Quasi-one-dimensional ${\mathrm{Pb}}_5{\mathrm{Re}}_3{\mathrm{O}}_{15}$: A $5d$ realization of the Heisenberg antiferromagnetic spin-1/2 chain

Quasi-one-dimensional (1D) magnetic compounds connect the exact solutions of low-dimensional magnetic geometries, which promise quantum spin liquid behavior and exotic quasiparticles, with real-world materials, in which competing magnetic interactions affect their implementation in quantum information science. Here, the structural determination and quasi-1D magnetic behavior of a previously unreported compound, ${\mathrm{Pb}}_5{\mathrm{Re}}_3{\mathrm{O}}_{15}$, is presented. Like the anisotropic triangular $A_3{\mathrm{ReO}}_5{\mathrm{Cl}}_2$ ($A$ = Ba, Sr, Ca) materials, ${\mathrm{Pb}}_5{\mathrm{Re}}_3{\mathrm{O}}_{15}$ contains $\left[{\mathrm{ReO}}_5\right]$ square pyramids inserted into anion-centered quasi-two-dimensional layers and hosts spin-1/2 moments on the ${\mathrm{Re}}^{6+}$ ions. ${\mathrm{Pb}}_5{\mathrm{Re}}_3{\mathrm{O}}_{15}$, however, has a more ideal quasi-1D geometry than the $A_3{\mathrm{ReO}}_5{\mathrm{Cl}}_2$ materials, with larger interchain distances and interlayer spacing. Quasi-1D magnetic behavior in ${\mathrm{Pb}}_5{\mathrm{Re}}_3{\mathrm{O}}_{15}$ is confirmed by fitting the temperature-dependent magnetic susceptibility with the Bonner-Fisher model for a spin-1/2 antiferromagnetically coupled chain, yielding an intrachain coupling constant of $\left|J\right|/k_{\mathrm{B}}=54.5\mathrm{K}$. ${\mathrm{Pb}}_5{\mathrm{Re}}_3{\mathrm{O}}_{15}$ is highly insulating at room temperature, and heat capacity data below 10 K reveal a linear-$T$ contribution that suggests the presence of low-temperature spinon excitations. With a lack of three-dimensional ordering down to at least 0.6 K, ${\mathrm{Pb}}_5{\mathrm{Re}}_3{\mathrm{O}}_{15}$ is proposed as a model system for studying the quantum magnetism of quasi-1D Heisenberg chains in a real-world $5d^1$ antiferromagnetic material.

Figure 1

(a) ${\mathrm{Pb}}_5{\mathrm{Re}}_3{\mathrm{O}}_{15}$ crystallizes in the orthorhombic Pnma space group. The structure shows kinked layers of edge-sharing $\left[{\mathrm{Pb}}_4\mathrm{O}\right]$ tetrahedra with inserted $\left[{\mathrm{ReO}}_5\right]$ square pyramids, while two distinct $\left[{\mathrm{ReO}}_4\right]$ tetrahedra sit between the layers. (b) Re1 (blue square pyramid) has a formal oxidation state of 6+, while Re2 (coral tetrahedron) and Re3 (gold disordered tetrahedra) are assigned 7+ oxidation states based on the Re–O bond lengths and charge neutrality. (c) ${\mathrm{Pb}}_5{\mathrm{Re}}_3{\mathrm{O}}_{15}$ depicted at an angle, emphasizing the anion-centered Pb-Re-O layers (left) and the quasi-1D chains of rhenium square pyramids connected by bridging lead atoms (right). (d) Rietveld refinement of neutron powder diffraction data obtained at 8 K ($\mathrm{wR}=7.14\%, \mathrm{R}=8.25\%$); observed data in red, calculated pattern in black, background in gray, difference pattern in blue, and (hkl) positions in green.

Figure 2

Comparison of the crystal structures of representative Aurivillius phases and ${\mathrm{Pb}}_5{\mathrm{Re}}_3{\mathrm{O}}_{15}$. (Left) Original Aurivillius phase compound ${\mathrm{Bi}}_4{\mathrm{Ti}}_3{\mathrm{O}}_{12}$ [38], (middle) $\alpha \text{−}{\mathrm{Bi}}_6{\mathrm{V}}_3{\mathrm{O}}_{16}$ shares structural similarities with ${\mathrm{Bi}}_4{\mathrm{Ti}}_3{\mathrm{O}}_{12}$ in edge-sharing $\left[{\mathrm{Bi}}_4\mathrm{O}\right]$ tetrahedral layers and interlayer $M$-O polyhedra [37], and (right) ${\mathrm{Pb}}_5{\mathrm{Re}}_3{\mathrm{O}}_{15}$ can be seen as a modification of $\alpha \text{−}{\mathrm{Bi}}_6{\mathrm{V}}_3{\mathrm{O}}_{16}$, where lead and rhenium replace bismuth and vanadium, and the $\left[M{\mathrm{O}}_6\right]$ octahedron (depicted in blue) is inserted into the $\left[{\mathrm{Pb}}_4\mathrm{O}\right]$ layer as a square pyramid ($M$ = Ti, V, or Re).

