Transverse structural modulation in nematic SrAl4_4 and elucidation of its origin in the BaAl4_4 family of compounds

At ambient conditions SrAl$_4$ adopts the BaAl$_4$ structure type with space group $I4/mmm$. It undergoes a charge-density-wave (CDW) transition at $T_{CDW}$ = 243 K, followed by a structural transition at $T_{S}$ = 87 K. Temperature-dependent single-crystal X-ray diffraction (SXRD) leads to the observation of incommensurate superlattice reflections at $\mathbf{q} = \sigma\,\mathbf{c}^{*}$ with $\sigma = 0.1116$ at 200 K. The CDW has orthorhombic symmetry with the superspace group $Fmmm(0\,0\,\sigma)s00$, where $Fmmm$ is a subgroup of $I4/mmm$ of index 2. Atomic displacements represent a transverse wave, and they are mainly along one of the diagonal directions of the $I$-centered unit cell. The breaking of fourfold rotational symmetry is indicative of the presence of nematic order in the material. The orthorhombic phase realized in SrAl$_4$ is analogous to that found in EuAl$_4$, albeit with the presence of higher order satellite reflections (up to $m = 3$) and a shorter modulation wave vector. A possible non-trivial band topology has prevented the determination by density functional theory (DFT) of the mechanism of CDW formation. However, DFT reveals that Al atoms dominate the density of states near the Fermi level, thus, corroborating the SXRD measurements. SrAl$_4$ remains incommensurately modulated at the structural transition, where the symmetry lowers from orthorhombic to $\mathbf{b}$-unique monoclinic. We have identified a simple criterion, that correlates the presence of a phase transition with the interatomic distances. Only those compounds $X$Al$_{4-x}$Ga$_x$ ($X$ = Ba, Eu, Sr, Ca; $0 < x <4$) undergo phase transitions, for which the ratio $c/a$ falls within the narrow range $2.51 < c/a < 2.54$

Disordered structure for long-range charge density wave order in annealed crystals of magnetic kagome FeGe

Recently, charge density wave (CDW) has been observed well below the order of antiferromagnetism (AFM) in kagome FeGe in which magnetism and CDW are intertwined to form an emergent quantum ground state. The mechanism of CDW precipitating from an A-type AFM of Fe kagome sublattice is intensively debated. The structural distortion originating from the CDW has yet to be accurately determined in FeGe. Here we resolved the structure model of the CDW in annealed FeGe crystals through single crystal x-ray diffraction via a synchrotron radiation source. The annealed crystals exhibit strong CDW transition signals exemplified by sharp magnetic susceptibility drop and specific heat jump, as well as intense superlattice reflections from 2 $\times$ 2 $\times$ 2 CDW order. Occupational disorder of Ge atoms resulting from short-range CDW correlations above $T_\mathrm{CDW}$ has also been identified from the structure refinements. The dimerization of Ge atoms along c axis has been demonstrated to be the dominant distortion for CDW. The Fe kagome and Ge honeycomb sublattices only undergo subtle distortions. Occupational disorder of Ge atoms is also proved to exist in the CDW phase due to the random selection of partial Ge sites to be dimerized to realize the structural distortion. Our work paves the way to understanding the unconventional nature of CDW in FeGe not only by solving the structural distortion below $T_\mathrm{CDW}$ and identifying fluctuations above it but also by rationalizing the synthesis of high-quality crystals for in-depth investigations in the future.Comment: 18 pages, 4 figures. Comments are welcom

Charge density wave without long-range structural modulation in canted antiferromagnetic kagome FeGe

Strongly correlated electron systems with a kagome lattice can host abundant exotic quantum states such as superconductivity and spin/charge density waves (CDW) due to the complicated interactions between different degrees of freedoms in the framework of a unique two-dimensional geometrically frustrated lattice structure. Recently, successive orders of A-type antiferromagnetism (AFM), $2\times2\times2$ CDW and canted double-cone AFM have been manifested upon cooling in magnetic kagome FeGe. However, the mechanism of the CDW order and its interaction with magnetism are presently enigmatic at best. Here we investigate the evolution of CDW order with temperature across the spin canting transition in FeGe by single-crystal x-ray diffraction. Refinements of its modulated structure are presented using the superspace approach. Interestingly, the superlattice reflections originating from CDW-induced long-range structural modulation become extremely weak after the system enters the canted AFM while a $2\times2$ CDW in the $ab$ plane persists as a long-range order demonstrated by strong electronic modulation in the d$I$/d$V$ map of scanning tunneling spectroscopy. We discovered a novel CDW order without long-range structural modulation in FeGe probably because of the competition between CDW and canted AFM in determining the underlying crystal structure. In addition, occupational modulations of Ge1 atoms located in the kagome plane and displacive modulations of all the atoms were extracted from the refinements, confirming the existence of Ge atom dimerization along the $c$ axis as the major distortion and indicating a dynamic transformation between different CDW domains.Comment: 22 pages, 6 figures. Comments on the manuscript are welcom

