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Structural disorder has been shown to enhance and modulate magnetic, electrical, dipolar, electrochemical, and mechanical properties of materials. However, the possibility of obtaining novel optical and optoelectronic properties from structural disorder remains an open question. Here, we show unambiguous evidence of disorder in the form of anisotropic, picoscale atomic displacements modulating the refractive index tensor and resulting in the giant optical anisotropy observed in BaTiS$_3$, a quasi-one-dimensional hexagonal chalcogenide. Single crystal X-ray diffraction studies reveal the presence of antipolar displacements of Ti atoms within adjacent TiS$_6$ chains along the c-axis, and three-fold degenerate Ti displacements in the a-b plane. $^{47/49}$Ti solid-state NMR provides additional evidence for those Ti displacements in the form of a three-horned NMR lineshape resulting from a low symmetry local environment around Ti atoms. We used scanning transmission electron microscopy to directly observe the globally disordered Ti a-b plane displacements and find them to be ordered locally over a few unit cells. First-principles calculations show that the Ti a-b plane displacements selectively reduce the refractive index along the ab-plane, while having minimal impact on the refractive index along the chain direction, thus resulting in a giant enhancement in the optical anisotropy. By showing a strong connection between structural disorder with picoscale displacements and the optical response in BaTiS$_3$, this study opens a pathway for designing optical materials with high refractive index and functionalities such as large optical anisotropy and nonlinearity., Comment: 24 pages, 3 figures

Magnetic materials with the spinel structure (A$^{2+}$B$^{3+}_2$O$^4$) form the core of numerous magnetic devices, but ZnFe$_2$O$_4$ constitutes a peculiar example where the nature of the magnetism is still unresolved. Susceptibility measurements revealed a cusp around $T_c=13\;\mathrm{K}$ resembling an antiferromagnetic transition, despite the positive Curie-Weiss temperature determined to be $\Theta_{CW}=102.8(1)\;\mathrm{K}$. Bifurcation of field-cooled and zero-field-cooled data below $T_c$ in conjunction with a frequency dependence of the peak position and a non-zero imaginary component below $T_c$ shows it is in fact associated with a spin-glass transition. Highly structured magnetic diffuse neutron scattering from single crystals develops between $50\;\mathrm{K}$ and $25\;\mathrm{K}$ revealing the presence of magnetic disorder which is correlated in nature. Here, the 3D-m$\Delta$PDF method is used to visualize the local magnetic ordering preferences, and ferromagnetic nearest-neighbor and antiferromagnetic third nearest-neighbor correlations are shown to be dominant. Their temperature dependence is extraordinary with some flipping in sign, and a strongly varying correlation length. The correlations can be explained by orbital interaction mechanisms for the magnetic pathways, and a preferred spin cluster. Our study demonstrates the power of the 3D-m$\Delta$PDF method in visualizing complex quantum phenomena thereby providing a way to obtain an atomic scale understanding of magnetic frustration.

Electron-lattice coupling effects in low dimensional materials give rise to charge density wave (CDW) order and phase transitions. These phenomena are critical ingredients for superconductivity and predominantly occur in metallic model systems such as doped cuprates, transition metal dichalcogenides, and more recently, in Kagome lattice materials. However, CDW in semiconducting systems, specifically at the limit of low carrier concentration region, is uncommon. Here, we combine electrical transport, synchrotron X-ray diffraction and optical spectroscopy to discover CDW order in a quasi-one-dimensional (1D), dilute d-band semiconductor, BaTiS3, which suggests the existence of strong electron-phonon coupling. The CDW state further undergoes an unusual transition featuring a sharp increase in carrier mobility. Our work establishes BaTiS3 as a unique platform to study the CDW physics in the dilute filling limit to explore novel electronic phases.

Quantum effects fundamentally engender exotic physical phenomena in macroscopic systems, which advance next-generation technological applications. Rotational tunneling that represents the quantum phenomenon of the librational motion of molecules is ubiquitous in hydrogen-contained materials. However, its direct manifestation in realizing macroscopic physical properties is elusive. Here we report an observation of reentrant ferroelectricity under low pressure that is mediated by the rotational tunneling of ammonium ions in molecule-based (NH$_4$)$_2$FeCl$_5 \cdot$H$_2$O. Applying a small pressure leads to a transition from spin-driven ferroelectricity to paraelectricity coinciding with the stabilization of a collinear magnetic phase. Such a transition is attributed to the hydrogen bond fluctuations via the rotational tunneling of ammonium groups as supported by theoretical calculations. Higher pressure lifts the quantum fluctuations and leads to a reentrant ferroelectric phase concomitant with another incommensurate magnetic phase. These results demonstrate that the rotational tunneling emerges as a new route to control magnetic-related properties in soft magnets, opening avenues for designing multi-functional materials and realizing potential quantum control., Comment: 4 figures. Supplemental Material available on request