Figure 3

Comparison of ${\mathrm{Pb}}_5{\mathrm{Re}}_3{\mathrm{O}}_{15}$ and the related oxychloride phases ${\mathrm{Sr}}_3{\mathrm{ReO}}_5{\mathrm{Cl}}_2$ and ${\mathrm{Ca}}_3{\mathrm{ReO}}_5{\mathrm{Cl}}_2$ (left to right) [21, 40]. (Top) A side view of the unit cells shows the similar Aurivillius-like $\left[A_4\mathrm{O}\right]$ tetrahedral layers with inserted $\left[{\mathrm{ReO}}_5\right]$ square pyramids ($A$ = Pb, Sr, Ca). ${\mathrm{Pb}}_5{\mathrm{Re}}_3{\mathrm{O}}_{15}$ has the most isolated Aurivillius layer with an interlayer Re-Re distance of 9.36 Å. (Middle) A perpendicular view of one Aurivillius layer shows the rectangular arrangement of ${\mathrm{Re}}^{6+}$ ions in ${\mathrm{Pb}}_5{\mathrm{Re}}_3{\mathrm{O}}_{15}$ and the triangular arrangement in $A_3{\mathrm{ReO}}_5{\mathrm{Cl}}_2$ ($A$ = Sr, Ca). ${\mathrm{Pb}}_5{\mathrm{Re}}_3{\mathrm{O}}_{15}$ has an intrachain Re-Re distance of 5.67 Å, which is comparable to ${\mathrm{Sr}}_3{\mathrm{ReO}}_5{\mathrm{Cl}}_2$ (5.65 Å) and ${\mathrm{Ca}}_3{\mathrm{ReO}}_5{\mathrm{Cl}}_2$ (5.57 Å). (Bottom) The ${\mathrm{Re}}^{6+}$ chains are highlighted in a tilted view of the Aurivillius layers. In ${\mathrm{Pb}}_5{\mathrm{Re}}_3{\mathrm{O}}_{15}$, the chains are separated by a full $\left[{\mathrm{Pb}}_4\mathrm{O}\right]$ tetrahedron, while they are only separated by an O-$A$-O linker in ${\mathrm{Sr}}_3{\mathrm{ReO}}_5{\mathrm{Cl}}_2$ and ${\mathrm{Ca}}_3{\mathrm{ReO}}_5{\mathrm{Cl}}_2$.

Figure 4

Direct (top) and indirect (bottom) Tauc plots and fits yielding potential bandgaps of $E_g\approx 1\mathrm{eV}$ (gray) and $E_g\approx 2\mathrm{eV}$ (red-orange), where the dotted fits are baselines. These transitions support the insulating behavior observed with room-temperature resistance.

Figure 5

(a) The temperature-dependent magnetic susceptibility $\left[\chi \right(T\left)\right]$ of polycrystalline ${\mathrm{Pb}}_5{\mathrm{Re}}_3{\mathrm{O}}_{15}$ obtained in an applied magnetic field of 2000 Oe, with a fit to the Bonner-Fisher spin-1/2 chain model (red) plus a paramagnetic $C_{\mathrm{imp}}/T$ component corresponding to the paramagnetic orphan spins and a negative ${\chi }_0$ term $(–0.0016\mathrm{emu}\mathrm{mo}{\mathrm{l}}^{–1}{\mathrm{Oe}}^{–1})$ arising from the diamagnetism of the compound's many core electrons and the brass sample holder (blue) [27, 28]. The total fit is shown in purple. This fit yields a reduced $g$ factor of 1.72 and an intrachain magnetic coupling constant, $\left|J\right|/k_{\mathrm{B}}=54.5\mathrm{K}$, which corresponds well to the broad hump in χ($T$), resulting from the short-range intrachain interactions between spin-1/2 moments. The paramagnetic orphan-spin component yields ${\mu }_{\mathrm{imp}}=0.14{\mu }_{\text{B}}$, approximately 5% of a spin-1 theoretical moment (where $g=2$). (b) The temperature-dependent heat capacity, $C_p/T$ versus $T^2$, is fit to the linear relationship $C_p/T=\beta T^2+\gamma$ from 4.1 to $98{\mathrm{K}}^2$ in order to determine the phonon ($\beta T^2$) and spinon ($\gamma$) contributions. We determine $\left|J\right|/k_{\mathrm{B}}\approx 65\mathrm{K}$ from $\gamma$ (details in Sec. 2). (Inset) $C_p$ versus $T$ from 0.5 to 2 K exhibits two anomalies with possible assignments of a paramagnetic Schottky anomaly from the orphan spins (1 to 1.5 K) and either a transition into a 3D-ordered state or a nuclear Schottky anomaly below 1 K.