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CuZn is Tetraauricupride structured and crystallizes in the cubic Pm-3m space group. The structure is three-dimensional. Cu is bonded in a body-centered cubic geometry to eight equivalent Zn atoms. All Cu–Zn bond lengths are 2.56 Å. Zn is bonded in a body-centered cubic geometry to eight equivalent Cu atoms.
CuZn(PO3)4 crystallizes in the triclinic P1 space group. The structure is three-dimensional. there are two inequivalent Cu2+ sites. In the first Cu2+ site, Cu2+ is bonded to six O2- atoms to form CuO6 octahedra that share corners with six PO4 tetrahedra and edges with two ZnO6 octahedra. There are a spread of Cu–O bond distances ranging from 2.05–2.13 Å. In the second Cu2+ site, Cu2+ is bonded to six O2- atoms to form CuO6 octahedra that share corners with six PO4 tetrahedra and edges with two ZnO6 octahedra. There are a spread of Cu–O bond distances ranging from 2.05–2.14 Å. There are two inequivalent Zn2+ sites. In the first Zn2+ site, Zn2+ is bonded to six O2- atoms to form ZnO6 octahedra that share corners with six PO4 tetrahedra and edges with two CuO6 octahedra. There are a spread of Zn–O bond distances ranging from 2.01–2.22 Å. In the second Zn2+ site, Zn2+ is bonded to six O2- atoms to form ZnO6 octahedra that share corners with six PO4 tetrahedra and edges with two CuO6 octahedra. There are a spread of Zn–O bond distances ranging from 2.03–2.21 Å. There are eight inequivalent P5+ sites. In the first P5+ site, P5+ is bonded to four O2- atoms to form PO4 tetrahedra that share a cornercorner with one ZnO6 octahedra, corners with two CuO6 octahedra, and corners with two PO4 tetrahedra. The corner-sharing octahedra tilt angles range from 27–56°. There are a spread of P–O bond distances ranging from 1.48–1.62 Å. In the second P5+ site, P5+ is bonded to four O2- atoms to form PO4 tetrahedra that share a cornercorner with one ZnO6 octahedra, corners with two CuO6 octahedra, and corners with two PO4 tetrahedra. The corner-sharing octahedra tilt angles range from 26–57°. There are a spread of P–O bond distances ranging from 1.48–1.61 Å. In the third P5+ site, P5+ is bonded to four O2- atoms to form PO4 tetrahedra that share a cornercorner with one ZnO6 octahedra, corners with two CuO6 octahedra, and corners with two PO4 tetrahedra. The corner-sharing octahedra tilt angles range from 25–57°. There are a spread of P–O bond distances ranging from 1.48–1.61 Å. In the fourth P5+ site, P5+ is bonded to four O2- atoms to form PO4 tetrahedra that share a cornercorner with one ZnO6 octahedra, corners with two CuO6 octahedra, and corners with two PO4 tetrahedra. The corner-sharing octahedra tilt angles range from 24–57°. There are a spread of P–O bond distances ranging from 1.48–1.61 Å. In the fifth P5+ site, P5+ is bonded to four O2- atoms to form PO4 tetrahedra that share a cornercorner with one CuO6 octahedra, corners with two ZnO6 octahedra, and corners with two PO4 tetrahedra. The corner-sharing octahedra tilt angles range from 19–58°. There are a spread of P–O bond distances ranging from 1.48–1.62 Å. In the sixth P5+ site, P5+ is bonded to four O2- atoms to form PO4 tetrahedra that share a cornercorner with one CuO6 octahedra, corners with two ZnO6 octahedra, and corners with two PO4 tetrahedra. The corner-sharing octahedra tilt