Magnetism in $M_{1/3}$NbS$_2$ ($M$ = Fe, V, Mn): insight into intercalated transition-metal dichalcogenides using $μ$SR

TL;DR

This work investigates magnetism in the intercalated TMDC family $M_{1/3}$NbS$_2$ ($M= ext{Fe, V, Mn}$) using muon-spin relaxation and density-functional theory to map local magnetic fields and muon stopping sites. Fe$_{1/3}$NbS$_2$ displays two coexisting AFM phases (stripe and zig-zag) with phase separation across $T_{c1} obreak ext{--} obreak T_{c2}$, while V$_{1/3}$NbS$_2$ orders at $T_c=52.7$ K with a single broad μSR frequency and exhibits a low-temperature dynamical peak near 9 K. Mn$_{1/3}$NbS$_2$ shows two μSR frequencies arising from a high-energy muon site in addition to the low-energy site, consistent with a helical or FM-like order and a sizable Mn moment; this material uniquely requires an extra muon site to account for the observed spectrum. Together, these results demonstrate that changing the intercalant species strongly tunes magnetic order and dynamics in $M_{1/3}$NbS$_2$, supporting a rigid-band filling scenario and highlighting μSR as a powerful probe of complex magnetism and muon-site physics in intercalated TMDCs.

Abstract

We present the results of muon-spin relaxation ($μ$SR) measurements of the static and dynamic magnetism of $M_{1/3}$NbS$_2$ ($M$ = Fe, V, Mn), three intercalated transition-metal dichalcogenides. Transitions to long-range magnetic order are observed in all three materials and local magnetic fields at muon sites are compared to dipole field calculations. Measurements on Fe$_{1/3}$NbS$_2$ capture the evolution of two coexisting magnetic phases. In V$_{1/3}$NbS$_2$ we observe a peak in the dynamic response at $9$ K, coincident with previous reports of a possible low-temperature phase transition. The observation of high-frequency muon precession in Mn$_{1/3}$NbS$_2$ suggests the existence of an additional muon site that implies a difference in electronic energy landscape compared to the other materials in the series. Taken together, this demonstrates that the change in intercalant species drives significant variations in magnetism, highlighting the $M_{1/3}$NbS$_2$ ($M$ = Fe, V, Mn) series as an ideal group of materials for investigating a wide range of magnetic phenomena.

Figures (6)

• Figure 1: Magnetic structure of Fe$_{1/3}$NbS$_2$ for a slice in the $ab$ plane, with up spins (red) and down spins (blue). (a) Straight lines of a given spin orientation in the $b$ direction giving stripe ordering and (b) undulating lines in the $b$ direction giving zig-zag ordering. The spin of the second Fe ion in the unit cell of Fe$_{1/3}$NbS$_2$ is given by shifting the magnetic structure one ion along $a$, producing alternating layers along the $c$ axis.
• Figure 2: Temperature evolution of the wTF amplitudes associated with (a) non-magnetic regions of Fe$_{1/3}$NbS$_2$ and (b) the stripe, $A_2$ (purple triangles), and zigzag, $A_3$ (green circles), phases. Lines show the transition between the mixed and stripe-dominated regions at $40.2$ K and the transition to between stripe-dominated ordering and paramagnetism at $45$ K. ZF spectra for Fe$_{1/3}$NbS$_2$ measured at 20 K (red circles, mixed), 43 K (green triangles, stripe-dominated) and 60 K (blue squares, paramagnetic) for polarization along (c) the $c$ axis and (d) the $a$-$b$ plane. (e) Temperature dependence of the relaxation rates $\lambda_{5_{ab}}$ (blue), $\lambda_{7_{ab}}$ (green) and $\lambda_{8_{ab}}$ (purple). (f) Temperature dependence of the precession frequency in the $a$-$b$ plane, with the fit described in the text.
• Figure 3: Location of candidate muon sites in $M_{1/3}$NbS$_2$ ($M$ = Fe, V, Mn), with the three low energy sites at the centre of triangles of 3 Nb ions shown in red and the high-energy muon site in Mn$_{1/3}$NbS$_2$ shown in green.
• Figure 4: (a) ZF spectra for V$_{1/3}$NbS$_2$ measured at 5 K (red circles) and 80 K (blue squares). (b) Temperature dependence of the precession frequency, with a fit of critical scaling shown in blue. (c) Dynamical relaxation rate of the $A_2$ component of the asymmetry, showing a peak at $9$ K.
• Figure 5: Simulated field spectra (red) for (a) the simple AFM and (b) the double-Q magnetic structures in the $N=$V material, compared to the field distribution measured using $\mu$SR (blue). The moment from neutron measurements has been scaled by a factor of $1.5$ for simulations of the double-Q spectra and all the spectra are normalised.