Consequences of magnetic ordering in chiral $\mathrm{M}{\mathrm{n}}_{1/3}\mathrm{Nb}{\mathrm{S}}_2$

We have investigated the structural, magnetic, thermodynamic, and charge-transport properties of $\mathrm{M}{\mathrm{n}}_{1/3}\mathrm{Nb}{\mathrm{S}}_2$ single crystals through x-ray and neutron diffraction, magnetization, specific heat, magnetoresistance, and Hall-effect measurements. $\mathrm{M}{\mathrm{n}}_{1/3}\mathrm{Nb}{\mathrm{S}}_2$ displays a magnetic transition at $T_C\sim 45\mathrm{K}$ with highly anisotropic behavior expected for a hexagonal-structured material. Below $T_C$, neutron diffraction reveals increased scattering near the structural Bragg peaks having a wider Q dependence along the $c$ axis than the nuclear Bragg peaks. This indicates either a short-range ferromagnetic (FM) order with a domain size of ∼250 nm along the $c$ axis or a possible magnetic modulation with a large pitch length. The expectation of a significant Dzyaloshinskii-Moriya interaction in this chiral-structured magnet, along with the helical state discovered in isostructural $\mathrm{C}{\mathrm{r}}_{1/3}\mathrm{Nb}{\mathrm{S}}_2$, suggest either a long period helical state with $q\sim 0.0025{\AA }^{-1}$, or FM regions separated by magnetic solitons, may be responsible for the apparent small size of the FM domains. Here, the domain length along the $c$ axis is substantially larger than the pitch length of 48 nm found for the helimagnetic state in $\mathrm{C}{\mathrm{r}}_{1/3}\mathrm{Nb}{\mathrm{S}}_2$. Specific-heat-capacity measurements confirm a second-order magnetic phase transition with a substantial magnetic contribution that persists to low temperature. The low-temperature specific-heat capacity is consistent with a large density of low-lying magnetic excitations that are likely associated with topologically interesting magnetic modes. Changes to the magnetoresistance, the magnetization, and the magnetic neutron diffraction, which become more apparent below 20 K, imply a modification in the character of the magnetic ordering corresponding to the magnetic contribution to the specific-heat capacity. These observations signify a more complex magnetic structure both at zero and finite fields for $\mathrm{M}{\mathrm{n}}_{1/3}\mathrm{Nb}{\mathrm{S}}_2$ than for the well-investigated $\mathrm{C}{\mathrm{r}}_{1/3}\mathrm{Nb}{\mathrm{S}}_2$.

Figure 1

Crystal and magnetic structure of $\mathrm{M}{\mathrm{n}}_{1/3}\mathrm{Nb}{\mathrm{S}}_2$. (a) Crystal structure demonstrating the intercalated Mn atoms which occupy the octahedral interstitial holes ($2c$ site) between trigonal prismatic layers of 2H-$\mathrm{Nb}{\mathrm{S}}_2$ in the ideal case. Arrows represent the Mn magnetic moments, as determined by a refinement of the neutron-scattering data. (b) Fourier map of electron-density residual structure factor $\left[\left(F_{\mathrm{obs}}\right)-\left(F_{\mathrm{cal}}\right)\right]$ with a resolution of $0.05e^{-}/{\AA }^3$. (c) Two-dimensional view of the crystal structure along the $c$ axis highlighting the triangular network of Mn. The top Mn layer is indicated via shading of the surrounding octahedron of sulfur. (d) Diffraction precession image of the (HK0) plane of the reciprocal lattice. All of the resolved intensity peaks have been identified with the crystal lattice structure of the chiral space group $P{6}_{3}22$. Blue circles identify reflections expected for the $\mathrm{Cd}{\mathrm{I}}_2$ structure type of the underlying $\mathrm{Nb}{\mathrm{S}}_2$ lattice, while reflections identified with yellow circles confirm the symmetry expected for the $P{6}_{3}22$ space group. The flaring associated with reflections such as those enclosed by blue circles is instrumental in origin.

