Magnetism, structure, and charge correlation at a pressure-induced Mott-Hubbard insulator-metal transition

We use synchrotron x-ray diffraction and electrical transport under pressure to probe both the magnetism and the structure of single-crystal NiS${}_2$ across its Mott-Hubbard transition. In the insulator, the low-temperature antiferromagnetic order results from superexchange among correlated electrons and couples to a (1/2, 1/2, 1/2) superlattice distortion. Applying pressure suppresses the insulating state, but enhances the magnetism as the superexchange increases with decreasing lattice constant. By comparing our results under pressure to previous studies of doped crystals, we show that this dependence of the magnetism on the lattice constant is consistent for both band broadening and band filling. In the high-pressure metallic phase the lattice symmetry is reduced from cubic to monoclinic, pointing to the primary influence of charge correlations at the transition. There exists a wide regime of phase separation that may be a general characteristic of correlated quantum matter.

Figure 1

(a) Superlattice intensity $I_{\mathit{SL}}$ at ambient $P$ plotted as a function of temperature. $I_{\mathit{SL}}$ is averaged over (3.5, 1.5, 1.5), (3.5, 0.5, 1.5), (2.5, 1.5, 1.5), and (2.5, 0.5, 1.5), and normalized to ($3,1,1$). Data were taken while warming (pink) and cooling (blue) through $T_{N2}=29.2$ K. The x-ray superlattice intensity scales linearly with the intensity of magnetic neutron diffraction from the (1/2, 1/2, 1/2) $M2$ magnetic order (open circles, data from Ref. 7), as well as the linear thermal expansion $|\Delta L/L|$ along ($1,1,1$) (black solid squares, data from Ref. 20). Solid line is a guide to the eye. Inset: $H$, $K$, $L$ scans of (1/2, 1/2, 1/2) superlattice diffraction at ambient $P$ and $T=5.8$ K. (b) Resistivity of NiS${}_2$ at several pressures. All data follow an Arrhenius form through the first-order phase transition at $T_{N2}$, which is marked by a kink. (c) P-x-T phase diagram of the $M2$ magnetic phase. $T_{N2}$ is plotted as a function of low-temperature cubic lattice constant $a_0$ for both NiS${}_2$ under pressure and NiS${}_{2-x}$Se${}_x$ (blue open symbols: Refs. 12,15, 16; blue solid circle: our transport measurements). The two dot-dash lines mark the first-order boundaries of the insulator-metal transition driven by pressure and chemical substitution, and bound the $M2$ order.

Figure 2

(a) Comparison of the high-resolution longitudinal line scans of the superlattice at four pressures between 0 and 2.84 GPa. Data are plotted from the center $q_0$ of each individual peak and displaced vertically with scale bars representing individual intensity relative to that of the ($3,1,1$) order. All line shapes are nearly resolution limited approaching the phase boundary. This indicates that the crystal remains cubic with long $M2$ correlation lengths throughout the insulating phase. The antiferromagnetic $M2$ order disappears at higher pressures as exemplified by two null scans through the superlattice positions at $2.90\pm 0.05$ and $3.86\pm 0.12$ GPa. (b) Calculated lower bounds of correlation lengths for the superlattice. Separate points at a given $P$ represent scans through different superlattice orders. All measurement temperatures were between 3.5 and 5.8 K.

Figure 3

(a) Longitudinal $\theta -2\theta$ scans of the ($2,1,1$) lattice reflection at $0.85\pm 0.10$ GPa, the lowest $P$ at which phase separation was observed. (b) Rocking curve recorded at $q=2.721\hspace{0.5em}{\AA }^{-1}$ for the same ($2,1,1$) reflection. The colored bars indicate the three different central $\theta$ values used in the scans in panel (a). (c) Longitudinal scan of the ($2,2,0$) lattice reflection at 3.86 GPa where only the high-$P$ phase is present. The fourfold splitting of ($2,2,0$) indicates a lattice symmetry of monoclinic or lower in the metal. (d) Lattice constants vs pressure for pure NiS${}_2$ at $T=5$ K. Both the low-$P$ and high-$P$ phases were observed in the phase-separated region, but with insufficient detail to determine the lattice parameters $a,b,c$ of the high-$P$ phase. The lattice constants $a_0$ of the low-$P$ phase were determined from the $d$ spacings of both the superlattice and cubic fcc reflections.