Superspace approach helps: determination of proton dynamics in the phase transition of modulated supramolecular ferroelectrics: 5,5′-dimethyl-2,2′-bipyridine and bromanilic acid

Temperature dependent crystal structures are reported for the co-crystal of 5,5′-dimethyl-2,2′-bipyridine (55DMBP) and bromanilic acid (H$_2$ba) across its phase transitions. 55DMBP–H$_2$ba is ferroelectric (FE) below T = 245 K and remains paraelectric (PE) at higher temperatures up to 360 K, but passes through two PE–PE phase transitions. X-ray diffraction data at 120 K reveals a ferroelectric phase (FE-I phase), which can be described as a commensurately modulated structure with superspace group P[1 with combining macron]$(σ_1σ_2σ_3)_0$ with modulation wave vector q = 0.5, 0.5, 0.5. At 250 K, the crystal transforms into the paraelectric phase PE-II, which possesses the same modulation wave vector. Above 320 K the modulation wave vector becomes incommensurate, q = (0.5000, 0.4944, 0.5221), while the superspace group remains the same in the FE-I, PE-II and PE-IC phases. Different choices of the phase of the modulation wave allow the PE-II to FE-I phase transition to be described by a phase shift in superspace. Above 338 K the satellite Bragg reflections disappear. The crystal structure at 346 K of this PE-III phase is periodic with space group P[1 with combining macron] and a unit cell that acts as basic structure for the modulated phases. Peak profiles become very broad at 350 K and at 360 K the crystal disintegrates, and the material becomes amorphous. Anharmonic atomic displacements are found for the Br atoms in the PE-IC and PE-III phases. The FE-I phase is ferroelectric due to proton transfer within part of the O–H⋯N intermolecular hydrogen bonds, a mechanism similar to that of phenazine-chloranilic acid. The PE-IC phase involves modulations of the proton between two tautomeric forms of H$_2$ba, thus leading to an exchange between O1–H1⋯N1 and O$_2$–H1⋯N1 hydrogen bonds. This mechanism is essentially different from the incommensurability in phenazine-chloranilic acid

Anion-directed assemblies of Cu(II) mono, di, and poly-nuclear coordination compounds with a 32-membered azacrown ligand: Synthesis, characterisation and crystal structures

A novel 32-membered azacrown ligand L was synthesized from the [2 + 2] condensation between 2-[3-(2-formylphenoxy)-2-hydroxy propoxy]benzaldehyde and 1,2-diaminopropane by following in situ reduction. Three metal-organic coordination compounds $[CuL(NCS)]NO_3·CH_3OH (1), [Cu_2L(CH_3COO)_4].0.5_H2O (2)$, and $[CuL(μ-Cl)(NO_3)]_n.2nCH_3CN (3)$, were prepared from reaction of L with copper(II) salts containing different anions. Depending on the reaction controlling factor, i.e. $NCS^−, CH_3COO^−$, , and $Cl^−$anions, mono, di and polynuclear metal-organic coordination compounds were constructed. Complexes were characterized by spectroscopic methods and single crystal X-ray diffraction. Crystal structures indicate that L in presence of $NCS^−$ and $Cu(NO_3)_2·3H_2O$ forms mononuclear complex 1. Dinuclear complex 2 was formed by the reaction of L in presence of $Cu(CH_3COO)_2·2H_2O$. Reaction of $Cu(NO_3)_2·3H_2O$ and $CuCl_2·3H_2O$ with L give rise complex 3 which is a 1-dimensional coordination polymer. The coordination polymer constructed from distorted octahedron shaped copper nucleus that are exomacrocylic in which two Cl atoms serve as bridge. Potentially decadentate ligand, L, with four N- and six O-donor sites in presence of Cu(II) salts reacts only with its N-donors. Complexes 1 and 3, both, are crystalized in a centrosymmetric space group $P2_{1/c}$ and dinuclear complex 2 is crystalized in a polar space group $P2_1$