Disorder-resilient transition of Helical to Conical ground states in M$_{1/3}$NbS$_2$, M=Cr,Mn

The discovery of chiral helical magnetism (CHM) in Cr$_{1/3}$NbS$2$ and the stabilization of a chiral soliton lattice (CSL) has attracted considerable interest in view of their potential technological applications. However, there is an ongoing debate regarding whether the sister compound, Mn${1/3}$NbS$2$, which shares the same crystal structure, exhibits similar nontrivial properties which rely on the stabilization of the lack of inversion symmetry at the magnetic ion. In this study, we conduct a comprehensive investigation of the magnetically ordered states of both compounds, using $^{53}$Cr, $^{55}$Mn and $^{93}$Nb nuclear magnetic resonance. Our results, supported by density functional calculations, detect in a high-quality single crystal of Cr${1/3}$NbS$2$ all the signatures of the monoaxial CHM in a magnetic field, identifying it as a textbook NMR case. The detailed understanding of this prototypic behavior provides a reference for Mn${1/3}$NbS$_2$. Despite the much larger density of specific defects in this second single crystal, we confirm the presence of a CHM phase in the Mn compound, characterized by a very large critical field for the forced ferromagnetic phase ($\approx 5$ T for H$\parallel\hat c$).

💡 Research Summary

This work presents a comprehensive nuclear magnetic resonance (NMR) investigation of the chiral helimagnetic (CHM) and field‑induced conical phases in the intercalated transition‑metal dichalcogenides Cr₁/₃NbS₂ and Mn₁/₃NbS₂, complemented by density‑functional theory (DFT) calculations. Both compounds crystallize in the non‑centrosymmetric space group P6₃22, where magnetic ions occupy a √3 × √3 super‑lattice within the van‑der‑Waals gaps. In the ideal structure only the 2c Wyckoff site should be filled; however, real crystals display site‑occupancy disorder (SOD) on the 2b and 2d positions. Cr₁/₃NbS₂ crystals used here exhibit a very low SOD (<2 %), whereas Mn₁/₃NbS₂ crystals contain a substantially larger fraction (≈5–10 %) of Mn on the auxiliary sites, providing a natural platform to test the robustness of chiral magnetism against disorder.

The NMR experiments were performed on the three relevant nuclei: $^{53}$Cr (I = 3/2), $^{55}$Mn (I = 5/2) and $^{93}$Nb (I = 9/2). In zero field the $^{53}$Cr spectrum consists of a sharp triplet centred at ≈61 MHz, corresponding to an internal hyperfine field of 25.3 T. The narrow linewidth confirms the near‑perfect ordering of Cr on the 2c site. When a magnetic field is applied perpendicular to the crystallographic c‑axis, the three lines shift linearly with a slope equal to the $^{53}$Cr gyromagnetic ratio, demonstrating that the external field simply adds to the internal hyperfine field—a hallmark of the forced‑ferromagnetic (FFM) phase. For fields parallel to c, the angular dependence of the quadrupolar term ($m\nu_Q\sin^2\theta$) causes the triplet splitting to vanish at $\theta=\sin^{-1}(1/\sqrt{3})$, in perfect agreement with the theoretical prediction. Numerical diagonalisation of the full spin Hamiltonian yields hyperfine coupling $A\approx-12$ T/μ_B, quadrupolar frequency $\nu_Q\approx0.8$ MHz and a critical field $H_c\approx1.35$ T, from which the ratio $D/J$ (Dzyaloshinskii‑Moriya to Heisenberg exchange) can be extracted. Temperature scans reveal a sharp, hysteresis‑free transition from the helical to the FFM state, indicating a first‑order phase transition.

In Mn₁/₃NbS₂ the $^{55}$Mn NMR spectrum is considerably broader and requires multiple Gaussian components to fit, reflecting the distribution of hyperfine fields caused by Mn atoms occupying the 2b and 2d sites. Despite this inhomogeneity, the field dependence mirrors that of Cr: for $H\parallel c$ the line positions evolve linearly up to ≈5 T, after which they collapse into a single peak, signalling the onset of the FFM phase. The critical field is therefore an order of magnitude larger than in Cr, while the Curie temperature is lower ($T_C\approx45$ K versus 111 K). These findings confirm that Mn₁/₃NbS₂ also hosts a chiral helix, but its magnetic parameters are modified by the stronger disorder and by the different electronic structure of Mn.

$^{93}$Nb NMR, probing the non‑magnetic Nb layers, shows nine equally spaced lines (I = 9/2) with relatively narrow widths in both compounds, indicating that the Nb nuclei sense the averaged internal field and are less sensitive to the local site disorder.

DFT calculations support the experimental observations. The projected density of states shows that the magnetic ions’ $d_{z^2}$ orbitals dominate near the Fermi level, providing the itinerant electrons that mediate the Ruderman‑Kittel‑Kasuya‑Yosida (RKKY) exchange. Hyperfine tensors computed for the 2c site reproduce the experimental $A$ values, while those for the 2b/2d sites are reduced by ~30 %, explaining the broadened Mn spectra. The electric‑field‑gradient tensors are nearly axially symmetric (asymmetry parameter $\eta<0.02$), consistent with the small quadrupolar splittings observed.

The central conclusion is that the chiral helimagnetic ground state is remarkably resilient to structural disorder. Even with a substantial population of Mn on the auxiliary sites, the Dzyaloshinskii‑Moriya interaction remains dominant enough to stabilise the helix, and the system undergoes the expected sequence of phases under magnetic field: helical → conical (for $H\parallel c$) → forced ferromagnetic. The work establishes NMR as a uniquely powerful local probe for disentangling hyperfine and quadrupolar contributions, quantifying disorder, and mapping the magnetic phase diagram with high precision.

From a technological perspective, the demonstrated disorder‑resilience suggests that device‑grade crystals need not be perfectly ordered to retain the topological spin textures (chiral soliton lattice, skyrmion‑like excitations) that are of interest for spin‑tronic and magnonic applications. Future directions include pressure‑tuned studies of the DM/Heisenberg ratio, time‑resolved μSR/NMR to explore spin dynamics, and extending the methodology to other 3d intercalants (Fe, Co, Ni) to delineate the limits of disorder‑tolerant chiral magnetism.