angles range from 19–59°. There are a spread of P–O bond distances ranging from 1.48–1.61 Å. In the seventh P5+ site, P5+ is bonded to four O2- atoms to form PO4 tetrahedra that share a cornercorner with one CuO6 octahedra, corners with two ZnO6 octahedra, and corners with two PO4 tetrahedra. The corner-sharing octahedra tilt angles range from 22–58°. There are a spread of P–O bond distances ranging from 1.48–1.62 Å. In the eighth P5+ site, P5+ is bonded to four O2- atoms to form PO4 tetrahedra that share a cornercorner with one CuO6 octahedra, corners with two ZnO6 octahedra, and corners with two PO4 tetrahedra. The corner-sharing octahedra tilt angles range from 19–58°. There are a spread of P–O bond distances ranging from 1.48–1.62 Å. There are twenty-four inequivalent O2- sites. In the first O2- site, O2- is bonded in a bent 150 degrees geometry to two P5+ atoms. In the second O2- site, O2- is bonded in a bent 150 degrees geometry to two P5+ atoms. In the third O2- site, O2- is bonded in a bent 150 degrees geometry to two P5+ atoms. In the fourth O2- site, O2- is bonded in a bent 150 degrees geometry to two P5+ atoms. In the fifth O2- site, O2- is bonded in a distorted bent 120 degrees geometry to two P5+ atoms. In the sixth O2- site, O2- is bonded in a distorted bent 120 degrees geometry to two P5+ atoms. In the seventh O2- site, O2- is bonded in a distorted bent 120 degrees geometry to two P5+ atoms. In the eighth O2- site, O2- is bonded in a distorted bent 120 degrees geometry to two P5+ atoms. In the ninth O2- site, O2- is bonded in a bent 150 degrees geometry to one Cu2+ and one P5+ atom. In the tenth O2- site, O2- is bonded in a bent 150 degrees geometry to one Cu2+ and one P5+ atom. In the eleventh O2- site, O2- is bonded in a bent 150 degrees geometry to one Cu2+ and one P5+ atom. In the twelfth O2- site, O2- is bonded in a bent 150 degrees geometry to one Cu2+ and one P5+ atom. In the thirteenth O2- site, O2- is bonded in a 3-coordinate geometry to one Cu2+, one Zn2+, and one P5+ atom. In the fourteenth O2- site, O2- is bonded in a distorted trigonal planar geometry to one Cu2+, one Zn2+, and one P5+ atom. In the fifteenth O2- site, O2- is bonded in a distorted trigonal planar geometry to one Cu2+, one Zn2+, and one P5+ atom. In the sixteenth O2- site, O2- is bonded in a distorted trigonal planar geometry to one Cu2+, one Zn2+, and one P5+ atom. In the seventeenth O2- site, O2- is bonded in a distorted trigonal planar geometry to one Cu2+, one Zn2+, and one P5+ atom. In the eighteenth O2- site, O2- is bonded in a distorted trigonal planar geometry to one Cu2+, one Zn2+, and one P5+ atom. In the nineteenth O2- site, O2- is bonded in a distorted trigonal planar geometry to one Cu2+, one Zn2+, and one P5+ atom. In the twentieth O2- site, O2- is bonded in a distorted trigonal planar geometry to one Cu2+, one Zn2+, and one P5+ atom. In the twenty-first O2- site, O2- is bonded in a distorted bent 150 degrees geometry to one Zn2+ and one P5+ atom. In the twenty-second O2- site, O2- is bonded in a distorted bent 150 degrees geometry to one Zn2+ and one P5+ atom. In the twenty-third O2- site, O2- is bonded in a bent 150 degrees geometry to one Zn2+ and one P5+ atom. In the twenty-fourth O2- site, O2- is bonded in a distorted bent 150 degrees geometry to one Zn2+ and one P5+ atom.