Charge density waves (CDW) are modulations of the electron density and the atomic lattice that develop in some crystalline materials at low temperature. We report an unusual example of a CDW in BaFe$_2$Al$_9$ below 100 K. In contrast to the canonical CDW phase transition, temperature dependent physical properties of single crystals reveal a first-order phase transition. This is accompanied by a discontinuous change in the size of the crystal lattice. In fact, this large strain has catastrophic consequences for the crystals causing them to physically shatter. Single crystal x-ray diffraction reveals super-lattice peaks in the low-temperature phase signaling the development of a CDW lattice modulation. No similar low-temperature transitions are observed in BaCo$_2$Al$_9$. Electronic structure calculations provide one hint to the different behavior of these two compounds; the d-orbital states in the Fe compound are not completely filled. Iron compounds are renowned for their magnetism and partly filled d-states play a key role. It is therefore surprising that BaFe$_2$Al$_9$ develops a structural modulation instead at low temperature instead of magnetic order., Comment: 34 pages, 8 figures Edits to text as well as figures 2 and 5. Added neutron diffraction (Fig. 6)

The van der Waals compound, MnBi$_2$Te$_4$, is the first intrinsic magnetic topological insulator, providing a materials platform for exploring exotic quantum phenomena such as the axion insulator state and the quantum anomalous Hall effect. However, intrinsic structural imperfections lead to bulk conductivity, and the roles of magnetic defects are still unknown. With higher concentrations of same types of magnetic defects, the isostructural compound MnSb$_2$Te$_4$ is a better model system for a systematic investigation of the connections among magnetic, topology and lattice defects. In this work, the impact of antisite defects on the magnetism and electronic structure is studied in MnSb$_2$Te$_4$. Mn-Sb site mixing leads to complex magnetic structures and tunes the interlayer magnetic coupling between antiferromagnetic and ferromagnetic. The detailed nonstoichiometry and site-mixing of MnSb$_2$Te$_4$ crystals depend on the growth parameters, which can lead to $\approx$40\% of Mn sites occupied by Sb and $\approx$15\% of Sb sites by Mn in as-grown crystals. Single crystal neutron diffraction and electron microscopy studies show nearly random distribution of the antisite defects. Band structure calculations suggest that the Mn-Sb site-mixing favors a FM interlayer coupling, consistent with experimental observation, but is detrimental to the band inversion required for a nontrivial topology. Our results suggest a long range magnetic order of Mn ions sitting on Bi sites in MnBi$_2$Te$_4$. The effects of site mixing should be considered in all layered heterostructures that consist of alternating magnetic and topological layers, including the entire family of MnTe(Bi$_2$Te$_3$)$_n$, its Sb analogs and their solid solution., Comment: The effects of Mn/Sb antisite mixing on the magnetic structure (experiment) and band topology (theory) in the van der Waals magnet MnSb$_2$Te$_4$. PRX in press

By combining single crystal x-ray and neutron diffraction, and the magnetodielectric measurements on single crystal Fe4Nb2O9, we present the magnetic structure and the symmetry-allowed magnetoelectric coupling in Fe4Nb2O9. It undergoes an antiferromagnetic transition at TN=93 K, followed by a displacive transition at TS=70 K. The temperature-dependent dielectric constant of Fe4Nb2O9 is strongly anisotropic with the first anomaly at 93 K due to the exchange striction as a result of the long range spin order, and the second one at 70 K emanating from the structural phase transition primarily driven by the O atomic displacements. Magneticfield induced magnetoelectric coupling was observed in single crystal Fe4Nb2O9 and is compatible with the solved magnetic structure that is characteristic of antiferromagnetically arranged ferromagnetic chains in the honeycomb plane. We propose that such magnetic symmetry should be immune to external magnetic fields to some extent favored by the freedom of rotation of moments in the honeycomb plane, laying out a promising system to control the magnetoelectric properties by magnetic fields.

Through analysis of single crystal neutron diffraction data, we present the magnetic structures of magnetoelectric Co4Nb2O9 under various magnetic fields. In zero-field, neutron diffraction experiments below TN=27 K reveal that the Co2+ moments order primarily along the a* direction without any spin canting along the c axis, manifested by the magnetic symmetry C2/c'. The moments of nearest neighbor Co atoms order ferromagnetically with a small cant away from the next nearest neighbor Co moments along the c axis. In the applied magnetic field H//a, three magnetic domains were aligned with their major magnetic moments perpendicular to the magnetic field with no indication of magnetic phase transitions. The influences of magnetic fields on the magnetic structures associated with the observed magnetoelectric coupling are discussed.