Figure 2

Magnetic susceptibility and magnetization of $\mathrm{M}{\mathrm{n}}_{1/3}\mathrm{Nb}{\mathrm{S}}_2$. (a) Temperature, T, dependence and anisotropy of the magnetic susceptibility, χ, taken with a field $H=90\mathrm{Oe}$. Inset: 1/χ vs T for H parallel to the $c$ axis. Line is a fit of the Curie-Weiss form to the data for $150<T<350\mathrm{K}$. (b) Magnetization, M, vs magnetic field, H, at 2 K with H parallel and perpendicular to the $c$ axis. Inset: low-field M. T dependence of the FC and ZFC magnetic susceptibility at $H=5\mathrm{Oe}$ with (c) $H\perp c$ and (d) $H//c$.

Figure 3

Magnetic structure of $\mathrm{M}{\mathrm{n}}_{1/3}\mathrm{Nb}{\mathrm{S}}_2$. (a) Neutron-diffraction intensity, I, for a scan along the (0 1 L) direction in proximity to the (0 1 1) nuclear Bragg position. (b) T dependence of integrated intensity and full width at half maximum of the (0 1 1) reflection indicating magnetic ordering with a critical temperature $T_C$ of 45 K. The solid line is a fit of a standard critical behavior model to the integrated intensity (see text).

Figure 4

Charge-transport properties of $\mathrm{M}{\mathrm{n}}_{1/3}\mathrm{Nb}{\mathrm{S}}_2$. (a) Temperature dependence of the resistivity measured with current, I, in the $ab$ plane, ${\rho }_{ab}$ at magnetic fields applied parallel to the $c$ axis. (b) Magnetoresistance, ${\rho }_{ab}\left(H\right)$, with fields applied parallel (filled symbols) and perpendicular (open symbols) to I. Magnetoresistance, $\mathrm{\Delta }\rho /{\rho }_0=\left[{\rho }_{ab}\left(H\right)--{\rho }_{ab}\left(0\right)\right]/{\rho }_{ab}\left(0\right)$, (MR) measured with H applied (c) parallel and (d) perpendicular to the $c$ axis. The solid lines are fits of the form $\mathrm{\Delta }\rho /\rho \sim H^{\alpha }$ to the data. Inset: MR at 10 and 45 K for H up to 350 kOe.

Figure 5

Magnetic-field dependence of the ac magnetic susceptibility. (a) Real, ${\chi }^{\prime }$, and (b) imaginary ${\chi }^{″}$ parts of the ac magnetic susceptibility vs magnetic field applied parallel to the $c$ axis. (c) χ′ after subtraction of χ′ at 45 K, ${\chi }^{\prime }-{\chi }_{45\mathrm{K}}^{\prime }$. Inset: Zero-crossing fields for the MR [see Fig. 4] and ${\chi }^{\prime }-{\chi }_{45\mathrm{K}}^{\prime }$ with H parallel to the $c$ axis vs T. (d) Derivative of the magnetization with respect to H, dM/dH vs H with H parallel to the $c$ axis.

Figure 6

Hall effect for $\mathrm{M}{\mathrm{n}}_{1/3}\mathrm{Nb}{\mathrm{S}}_2$. (a) Hall resistivity, ${\rho }_{xy}$, vs magnetic field, H, at 5, 45, and 70 K, (b) ${\rho }_{xy}$/H vs the magnetization divided by field (M/H), (c) Ordinary Hall coefficient $R_0$ and anomalous Hall coefficient, $R_S$, vs temperature divided by the Curie temperature (T/$T_C$), (d) Anomalous Hall parameter, $S_H(=R_S/{{\rho }_{ab}}^2)$ vs T/$T_C$.

Figure 7

Temperature and field dependence of the specific-heat capacity of $\mathrm{M}{\mathrm{n}}_{1/3}\mathrm{Nb}{\mathrm{S}}_2$. (a) Specific-heat capacity at constant pressure, $C_P$, divided by the temperature, T, vs T at zero magnetic field for $\mathrm{M}{\mathrm{n}}_{1/3}\mathrm{Nb}{\mathrm{S}}_2$. Data for $\mathrm{C}{\mathrm{r}}_{1/3}\mathrm{Nb}{\mathrm{S}}_2$ taken from Ref. [33] with permission of the authors. (b) T dependence of $C_P$ for 0≤H≤9 T. Inset: $C_p/T$ vs $T^2$ at the same fields as in the main frame. (c) Change in entropy with application of field, $\mathrm{\Delta }S=S\left(H\right)--S\left(0\right)$, vs T. Inset: The entropy, S, determined from the integral of the data shown in frame (b). (d) The T derivative of the resistivity, $d{\rho }_{ab}/dT$ vs T.