By appropriately perturbing a critical transverse-field Ising chain away from its critical point, the system can develop a finite correlation length with a characteristic purely massive spectrum, whose ratios and correlations are precisely described by an integrable field theory and an infinite set of integrals of motion corresponding to the $E_8$ Lie algebra. In this work, we report on experimental observation of a characteristic massive spectrum close to transverse field-induced dimensional reduction in a quasi-two-dimensional quantum magnet Cu$_2$(OH)$_3$Br, providing evidence for an emergent $E_8$ symmetry and the corresponding excitations of bound states in the sublattice of its ferromagnetic chains. These results demonstrate the power of integrable field theory in describing emergent many-body quantum critical phenomena in condensed matter systems.

We present magnetic-field-dependent evolution of magnetization and spin dynamics in the quasi-two-dimensional spin-1/2 magnet Cu_2(OH)_3Br, consisting of alternately coupled ferromagnetic Cu1 and antiferromagnetic Cu2 spin chains. Terahertz spectroscopy reveals a pronounced field-direction dependence of the low-energy magnetic excitation spectrum. For magnetic fields applied perpendicular to the spin chains, B∥ a and B∥ c^*, the spectra undergo abrupt reconstructions at the spin-flop transitions identified independently by high-field magnetization measurements. For B∥ b, by contrast, no spin-flop occurs; instead, the excitation spectrum evolves continuously with field and exhibits a strong terahertz radiation polarization dependence as the ferromagnetic Cu1 subsystem becomes progressively polarized. At higher fields, the complex low-field spectrum is replaced by a reduced set of broad excitations, consistent with a weakening of the coupling between the ferromagnetic and antiferromagnetic chain subsystems. Complementary Raman spectroscopy resolves magnon and spinon excitations alongside several phonon modes and traces the characteristic temperature- and magnetic-field-dependent evolution of the magnetic excitations. The combined spectroscopic and magnetization results map out how a magnetic field reorganizes the coupled ferromagnetic and antiferromagnetic subsystems in Cu_2(OH)_3Br across field-induced phase transitions.

We present the experimental observation of a drastically enhanced thermal Hall effect in the topological insulator material TlBi_0.15Sb_0.85Te_2. Although heat transport is dominated by phonons, moderate magnetic fields generate a thermal Hall ratio (κ_xy/κ_xx) above 2%, an unprecedented value for a nonmagnetic material. The transverse thermal conductivity κ_xy exhibits a pronounced maximum in fields of a few Tesla. This characteristic field dependence allows us to identify the microscopic origin of the thermal Hall effect in this system. Small densities of charged impurities induce locally conducting regions, so-called charge puddles, within the bulk insulating matrix. Via electron-phonon coupling, these charge puddles imprint a large thermal Hall effect onto the phonons accounting for both the magnitude and the magnetic-field dependence of the observed effect.

Reactions between carbon and lithium hydride in a mixed metal europium/lithium flux led to the synthesis of Eu2Li(C3)H. At room temperature, the compound crystallizes in the tetragonal space group P4/mbm (no. 127, Z = 2; Ca2Li(C3)H type) and undergoes a second-order structural phase transition below ∼250 K to an orthorhombic low-temperature modification (no. 55, Pbam; Z = 4), crystallizing in a new structure type. The phase transition was monitored by using single-crystal X-ray diffraction (SCXRD) and temperature-dependent high-resolution powder diffraction data. Infrared (IR) spectroscopy and gaschromatographic analysis (GC) of the hydrolysis products confirm the existence of a first europium compound with an allylenide anion (C34-). Magnetic susceptibility measurements and 151Eu Mössbauer spectroscopy reveal the presence of divalent europium, suggesting a charge-balanced carbide hydride (Eu2+)2(Li+)(C34-)(H-). A transition to a (soft) ferromagnetic ground state is observed below 42 K. In situ high-pressure, high-temperature (HPHT) investigations indicate a surprisingly high stability of Eu2Li(C3)H and yield a bulk modulus K0 = 65 GPa. Quantum chemical calculations (DFT + U) reveal a pseudogap at the Fermi level and allow the classification as a rare-earth metal Zintl phase exhibiting both ionic and covalent bonding contributions.