Dirac states hosted by Sb/Bi square nets are known to exist in the layered antiferromagnetic AMnX$_2$ (A = Ca/Sr/Ba/Eu/Yb, X=Sb/Bi) material family the space group to be P4/nmm or I4/mmm. In this paper, we present a comprehensive study of quantum transport behaviors, angle-resolved photoemission spectroscopy (ARPES) and first-principles calculations on SrZnSb2, a nonmagnetic analogue to AMnX2, which crystallizes in the pnma space group with distorted square nets. From the quantum oscillation measurements up to 35 T, three major frequencies including F$_1$ = 103 T, F$_2$ = 127 T and F$_3$ = 160 T, are identified. The effective masses of the quasiparticles associated with these frequencies are extracted, namely, m*$_1$ = 0.1 m$_e$, m*$_2$ = 0.1 m$_e$ and m*$_3$ = 0.09m$_e$, where m$_e$ is the free electron mass. From the three-band Lifshitz-Kosevich fit, the Berry phases accumulated along the cyclotron orbit of the quasiparticles are 0.06$\pi$, 1.2$\pi$ and 0.74$\pi$ for F$_1$, F$_2$ and F$_3$, respectively. Combined with the ARPES data and the first-principles calculations, we reveal that F2 and F3 are associated with the two nontrivial Fermi pockets at the Brillouin zone edge while F1 is associated with the trivial Fermi pocket at the zone center. In addition, the first-principles calculations further suggest the existence of Dirac nodal line in the band structure of SrZnSb$_2$., Comment: 5 figures. New results from DFT calculations and ARPES experiments are summarized in Figure 5

Frustrated magnetic systems exhibit extraordinary physical properties but quantification of their magnetic correlations poses a serious challenge to experiment and theory. Current insight into frustrated magnetic correlations relies on modelling techniques such as reverse Monte Carlo methods, which require knowledge about the exact ordered atomic structure. Here we present a method for direct reconstruction of magnetic correlations in frustrated magnets by three-dimensional difference pair distribution function analysis of neutron total scattering data. The methodology is applied to the disordered frustrated magnet bixbyite, (Mn1-xFex)2O3, which reveals nearest-neighbor antiferromagnetic correlations for the metal sites up to a range of approximately 15 {\AA}. Importantly, this technique allows for magnetic correlations to be determined directly from the experimental data without any assumption about the atomic structure.

We use single-crystal neutron diffraction to determine the crystal structure symmetry and the magnetic evolution in the rhodium doped iridates $\rm Sr_2Ir_{1-x}Rh_{x}O_4$ ($0\leq x \leq 0.16$). Throughout this doping range, the crystal structure retains a tetragonal symmetry (space group $I4_1/a$) with two distinct magnetic Ir sites in the unit cell forming staggered $\rm IrO_6$ rotation. Upon Rh doping, the magnetic order is suppressed and the magnetic moment of Ir$^{4+}$ is reduced from 0.21 $\rm \mu_B$/Ir for $x=0$ to 0.18 $\rm \mu_B$/Ir for $x=0.12$. The magnetic structure at $x=0.12$ is different from that of the parent compound while the moments remain in the basal plane., Comment: Accepted for publication in Phys. Rev. B

Structural and physical properties determined by measurements on large single crystals of the anisotropic ferromagnet MnBi are reported. The findings support the importance of magneto-elastic effects in this material. X-ray diffraction reveals a structural phase transition at the spin reorientation temperature $T_{SR}$ = 90 K. The distortion is driven by magneto-elastic coupling, and upon cooling transforms the structure from hexagonal to orthorhombic. Heat capacity measurements show a thermal anomaly at the crystallographic transition, which is suppressed rapidly by applied magnetic fields. Effects on the transport and anisotropic magnetic properties of the single crystals are also presented. Increasing anisotropy of the atomic displacement parameters for Bi with increasing temperature above $T_{SR}$ is revealed by neutron diffraction measurements. It is likely that this is directly related to the anisotropic thermal expansion in MnBi, which plays a key role in the spin reorientation and magnetocrystalline anisotropy. The identification of the true ground state crystal structure reported here may be important for future experimental and theoretical studies of this permanent magnet material, which have to date been performed and interpreted using only the high temperature structure., Comment: 9 pages, 6 figures, accepted for publication in Physical Review B

We used X-ray/neutron diffraction to determine the low temperature (LT) structure of IrTe2. A structural modulation was observed with a wavevector of k =(1/5, 0, 1/5) below Ts?285 K, accompanied by a structural transition from a trigonal to a triclinic lattice. We also performed the first principles calculations for high temperature (HT) and LT structures, which elucidate the nature of the phase transition and the LT structure. A local bonding instability associated with the Te 5p states is likely the origin of the structural phase transition in IrTe2., Comment: 6 pages, 6 figures

