Electrical and thermal transport in van der Waals magnets $2\mathrm{H}\text{−}{\mathrm{M}}_x{\mathrm{TaS}}_2 (\mathrm{M}=\mathrm{Mn}, \mathrm{Co})$

We report a detailed study of electrical and thermal transport properties in $2\mathrm{H}\text{−}{\mathrm{M}}_x{\mathrm{TaS}}_2 (\mathrm{M}=\mathrm{Mn}, \mathrm{Co})$ magnets where M atoms are intercalated in the van der Waals gap. The intercalation induces ferromagnetism (FM) with an easy-plane anisotropy in $2\mathrm{H}\text{−}{\mathrm{Mn}}_x{\mathrm{TaS}}_2$, but FM with a strong uniaxial anisotropy in $2\mathrm{H}\text{−}{\mathrm{Co}}_{0.22}{\mathrm{TaS}}_2$, which finally evolves into a three-dimensional antiferromagnetism (AFM) in $2\mathrm{H}\text{−}{\mathrm{Co}}_{0.34}{\mathrm{TaS}}_2$. Temperature-dependent electrical resistivity shows metallic behavior for all samples. Thermopower is negative in the whole temperature range for $2\mathrm{H}\text{−}{\mathrm{Co}}_x{\mathrm{TaS}}_2$, whereas the sign changes from negative to positive with increasing Mn for $2\mathrm{H}\text{−}{\mathrm{Mn}}_x{\mathrm{TaS}}_2$. The diffusive thermoelectric response dominates in both high- and low-temperature ranges for all samples. A clear kink in electrical resistivity, a weak anomaly in thermal conductivity, as well as a slope change in thermopower were observed at the magnetic transitions for $2\mathrm{H}\text{−}{\mathrm{Mn}}_{0.28}{\mathrm{TaS}}_2$ ($T_{\text{c}}\approx$ 82 K) and $2\mathrm{H}\text{−}{\mathrm{Co}}_{0.34}{\mathrm{TaS}}_2$ ($T_{\text{N}}\approx$ 36 K), respectively, albeit weaker for lower $x$ crystals. Co-intercalation promoted FM to AFM transition is further confirmed by Hall resistivity; the sign change of the ordinary Hall coefficient indicates a multiband behavior in $2\mathrm{H}\text{−}{\mathrm{Co}}_x{\mathrm{TaS}}_2$.

Figure 1

Crystal structure of $2\mathrm{H}\text{−}{\mathrm{M}}_x{\mathrm{TaS}}_2$ (M = Mn, Co) shown from the (a) side view and (b) top view, respectively. (c) Single crystal XRD patterns of $2\mathrm{H}\text{−}{\mathrm{M}}_x{\mathrm{TaS}}_2$ (M = Mn, Co) and the evolution of lattice parameter $c$ with intercalation content $x$. (d) STM topography of the sample surface for $2\mathrm{H}\text{−}{\mathrm{Mn}}_{0.28}{\mathrm{TaS}}_2$. (e) Laue x-ray pattern on the shown surface of $2\mathrm{H}\text{−}{\mathrm{Co}}_{0.34}{\mathrm{TaS}}_2$ crystal with the sixfold symmetry of the hexagon structure.

Figure 2

(a–c) Temperature-dependent magnetic susceptibility $\chi$(T) in both ZFC and FC modes with the $\mathbf{H}\parallel \mathbf{ab}$ plane and the $\mathbf{H}\parallel \mathbf{c}$ axis at $H=1$ kOe for $2\mathrm{H}\text{−}{\mathrm{Mn}}_x{\mathrm{TaS}}_2$. (d) The inverse susceptibility $1/\chi$(T) with the $\mathbf{H}\parallel \mathbf{ab}$ plane fitted by the Curie-Weiss law (solid lines) for $2\mathrm{H}\text{−}{\mathrm{Mn}}_x{\mathrm{TaS}}_2$. (e) Field-dependent magnetization with both the $\mathbf{H}\parallel \mathbf{ab}$ plane and the $\mathbf{H}\parallel \mathbf{c}$ axis at $T=2\mathrm{K}$ for $2\mathrm{H}\text{−}{\mathrm{Mn}}_x{\mathrm{TaS}}_2$. (f–h) Temperature-dependent magnetic susceptibility $\chi$(T) in both ZFC and FC modes with the $\mathbf{H}\parallel \mathbf{ab}$ plane and the $\mathbf{H}\parallel \mathbf{c}$ axis at $H=1$ kOe for $2\mathrm{H}\text{−}{\mathrm{Co}}_x{\mathrm{TaS}}_2$. (i) The inverse susceptibility $1/\chi$(T) with the $\mathbf{H}\parallel \mathbf{c}$ axis fitted by the Curie-Weiss law (solid lines) for $2\mathrm{H}\text{−}{\mathrm{Co}}_x{\mathrm{TaS}}_2$. (j) Field-dependent magnetization with both the $\mathbf{H}\parallel \mathbf{ab}$ plane and the $\mathbf{H}\parallel \mathbf{c}$ axis at $T=2\mathrm{K}$ for $2\mathrm{H}\text{−}{\mathrm{Co}}_x{\mathrm{TaS}}_2$.