CuZn(WO4)2 crystallizes in the triclinic P1 space group. The structure is three-dimensional. there are two inequivalent W6+ sites. In the first W6+ site, W6+ is bonded to six O2- atoms to form distorted WO6 octahedra that share corners with four equivalent CuO6 octahedra, corners with four equivalent ZnO6 octahedra, and edges with two equivalent WO6 octahedra. The corner-sharing octahedra tilt angles range from 47–58°. There are a spread of W–O bond distances ranging from 1.84–2.17 Å. In the second W6+ site, W6+ is bonded to six O2- atoms to form distorted WO6 octahedra that share corners with four equivalent CuO6 octahedra, corners with four equivalent ZnO6 octahedra, and edges with two equivalent WO6 octahedra. The corner-sharing octahedra tilt angles range from 46–57°. There are a spread of W–O bond distances ranging from 1.82–2.12 Å. Cu2+ is bonded to six O2- atoms to form CuO6 octahedra that share corners with eight WO6 octahedra and edges with two equivalent ZnO6 octahedra. The corner-sharing octahedra tilt angles range from 46–56°. There are a spread of Cu–O bond distances ranging from 1.97–2.39 Å. Zn2+ is bonded to six O2- atoms to form distorted ZnO6 octahedra that share corners with eight WO6 octahedra and edges with two equivalent CuO6 octahedra. The corner-sharing octahedra tilt angles range from 48–58°. There are a spread of Zn–O bond distances ranging from 2.02–2.50 Å. There are eight inequivalent O2- sites. In the first O2- site, O2- is bonded in a distorted trigonal planar geometry to two W6+ and one Zn2+ atom. In the second O2- site, O2- is bonded in a distorted trigonal planar geometry to two W6+ and one Cu2+ atom. In the third O2- site, O2- is bonded in a distorted trigonal planar geometry to one W6+, one Cu2+, and one Zn2+ atom. In the fourth O2- site, O2- is bonded in a distorted trigonal planar geometry to one W6+, one Cu2+, and one Zn2+ atom. In the fifth O2- site, O2- is bonded in a distorted trigonal planar geometry to two W6+ and one Zn2+ atom. In the sixth O2- site, O2- is bonded in a distorted trigonal planar geometry to two W6+ and one Cu2+ atom. In the seventh O2- site, O2- is bonded in a 3-coordinate geometry to one W6+, one Cu2+, and one Zn2+ atom. In the eighth O2- site, O2- is bonded in a 3-coordinate geometry to one W6+, one Cu2+, and one Zn2+ atom.
CuZn crystallizes in the orthorhombic Cmmm space group. The structure is two-dimensional and consists of two CuZn sheets oriented in the (0, 1, 0) direction. Cu is bonded in a 8-coordinate geometry to four equivalent Zn atoms. All Cu–Zn bond lengths are 2.55 Å. Zn is bonded in a 8-coordinate geometry to four equivalent Cu atoms.
CuZn(SeO3)2 crystallizes in the monoclinic P2_1/c space group. The structure is three-dimensional. Cu2+ is bonded to six O2- atoms to form CuO6 octahedra that share corners with six equivalent ZnO6 octahedra. The corner-sharing octahedra tilt angles range from 50–57°. There are a spread of Cu–O bond distances ranging from 1.99–2.44 Å. Zn2+ is bonded to six O2- atoms to form ZnO6 octahedra that share corners with six equivalent CuO6 octahedra. The corner-sharing octahedra tilt angles range from 50–57°. There are a spread of Zn–O bond distances ranging from 1.99–2.41 Å. Se4+ is bonded in a trigonal non-coplanar geometry to three O2- atoms. There is one shorter (1.74 Å) and two longer (1.76 Å) Se–O bond length. There are three inequivalent O2- sites. In the first O2- site, O2- is bonded in a distorted trigonal non-coplanar geometry to one Cu2+, one Zn2+, and one Se4+ atom. In the second O2- site, O2- is bonded in a distorted trigonal planar geometry to one Cu2+, one Zn2+, and one Se4+ atom. In the third O2- site, O2- is bonded in a distorted trigonal planar geometry to one Cu2+, one Zn2+, and one Se4+ atom.