We report a single-crystal neutron diffraction study of the layered $\rm Sr_2IrO_4$. This work unambiguously determines the magnetic structure of the system and reveals that the spin orientation rigidly tracks the staggered rotation of the $\rm IrO_6$ octahedra in $\rm Sr_2IrO_4$. The long-range antiferromagnetic order has a canted spin configuration with an ordered moment of 0.208(3) $\mu_B$/Ir site within the basal plane; a detailed examination of the spin canting yields 0.202(3) and 0.049(2) $\mu_B$/site for the a axis and the b axis, respectively. It is intriguing that forbidden nuclear reflections of space group $I4_1/acd$ are also observed in a wide temperature range from 4 K to 600 K, which suggests a reduced crystal structure symmetry. This neutron-scattering work provides a direct, well-refined experimental characterization of the magnetic and crystal structures that are crucial to the understanding of the unconventional magnetism exhibited in this unusual magnetic insulator., Comment: the version appeared in PRB

The relationship between vacancy ordering and magnetism in TlFe1.6Se2 has been investigated via single crystal neutron diffraction, nuclear forward scattering, and transmission electron microscopy. The examination of chemically and structurally homogenous crystals allows the true ground state to be revealed, which is characterized by Fe moments lying in the ab-plane below 100K. This is in sharp contrast to crystals containing regions of order and disorder, where a competition between c-axis and ab-plane orientations of the moments is observed. The properties of partially-disordered TlFe1.6Se2 are therefore not associated with solely the ordered or disordered regions. This contrasts the viewpoint that phase separation results in independent physical properties in intercalated iron selenides, suggesting a coupling between ordered and disordered regions may play an important role in the superconducting analogues., Comment: Minor changes; updated references and funding acknowledgement

The evolution of the nuclear and magnetic structures of TlFe$_{1.6}$Se$_2$ was determined in the temperature range of 5-450\,K using single crystal neutron diffraction. The Fe layers in these materials develop a corrugation in the magnetically ordered state. A canting away from the block checkerboard magnetic structure is observed in the narrow temperature range between approximately 100 and 150\,K. In this same temperature range, an increase in the corrugation of the Fe layers is observed. At lower temperatures, the block checkerboard magnetic structure is recovered with a suppressed magnetic moment and abrupt changes in the lattice parameters. Microstructure analysis at 300\,K using atomic-resolution Z-contrast scanning transmission electron microscopy reveals regions with ordered and disordered Fe vacancies, and the iron content is found to be uniform across the crystal. These findings highlight the differences between the alkali-metal and thallium materials, and indicate competition between magnetic ground states and a strong coupling of magnetism to the lattice in TlFe$_{1.6}$Se$_2$., Comment: in press, Phys. Rev. B

We have combined single crystal neutron and x-ray diffractions to investigate the magnetic and crystal structures of the honeycomb lattice $\rm Na_2IrO_3$. The system orders magnetically below $18.1(2)$ K with Ir$^{4+}$ ions forming zigzag spin chains within the layered honeycomb network with ordered moment of $\rm 0.22(1) \mu_B$/Ir site. Such a configuration sharply contrasts the N{\'{e}}el or stripe states proposed in the Kitaev-Heisenberg model. The structure refinement reveals that the Ir atoms form nearly ideal 2D honeycomb lattice while the $\rm IrO_6$ octahedra experience a trigonal distortion that is critical to the ground state. The results of this study provide much-needed experimental insights into the magnetic and crystal structure crucial to the understanding of the exotic magnetic order and possible topological characteristics in the 5$d$-electron based honeycomb lattice., Comment: Revised version as that to appear in PRB

Structural, magnetic, electrical transport, and heat capacity data are reported for single crystals of TlFe1.6Se2. This compound crystallizes in a tetragonal structure similar to the ThCr2Si2 structure, but with vacancies in the Fe layer. The vacancies can be ordered or disordered depending on temperature and thermal history. If the vacancies are ordered, the basal plane lattice constant increases from a to \sqrt{5}a. Antiferromagnetic order with the Fe spins along the c-axis occurs below T_N ~ 430K as shown by single crystal neutron diffraction and the magnetic structure is reported. In addition, for the vacancy ordered crystal, two other phase transitions are found at T_1 ~ 140K, and T_2 ~ 100K. The phase transitions at T_1 and T_2 are evident in heat capacity, magnetic susceptibility, resistivity data, a and c lattice parameters, and in the unusual temperature dependence of the magnetic order parameter determined from neutron scattering. The phase transitions at T_1 and T_2 result in significant changes in the magnetic moment per iron, with 1.72(6)\mu_B observed at 300K, 2.07(9)\mu_B at 140\,K, 1.90(9)\,\mu_B at 115\,K, and 1.31(8)\mu_B for 5\,K if the same "block checkerboard" magnetic structure is used at all temperatures. The phase transitions appear to be driven by small changes in the c lattice constant, large magnetoelastic coupling, and the localization of carriers with decreasing temperature., Comment: Accepted for publication in Physical Review B