. Therefore, the peaks observed in the spectra above ∼310 cm⁻¹ are associated with the higher-order scattering processes, except the Si substrate peak at ∼520 cm⁻¹. We plotted the spectral position and full-width-at-half-maximum (FWHM) of three well-defined peaks, labeled as “p₁,” “p₂,” and “p₃” [Fig. 2(a)], as a function of temperature. These peaks have Ag, B₁g, and B₃g vibrational symmetries. The results are presented in Figs. 2(c) and 2(d).

Generally, the phonon features in Raman spectra of different materials shift to lower frequencies with increasing temperature, which is explained by the crystal lattice expansion and phonon anharmonic effects.²⁹ This is the case for the Raman peak p₃ at ∼210 cm⁻¹. The spectral positions of the other two peaks at ∼57 and ∼88 cm⁻¹ blueshift with increasing temperature. Phonon hardening with increasing temperature, observed for the peaks labeled as p₁ and p₂, is unusual. Similar anomalous behavior has been previously reported for the so-called soft phonon modes in ferroelectric materials such as SrTiO₃, the transverse acoustic modes in Invar alloys, and magnetic random solid solutions such as Fe_1−xPd_x.^30,31 In the latter case, the phonon hardening was attributed to thermal magnetic fluctuations.³² One can further notice a deviation in the FWHM temperature dependence from a linear behavior with a pronounced kink at ∼150 K for both Raman features (p₁ and p₂). Such a non-monotonic characteristic of FWHM could indicate a magnetic phase transition in MoI₃.

The intensity of the peaks associated with scattering processes involving magnons tends to weaken with temperature and eventually fall to zero beyond the magnetic phase transition temperature.³³ One can see in Figs. 2(a) and 2(b) that the intensity decreases for all peaks with increasing temperature, leaving the task of distinguishing possible magnon peaks from phonon peaks extremely difficult. It should be noted that the spectral position of the peaks is insensitive to the magnetic field of 9 T applied along the crystal's “c” axis as well. Yet, this does not exclude the possibility of magnetic order. It is known that in many AFM materials, e.g., NiO, even a strong magnetic field produces small effects on the Raman spectrum.³⁴ Three broad Raman features at ∼465, ∼580, and ∼625 cm⁻¹ (labeled as “m₁,” “m₂,” and “m₃”) encompassed by the rectangular dashed lines in Fig. 2(a) contain additional valuable information. The theory described below indicates that these spectral features are associated with two-magnon scattering processes. They disappear completely in the temperature range from 125 to 150 K, and their energy exactly matches the calculated magnon energy at the BZ edge along the $Γ−Y$ direction, multiplied by a factor of two, as it should be for the two-magnon processes.

To further elucidate the nature of the observed phase transition in MoI₃, we plot the intensity color map of the Raman spectra shown in Fig. 2(a) as a function of the temperature and frequency in the low and high wavenumber regions. The results are presented in Figs. 3(a) and 3(b). The difference in the intensity of the Raman peaks in these two frequency ranges is significant; the latter explains the reason for plotting them separately. In both plots, the color change from violet to red indicates the peaks become more intense. The white regions in Figs. 3(a) and 3(b) are the strong peaks at 88 and 207 cm⁻¹ and the Si peak at 520 cm⁻¹ [see Fig. 2(a)]. They are shown with white color because their intensity is beyond the defined maximum level in the colormap (the red color) to avoid overshadowing the weak features of interest. One can see in Fig. 3(a) that none of the peaks has its intensity vanishing as the temperature rises. This confirms that all these peaks are associated with the phonon scattering processes. Interestingly, the broad Raman features at 465, 580, and 625 cm⁻¹ completely vanish at the same temperature range. Similar broad features associated with the two-magnon scattering processes are common in AFM materials such as MnF₂, NiO₂, MnPSe₃, and VI₃.^35–38 

A recent study predicted the AFM spin-ordering in MoI₃ using machine learning algorithms.⁵ This report did not describe the specific type of AFM ordering or the Néel temperature of the transition in MoI₃. To compare directly the theory prediction with our experimental results, we performed ab initio calculations of the phonon and magnon dispersion of MoI₃. Density functional theory (DFT) calculations were carried out with the generalized gradient approximation (GGA)³⁹ exchange-correlation functional of Perdew, Burke, and Ernzerhof (PBE)^40,41 as implemented in the Vienna ab initio simulation package (VASP).⁴² The ion–electron interactions use the projected augmented wave (PAW) method. The energy cutoff for the plane wave basis was set to 520 eV. All the structures were allowed to relax during this process with a conjugate gradient algorithm until the energy on the atoms was less than 10⁻⁴eV. The DFT-D3 approach proposed by Grimme⁴³ was used for the vdW interactions. A Hubbard + U value of 4.0 was used on the Mo atoms. This value was found to minimize the negative modes in the phonon dispersion. Phonon calculations were performed using the finite-displacement supercell approach as implemented in Phonopy.^44,45 For the phonon calculations, the Brillouin zone was sampled by a 4 × 7 × 4 Monkhorst–Pack k-point grid. The results of the calculations are presented in Fig. 4(a). The green spheres are the spectral position of Raman peaks in the range of 10–250 cm⁻¹ in the parallel polarization configuration [see Fig. 2(a)]. The theoretical calculations are in excellent agreement with the experimental data.