Figure 3

(a) Temperature dependence of in-plane resistivity $\rho$(T) for $2\mathrm{H}\text{−}{\mathrm{M}}_x{\mathrm{TaS}}_2$ (M = Mn, Co) single crystals. Inset shows the $d\rho /dT$ for $2\mathrm{H}\text{−}{\mathrm{Co}}_{0.34}{\mathrm{TaS}}_2$ around $T_{\text{N}}$. (b) The evolution of residual resistivity ${\rho }_0$ (left axis) at $T=4\mathrm{K}$ and RRR = ${\rho }_{\text{300}\text{K}}/{\rho }_{\text{4}\text{K}}$ (right axis) for $2\mathrm{H}\text{−}{\mathrm{M}}_x{\mathrm{TaS}}_2$ (M = Mn, Co). (c) The temperature-dependent $\rho -{\rho }_0$ for $2\mathrm{H}\text{−}{\mathrm{TaS}}_2$, $2\mathrm{H}\text{−}{\mathrm{Mn}}_{0.28}{\mathrm{TaS}}_2$, and $2\mathrm{H}\text{−}{\mathrm{Co}}_{0.34}{\mathrm{TaS}}_2$ with power-law fits from 30 to 4 K (solid lines). (d) Temperature dependence of in-plane thermopower $S$(T) for $2\mathrm{H}\text{−}{\mathrm{M}}_x{\mathrm{TaS}}_2$ (M = Mn, Co) and (e) $2\mathrm{H}\text{−}{\mathrm{TaS}}_2$ single crystals with linear fits from 150 to 300 K. Inset in (e) shows the $S$(T) for $2\mathrm{H}\text{−}{\mathrm{Co}}_{0.34}{\mathrm{TaS}}_2$. (f) The $S$(T) at low temperatures for $2\mathrm{H}\text{−}{\mathrm{M}}_x{\mathrm{TaS}}_2$ with linear fits. Temperature dependence of (g) total thermal conductivity $\kappa$(T), (h) electronic part ${\kappa }_{\text{e}}$(T), and (i) phonon part ${\kappa }_{\text{L}}$(T) for $2\mathrm{H}\text{−}{\mathrm{M}}_x{\mathrm{TaS}}_2$ (M = Mn, Co). Inset in (g) shows the $d\kappa /dT$ curves for $2\mathrm{H}\text{−}{\mathrm{Mn}}_{0.28}{\mathrm{TaS}}_2$ and $2\mathrm{H}\text{−}{\mathrm{Co}}_{0.34}{\mathrm{TaS}}_2$.

Figure 4

(a–c) Out-of-plane field dependence of Hall resistivity ${\rho }_{xy}$(H) for $2\mathrm{H}\text{−}{\mathrm{Co}}_x{\mathrm{TaS}}_2$ at indicated temperatures with linear fits from 6 to 9 T. (d–f) The estimated carrier concentration $n$ from ordinary Hall efficient ($R_0=1/nq$) for $2\mathrm{H}\text{−}{\mathrm{Co}}_x{\mathrm{TaS}}_2$. Temperature dependence of (g) heat-capacity $C_p$(T), (h) the magnetic contribution $C_m$(T) (left axis) and the derived magnetic entropy $S_m$(T) (right axis), and (i) low-temperature $C_p/T$ vs $T^2$ data fitted by $C_p/T=\gamma +\beta T^2$ for $2\mathrm{H}\text{−}{\mathrm{Co}}_x{\mathrm{TaS}}_2$.