Here, we use 79 Br nuclear quadrupole resonance (NQR) to demonstrate that ultraslow lattice dynamics set in below the temperature scale set by the Cu-Cu superexchange interaction J (≃160 K) in the kagome lattice Heisenberg antiferromagnet Zn-barlowite. The lattice completely freezes below 50 K, and 79 Br NQR line shapes become twice broader due to increased lattice distortions. Moreover, the frozen lattice exhibits an oscillatory component in the transverse spin echo decay, a typical signature of pairing of nuclear spins by indirect nuclear spin-spin interaction. This indicates that some Br sites form structural dimers via a pair of kagome Cu sites prior to the gradual emergence of spin singlets below ~30 K. Our findings underscore the significant roles played by subtle structural distortions in determining the nature of the disordered magnetic ground state of the kagome lattice.
The kagome Heisenberg antiferromagnet formed by frustrated spins arranged in a lattice of corner-sharing triangles is a prime candidate for hosting a quantum spin liquid (QSL) ground state consisting of entangled spin singlets. However, the existence of various competing states makes a convincing theoretical prediction of the QSL ground state difficult, calling for experimental clues from model materials. The kagome lattice materials Zn-barlowite (ZnCu 3 (OD) 6 FBr) and herbertsmithite (ZnCu 3 (OD) 6 Cl 2 ) do not exhibit long-range order and are considered the best realizations of the kagome Heisenberg antiferromagnet known so far. In this study, we use 63 Cu nuclear quadrupole resonance combined with the inverse Laplace transform to locally probe the inhomogeneity of delicate quantum ground states affected by disorder. We present direct evidence for the gradual emergence of spin singlets with spatially varying excitation gaps, but even at temperatures far below the super-exchange energy scale their fraction is limited to ~60% of the total spins. Theoretical models need to incorporate the role of disorder to account for the observed inhomogeneously gapped behaviour.
The development of next-generation quaternary chalcogenides, such as Cu2ZnSnS4 (CZTS) and Cu2ZnGeS4 (CZGS), for solar energy and thermoelectric applications hinges upon both careful experimentation and accurate quantum mechanical modeling. To address the latter, many have turned to density functional theory (DFT), which offers several choices for the approximate treatment of electron exchange and correlation (XC). Popular XC functionals include the Perdew-Burke-Ernzerhof (PBE) generalized gradient approximation (GGA) and the recently developed strongly constrained and appropriately normed (SCAN) meta-GGA. Extensions of DFT functionals, such as adding a Hubbard U correction and introducing a fraction of the Fock exchange (hybrid functionals), have been used widely to model systems containing 3d metal ions. However, no studies yet have compared comprehensively PBE(+U) and SCAN(+U) in the quality of their predictions of the bulk and defect thermodynamics of quaternary chalcogenides, which play a critical role in device fabrication and performance. Hence, here we calculate the (i) 0 K formation energies of bulk Ge compounds and (ii) neutral defect formation energies including charge-balanced (e.g., CuZn + ZnCu) and charge-imbalanced (e.g., CuSn) combinations of antisites and vacancies in CZTS and CZGS using the PBE, PBE +U, SCAN, SCAN +U, and the hybrid Heyd-Scuseria-Ernzerhof XC frameworks. We find that the formation energies of charge-imbalanced defects are more sensitive to the choice of the XC functional than those of charge-balanced defects, which can be explained by the differences in the extent of penalization of defect-generated delocalized electrons/holes by PBE, PBE +U, SCAN, and SCAN +U. Additionally, our results show that SCAN systematically underbinds Ge-containing compounds, thus highlighting the need for even further improvement of XC functionals. Based on our findings, we recommend the use of SCAN for modeling quaternary chalcogenides because its errors are systematic, and it has the firmest theoretical underpinning. Our work provides guidance for future modeling of quaternary chalcogenides.