The magnetic properties were calculated with PBE + U, as described above, with the inclusion of spin–orbit coupling (SOC). To determine the magnetic ground state, total energy calculations were performed with the magnetic moments of the Mo atoms in ferromagnetic (FM) order and two different anti-ferromagnetic (AFM) orders (see Fig. S3 in the supplementary material). The ground state energy of the FM order was approximately 1.5 eV higher per unit cell than the ground state energies of the two different AFM configurations. In both AFM configurations, alternating spins were anti-aligned along the chains. From total energy calculations with different spin configurations, the exchange coupling constants and the magnetic anisotropy energy (MAE) were determined for the magnetic Hamiltonian given by the following equation:

Here, greek indices label the different chains, and Roman indices label the atoms within the chain. There are three non-zero values for the exchange constants $Jαm;βn$⁠. Within the same chain, $J1=187$ and $J2=0.884$ meV are the exchange couplings corresponding to the shorter Mo–Mo distance and longer Mo–Mo distance, respectively, as illustrated in Fig. 4(b). $J3=0.119$ meV is the exchange coupling between Mo atoms in the same plane on different chains, as illustrated in Figs. 4(b) and 4(c). All exchange terms are positive. The positive magnetic anisotropy energy (MAE) $A=0.17$ meV causes the spins to lie in the $a$–$c$ plane perpendicular to the chain direction. Magnetic anisotropy within the $a$–$c$ plane is too small to be resolved from our DFT calculations. The third term of the Hamiltonian is the external magnetic field. MoI₃ consists of dimerized AFM chains arranged in a triangular lattice as shown in Figs. 4(b) and 4(c). Total energy calculations based on the magnetic Hamiltonian of Eq. (1) found that the chain-to-chain spins in the same plane form spin-spirals with 120° rotation angles between chains, typical of a triangular lattice. The magnon dispersion for bulk MoI₃ was calculated from Eq. (1) using the linear spin wave theory as implemented in SpinW⁴⁶ and is shown in Fig. 4(d). The numbers in this plot are the frequencies of different magnon branches at high symmetry points. The green spheres are the experimental spectral position of the two-magnon Raman peaks shown in Fig. 3(b) divided by two. The frequency of the two-magnon peaks exactly matches the energy of the magnon branches at the BZ edge along the $Γ−Y$ direction. We can state that the theory of the phonon and magnon states in this true-1D vdW material is consistent with our experimental Raman data.

We also theoretically considered the effects of an external applied magnetic field on the magnon dispersion. By introducing a magnetic field of 10 T in the theory, we observed that the bands at the gamma point are split by a small value of ∼0.5 cm⁻¹, which was not present in the dispersion without the field. The experimental efforts to detect this difference in the energies of the split bands were not conclusive as these calculated frequency differences are at the limit of the instrumental resolution of our Raman systems. The Raman spectra collected under a magnetic field of 9 T at 1.6 K do not exhibit any pronounced changes in the spectral position of the peaks nor any splitting of the magnon peaks. It is important to emphasize again that the phonon dispersion calculations are in excellent agreement with the experimentally measured spectral position of the peaks at the Γ point. Our preliminary magnetometry data reveal a weak signal. This can be attributed to the difficulty in the measurements of the exfoliated nanowires. Further studies are needed with larger quantities of the material for a direct comparison of magnetometry and Raman data.

In summary, we described here the elemental excitations in crystals of MoI₃, a vdW material with a true-1D crystal structure. Our measurements reveal anomalous temperature dependence of the Raman spectral features of MoI₃, which suggest magnetic phase transitions. The theoretical calculations of the phonon and magnon dispersion are in excellent agreement with the experimental data. The magnon zone-edge frequencies are consistent with the interpretation of the Raman data and the assignment of the two-magnon scattering. The results shed light on the phononic and magnonic properties of 1D MoI₃ nanowires and provide a strong motivation for future study of this unique material.

See the supplementary material for additional data on material synthesis and characterization.

A.A.B. was supported by the Vannevar Bush Faculty Fellowship from the Office of Secretary of Defense (OSD) under the Office of Naval Research (ONR) via Contract No. N00014-21-1-2947 on One-Dimensional Quantum Materials. The work of T.T.S. and R.K.L. was supported by the subcontract of this ONR award. F.H.J., A.A.B., and L.B. also acknowledge the support from the National Science Foundation (NSF) Program Designing Materials to Revolutionize and Engineer our Future (DMREF) via Project No. DMR-1921958 entitled Collaborative Research: Data-Driven Discovery of Synthesis Pathways and Distinguishing Electronic Phenomena of 1D van der Waals Bonded Solids. This work used the Extreme Science and Engineering Discovery Environment (XSEDE), which is supported by the National Science Foundation via Grant No. ACI-1548562 and allocation ID TG-DMR130081. H.Z. acknowledges support from the U.S. Department of Commerce, NIST under Financial Assistance Award No. 70NANB19H138. A.V.D. acknowledges support from the Material Genome Initiative Funding allocated to NIST.

Certain commercial equipment, instruments, software, or materials are identified in this paper in order to specify the experimental procedure adequately. Such identifications are not intended to imply recommendation or endorsement by NIST, nor is it intended to imply that the materials or equipment identified are necessarily the best available for the purpose.