Anisotropic thermal transport in magnetic intercalates ${\mathrm{Fe}}_x{\mathrm{TiS}}_2$

We present a study of the thermal transport in thin single crystals of iron-intercalated titanium disulphide, ${\mathrm{Fe}}_x{\mathrm{TiS}}_2$, for $0\le x\le 0.20$. We determine the distribution of intercalants using high-resolution crystallographic and magnetic measurements, confirming the insertion of Fe without long-range ordering. We find that iron intercalation perturbs the lattice very little, and suppresses the tendency of ${\mathrm{TiS}}_2$ to self-intercalate with excess Ti. We observe trends in the thermal conductivity that are compatible with our ab initio calculations of thermal transport in perfectly stoichiometric ${\mathrm{TiS}}_2$.

Figure 1

ED patterns along the main zone axis: (a) 001 and [100], (b) EDX mapping of elemental Ti K (green), S K (blue), Fe K (red), and overlaid color map of selected crystallite. Note the presence of Fe-rich line defects. (c),(d) Corresponding high-resolution HAADF-STEM images of the ${\mathrm{Fe}}_{0.20}{\mathrm{TiS}}_2$ crystal along [001] and [100] zone axis. The inset shows enlarged images overlaid with the structural model (Ti, blue; S, yellow; Fe, orange).

Figure 2

(a) [100] HAADF-STEM image and corresponding FT patterns of intergrowth of two related local structures—A, basic and B, showing superstructure as it is evidence from FT patterns. The superstructure spots are denoted with white arrows. (b) Enlargement of superstructure (B) area with superimposed structural model and proposed model of Fe vacancies ordering (Ti, blue; S, yellow; Fe, orange; vacancy, red square).

Figure 3

High-resolution [100] HAADF-STEM image of a defective area showing stacking faults (marked with red arrows) and misfit dislocations. The enlarged image of a stacking fault (marked with white rectangle) and proposed structural model are shown as insets.

Figure 4

The thermoelectric power of ${\mathrm{Fe}}_x{\mathrm{TiS}}_2$. A monotonic reduction of the thermoelectric power with $x$ indicates a steady increase of the carrier concentration. Inset: Measured in-plane resistivity of ${\mathrm{Fe}}_x{\mathrm{TiS}}_2$. The temperature dependence is reduced as $x$ increases. The fit to the resistivity at $x=0$ (see text for details) is shown as a dashed cyan line.

Figure 5

Top: In-plane thermal conductivity of ${\mathrm{Fe}}_x{\mathrm{TiS}}_2$. At 300 K, There is little change from $x=0$ to $x=0.10$ within the uncertainty of the measurement. Thermal conductivity is strongly suppressed for $x=0.20$. The electronic contribution to the thermal conductivity (solid lines) is derived from the resistivity data using the Wiedemann-Franz law, ${\kappa }_e=LT/\rho$, where $\rho \left(T\right)$ is taken from Fig. 4. The symbols and colors indicate to which measured thermal conductivity curve these lines correspond. Bottom: the in-plane lattice contribution to the thermal conductivity resulting from the subtraction of the electronic contribution. The green dashed curves show the calculated lattice thermal conductivities in the in-plane (${\kappa }_{ab}$) and out-of-plane (${\kappa }_c$) directions.

Figure 6

Top: Thermoreflectance signals from ${\mathrm{Fe}}_x{\mathrm{TiS}}_2$ samples at 300 K. An analytical model of the experiment is used to extract the out-of-plane thermal conductivity by fitting the curves from the peak of the signal up to 50 ns. For more details see Refs. [26, 27]. Bottom: The lattice thermal conductivities ${\kappa }_c$ (red circles) and ${\kappa }_{ab}$ (black squares) at 300 K as a function of the carrier concentration $n_H$. The calculated results at $x=0$ are also shown (yellow circle/square), as well as the data point of Ref. [9] (blue circle/square). The electronic contribution to ${\kappa }_c$ is assumed to be negligible.