Magnetic structure investigation of the intercalated transition metal dichalcogenide ${\mathrm{V}}_{1/3}{\mathrm{NbS}}_2$

We investigate the temperature evolution of the magnetic structure of ${\mathrm{V}}_{1/3}{\mathrm{NbS}}_2$ using neutron diffraction techniques. We find that ${\mathrm{V}}_{1/3}{\mathrm{NbS}}_2$ has two propagation vectors: ${\mathbf{k}}_{\mathbf{0}}=(0,0,0)$ and ${\mathbf{k}}_{\mathbf{1}}=(0,0,\frac{1}{3})$. The ${\mathbf{k}}_{\mathbf{0}}$ vector can be associated with an antiferromagnetic ordering of in-plane moments with a refined value of $0.90\left(5\right){\mu }_{\mathrm{B}}$, and ${\mathbf{k}}_{\mathbf{1}}$ can be associated with moments along the $c$ axis in an up-down-down configuration with refined values of $1.21\left(12\right){\mu }_{\mathrm{B}}$ and $0.61\left(6\right){\mu }_{\mathrm{B}}$. Both ${\mathbf{k}}_{\mathbf{0}}$ and ${\mathbf{k}}_{\mathbf{1}}$ magnetic components couple with an out-of-plane ferromagnetic moment consistent with magnetization data. Furthermore, single-crystal neutron diffraction shows evidence of diffuse magnetic scattering between the (010) and ($01\pm \frac{1}{3}$) Bragg peaks. We also characterize the field and temperature evolution of the magnetic structure in ${\mathrm{V}}_{1/3}{\mathrm{NbS}}_2$ by magnetic susceptibility and heat capacity measurements. The dc susceptibility measurements give an antiferromagnetic transition temperature of $T_{\mathrm{N}}=50$ K, and the field scans reveal that the moment does not saturate at magnetic fields up to 100 kOe.

Figure 1

Structure of ${\mathrm{V}}_{1/3}{\mathrm{NbS}}_2$, which crystallizes in the hexagonal, chiral, noncentrosymmetric $P{6}_{3}22$ space group, with lattice parameters $a=5.75$ Å, $c=12.17$ Å, viewed along the $a^{*}$ direction. The intercalate, V, is shown in dark red between layers of S and Nb. The octahedra around the V atoms are shown.

Figure 2

Laue back-reflection pattern along the [001] orientation of an aligned ${\mathrm{V}}_{1/3}{\mathrm{NbS}}_2$ crystal.

Figure 3

Temperature dependence of the dc magnetic susceptibility ${\chi }_{\mathrm{dc}}$ for ${\mathrm{V}}_{1/3}{\mathrm{NbS}}_2$ collected in ZFC and FCC modes in an applied field of $H=330$ Oe for $H\parallel c$ and $H\perp c$. The inset shows the magnetic susceptibility for $H\perp c$ between 1.8 and 50 K, with a magnetic transition visible at 50 K.

Figure 4

Field dependence of the magnetization $M$ per formula unit of ${\mathrm{VNb}}_3{\mathrm{S}}_6$ for various temperatures. The field was applied (a) parallel and (b) perpendicular to the $c$ axis. The insets show the low-field hysteresis for both field directions.

Figure 5

Heat capacity $C$ of ${\mathrm{V}}_{1/3}{\mathrm{NbS}}_2$ as a function of temperature $T$ from 1.8 to 300 K. The line is a fit using the Debye-Einstein model. The inset shows the linear behavior of $C/T$ as a function of $T^2$ at low temperatures, giving $\gamma =7.5\left(2\right)$ mJ/mol ${\mathrm{K}}^2$ and ${\mathrm{\Theta }}_{\mathrm{D}}=382\left(2\right)$ K.

Figure 6

(a) Evolution of the powder neutron diffraction profiles with temperatures for ${\mathrm{V}}_{1/3}{\mathrm{NbS}}_2$ between 5 and 52 K. For clarity, each profile is offset by 50 units. (b) Powder diffraction profile at 5 K with a calculated fit using a hexagonal, $P{6}_{3}22$ structure and magnetic components with propagation vectors ${\mathbf{k}}_{\mathbf{0}}=(0,0,0)$ and ${\mathbf{k}}_{\mathbf{1}}=(0,0,\frac{1}{3})$. The Bragg positions for each phase are shown below the pattern. The reliability factors are $R_{\mathrm{Bragg}}=6.1$ for the atomic structure and $R_{\mathrm{Mag}}=19.2$ and 30.9 for the magnetic structures with the ${\mathbf{k}}_{\mathbf{0}}$ and ${\mathbf{k}}_{\mathbf{1}}$ propagation vectors, respectively.

Figure 7

Magnetic moments on the vanadium atoms in a unit cell of ${\mathrm{V}}_{1/3}{\mathrm{NbS}}_2$ viewed along the $a^{*}$ direction. (a) In-plane moments associated with the ${\mathbf{k}}_{\mathbf{0}}=(0,0,0)$ propagation vector, (b) the out-of-plane up-down-down moments associated with the ${\mathbf{k}}_{\mathbf{1}}=(0,0,\frac{1}{3})$ propagation vector, and (c) the superposition of these two components.

Figure 8

(a) Area detector image depicting the (010) and ($01\pm \frac{1}{3}$) Bragg peaks and the diffuse scattering between them, with $H\parallel c$. (b) Cut taken from the area detector image along $\left[01l\right]$ at 1.5 and 300 K to compare the intensities of the peaks with the intensity of the diffuse scattering. The limits of the detector are shown as dashed blue lines.

Figure 9

Integrated intensity $I$ of several different structural and magnetic peaks and their dependence on applied magnetic field. Field dependence of the integrated intensities of the (010) and ($01\frac{1}{3}$) peaks with the field directed $H\parallel c$ (top). Integrated intensities of the (100) and ($10\frac{1}{3}$) peaks (middle) and (001) peaks (bottom) in the $\left(h0l\right)$ scattering plane with the field directed along [110].

Figure 10

Integrated intensity $I$ of several different structural and magnetic peaks and their dependence on temperature. The integrated intensities of the (100), ($10\frac{1}{3}$) and (001) peaks between 1.5 and 54 K are plotted on the same axes. The inset depicts the region of interest for the (100) and ($10\frac{1}{3}$) peaks.