Insulator-metal-superconductor transition in the medium-entropy van der Waals compound $M\mathrm{P}{\mathrm{Se}}_3 (M=\mathrm{Fe},\mathrm{Mn},\mathrm{Cd},\text{and}\mathrm{In})$ under high pressure

$M\mathrm{P}{X}_3$ ($M=\mathrm{metals}$; $X=\mathrm{S}\mathrm{or}\mathrm{Se}$) represents a large family of van der Waals (vdW) materials featuring P-P dimers of $\sim 2.3\AA$ separation. A dramatic alteration of its electrical transport properties, such as metal-insulator transition, has not been realized by intentional chemical doping and ionic intercalation. Here, we employ an entropy-enhancement strategy to successfully obtain a series of medium-entropy $M\mathrm{P}{\mathrm{Se}}_3$ $(M=\mathrm{Fe},\mathrm{Mn},\mathrm{Cd},\mathrm{and}\mathrm{In})$, in which the electrical and magnetic properties change simultaneously. Lone-pair electrons of P emerge due to the dissociation of the dimers as evidenced by a 35% elongation in the P-P interatomic distance. The band gap widens from 0.1 to 0.7 eV by this dissociation. Under external physical pressure up to $\sim 50$ GPa, a giant collapse of up to 15% in the $c$ axis happens, which is in contrast to the in-plane shrinkage of their counterparts $\mathrm{Fe}/\mathrm{MnP}{\mathrm{Se}}_3$. It leads to the recombination of ${\mathrm{P}}^{3-}$ with lone-pair electrons into a P-P dimer and the smallest bulk modulus of 28 GPa in $M\mathrm{P}{X}_3$. The medium-entropy $M\mathrm{P}{\mathrm{Se}}_3$ transitions from a spin-glass insulator to metal, and to superconductor, which is rarely observed in $M\mathrm{P}{X}_3$. Our findings highlight the P-P dimer as an indicator to probe diverse electronic structure and the effectiveness of entropy enhancement in materials science.

Figure 1

(a), (b) Top and side view of ${\left(\mathrm{FeMnCd}\right)}_{0.25}{\mathrm{In}}_{0.17}\mathrm{P}{\mathrm{Se}}_3$ along the $c$ axis and $a$ axis. (c) HRTEM image of ${\left(\mathrm{FeMnCd}\right)}_{0.25}{\mathrm{In}}_{0.17}\mathrm{P}{\mathrm{Se}}_3$ taken along the $c$ axis. Inset is indexed SAED (selected area electron diffraction) image. (d) EDS mapping of Fe (orange), Mn (blue), Cd (magenta), In (purple), P (brown), and Se (green) of ${\left(\mathrm{FeMnCd}\right)}_{0.25}{\mathrm{In}}_{0.17}\mathrm{P}{\mathrm{Se}}_3$. The scale bar is 1 μm.

Figure 2

Rietveld refinements of PXRD patterns collected at ambient pressure of (a) $\mathrm{FeP}{\mathrm{Se}}_3$, (b) ${\mathrm{Fe}}_{0.8}{\mathrm{Mn}}_{0.1}{\mathrm{Cd}}_{0.05}{\mathrm{In}}_{0.03}\mathrm{P}{\mathrm{Se}}_3$, (c) ${\mathrm{Fe}}_{0.7}{\left(\mathrm{MnCd}\right)}_{0.1}{\mathrm{In}}_{0.07}\mathrm{P}{\mathrm{Se}}_3$, and (d) ${\left(\mathrm{FeMnCd}\right)}_{0.25}{\mathrm{In}}_{0.17}\mathrm{P}{\mathrm{Se}}_3$. Minor phase of $\mathrm{Mn}{\mathrm{In}}_2{\mathrm{Se}}_4$ was detected.

Figure 3

(a) Lattice constants $a$ and $c$ of $\mathrm{FeP}{\mathrm{Se}}_3$ and three medium-entropy $M\mathrm{P}{\mathrm{Se}}_3$ samples. (b) P-P distance and band gap $\left(E_{\mathrm{a}}\right)$ estimated from temperature dependence of conductivity in four samples. (c) P $2p$ XPS of three samples. (d), (e) DC susceptibility $\left(\chi \right)$ and $1/\chi$ of four samples as a function of temperature from 2 to 300 K. (f) AC susceptibility of ${\left(\mathrm{MnFeCd}\right)}_{0.25}{\mathrm{In}}_{0.17}\mathrm{P}{\mathrm{Se}}_3$ under different frequencies. Inset is frequency-dependent freeze temperature $\left(T_{\mathrm{r}}\right)$. Solid lines are fitting curves based on equation of $K=\mathrm{\Delta }{T}_{\mathrm{f}}/\left(T_{\mathrm{f}}\mathrm{\Delta }\log f\right)$. The obtained $K=0.0741\left(5\right)$ falls into the range of $0.0045\le K\le 0.08$ for canonical spin-glass systems.

Figure 4

(a), (b) Color contour of the (113) and (300) diffraction peaks for ${\mathrm{Fe}}_{0.8}{\mathrm{Mn}}_{0.1}{\mathrm{Cd}}_{0.05}{\mathrm{In}}_{0.05}\mathrm{P}{\mathrm{Se}}_3 \left({\mathrm{Fe}}_{0.8}\right)$ and ${\left(\mathrm{FeMnCd}\right)}_{0.25}{\mathrm{In}}_{0.17}\mathrm{P}{\mathrm{Se}}_3$ (${\mathrm{Fe}}_{0.25}$) under external physical pressure. (c)–(e) Pressure-dependent lattice parameters and volume of unit cell for both samples.

Figure 5

(a), (c) Temperature dependence of $R\text{−}T$ curves of ${\mathrm{Fe}}_{0.8}$ below and above 12 GPa. (b), (d) Temperature dependence of $R\text{−}T$ curves of ${\mathrm{Fe}}_{0.25}$ below and above 26 GPa. Temperature-dependent upper critical fields of (e) ${\mathrm{Fe}}_{0.8}$ at 50 GPa and (f) ${\mathrm{Fe}}_{0.25}$ at 53 GPa. Fitting curves are GL equation shown in main text. Insets are temperature dependence of the normalized resistances, respectively. (g), (h) Electronic phase diagram of both samples versus pressure.