Thermoelectric properties, metal-insulator transition, and magnetism: Revisiting the $\mathrm{N}{\mathrm{i}}_{1-x}\mathrm{C}{\mathrm{u}}_x{\mathrm{S}}_2$ system

The $\mathrm{N}{\mathrm{i}}_{1-x}\mathrm{C}{\mathrm{u}}_x{\mathrm{S}}_2$ pyrite ($x\le 0.07$) is a model material where the impact of electron filling on a half-filled $e_{\mathrm{g}}$ band system can be separated from changes in the bandwidth, since the unit cell volume does not change with $x$. This contrasts with the $\mathrm{Ni}{\mathrm{S}}_{2-x}\mathrm{S}{\mathrm{e}}_x$ system where the size difference between ${\mathrm{S}}^{2-}$ and $\mathrm{S}{\mathrm{e}}^{2-}$ makes the bandwidth vary at constant band filling. Our magnetic measurements show that there exists a clear relation between the presence of the antiferromagnetic phase developing below $T_{\mathrm{N}2}=29.75\mathrm{K}$ and charge localization. With the addition of Cu in $\mathrm{N}{\mathrm{i}}_{1-x}\mathrm{C}{\mathrm{u}}_x{\mathrm{S}}_2$, the ground state evolves towards a metallic paramagnetic state. These findings are discussed with the scenario based on charge ordering at low temperature in the charge transfer insulator $\mathrm{Ni}{\mathrm{S}}_2$ pyrite, and also considering possible conducting surface states at low temperatures. At 300 K, the thermal conductivity decreases by 2.5 as $x$ increases from 0.00 to 0.07, even though the latter is much more electrically conductive than the former. This considerably extends the range of values for the thermal conductivity of the $\mathrm{M}{\mathrm{S}}_2$ pyrites, from the largest in $\mathrm{Fe}{\mathrm{S}}_2$ to the lowest in the present $\mathrm{N}{\mathrm{i}}_{1-x}\mathrm{C}{\mathrm{u}}_x{\mathrm{S}}_2$ samples.

Figure 1

Powder x-ray diffraction patterns of the $\mathrm{N}{\mathrm{i}}_{1-x}\mathrm{C}{\mathrm{u}}_x{\mathrm{S}}_2$ samples ($x=0.00$, $x=0.01$, and $x=0.07$).

Figure 2

$\mathrm{Ni}{\mathrm{S}}_2$: T dependence (below 300 K) of ρ (top; inset: the ln (ρ) data as a function of 1/T), χ (field-cooling mode, ${10}^{-2}\mathrm{T}$, middle, (□)] and S (bottom). The reciprocal magnetic susceptibility is also given in the middle panel (○). An enlargement of S at low T is given as an inset in the bottom panel.

Figure 3

$\mathrm{Ni}{\mathrm{S}}_2$: isothermal H dependence of the magnetization M collected up to 5 T. Inset: $M{\left(H\right)}_{\mathrm{T}=30\mathrm{K}}$ curve up to 9 T.

Figure 4

$\mathrm{N}{\mathrm{i}}_{1-x}\mathrm{C}{\mathrm{u}}_x{\mathrm{S}}_2$: (a) ρ(T) and (b) χ(T) registered in field-cooling mode (${10}^{-2}\mathrm{T}$). $x$ values are labeled in the graphs.

Figure 5

$\mathrm{N}{\mathrm{i}}_{1-x}\mathrm{C}{\mathrm{u}}_x{\mathrm{S}}_2$: $M{\left(H\right)}_{5\mathrm{K}}$. $x$ values are labeled in the graphs.

Figure 6

Phase diagram of $\mathrm{N}{\mathrm{i}}_{1-x}\mathrm{C}{\mathrm{u}}_x{\mathrm{S}}_2$ presenting as a function of $x$ the values of ρ at 5 K and of χ (left scale), and the values of the magnetic transitions $T_{\mathrm{N}2}$ and $T_{\mathrm{onset}}$ (right scale) extracted from the χ(T) curves in Fig. 4.

Figure 7

S(T) curves of the SPS densified $\mathrm{N}{\mathrm{i}}_{1-x}\mathrm{C}{\mathrm{u}}_x{\mathrm{S}}_2$ samples ($x=0.00$, $x=0.01$, and $x=0.07$) as a function of T. $x$ values are labeled in the graph.

Figure 8

κ(T) curves of the SPS densified $\mathrm{N}{\mathrm{i}}_{1-x}\mathrm{C}{\mathrm{u}}_x{\mathrm{S}}_2$ samples ($x=0.00$, $x=0.01$, and $x=0.07$). $x$ values are labeled in the graphs.