We report on a comprehensive thermodynamic study of a quasi-two-dimensional (quasi-2D) quantum magnet Cu-2(OH)(3)Br which in the 2D layer can be viewed as strongly coupled alternating antiferromagnetic and ferromagnetic chains. In an applied magnetic field transverse to the ordered spins below TN = 9.3 K, a field- induced phase transition from the 3D ordered to a disordered phase occurs at Bc = 16.3 T for the lowest temperature, which is featured by an onset of a one-half plateaulike magnetization. By performing quantum Monte Carlo simulations of the relevant 2D model, we find that the plateaulike magnetization corresponds to a partial symmetry restoration and the full polarization in the ferromagnetic chains. Our numerical simulations also show that the magnetization saturation occurs with full symmetry restoration at a much higher field of Bs similar or equal to 95 T, corresponding to a 1D quantum phase transition in the antiferromagnetic chains. We argue that the experimentally observed field-induced phase transition at Bc follows from the partial symmetry restoration and the concomitant dimensional reduction.

We report an investigation of the phonon thermal Hall effect in single crystal samples of Y2Ti2O7, Dy2Ti2O7, and DyYTi2O7. We measured the field-linear thermal Hall effect in all three samples. The temperature dependence of thermal Hall conductivities shows a peak around 15 K, which coincides with the peak positions of the longitudinal thermal conductivities. The temperature-dependent longitudinal thermal conductivities indicates that phonons dominate thermal transport in all three samples. However, the presence of Dy3+ magnetic ions introduces significant effects on the field dependence of the longitudinal thermal conductivities. The thermal Hall ratio is sizable in all three samples and consistent with the values reported for other insulating materials exhibiting a phononic thermal Hall effect, though their exact underlying mechanism remains yet to be identified. The thermal Hall ratio is nearly the same for Y2Ti2O7 and DyYTi2O7, and slightly larger for Dy2Ti2O7, suggesting that magnetic impurities are less significant in generating the phononic thermal Hall effect. Our observations of the phononic thermal Hall effect support an intrinsic origin in Y2Ti2O7 and suggest a combination of intrinsic and extrinsic effects in Dy2Ti2O7 and DyYTi2O7.

We report an investigation of the phonon thermal Hall effect in single crystal samples of Y_2Ti_2O_7, Dy_2Ti_2O_7, and DyYTi_2O_7. We measured the field-linear thermal Hall effect in all three samples. The temperature dependence of thermal Hall conductivities shows a peak around 15 K, which coincides with the peak positions of the longitudinal thermal conductivities. The temperature-dependent longitudinal thermal conductivities indicates that phonons dominate thermal transport in all three samples. However, the presence of Dy^3+ magnetic ions introduces significant effects on the field dependence of longitudinal thermal conductivities. The thermal Hall ratio is sizeable in all three samples and consistent with the values reported for other insulating materials exhibiting a phononic thermal Hall effect, though their exact underlying mechanism remains yet to be identified. The thermal Hall ratio is nearly the same for Y_2Ti_2O_7 and DyYTi_2O_7, and slightly larger for Dy_2Ti_2O_7, suggesting that magnetic impurities are less significant in generating the phononic thermal Hall effect. Our observations of the phononic thermal Hall effect support an intrinsic origin in Y_2Ti_2O_7, but suggest a combination of intrinsic and extrinsic effects in Dy_2Ti_2O_7 and DyYTi_2O_7.

The magnetic and structural phase transitions occurring in K2ReCl6 were studied by macroscopic and microscopic techniques. Structural phase transitions associated with rotations of the ReCl6 octahedra lower the symmetry from cubic to monoclinic, form ferroelastic domains, and are visible in susceptibility, specific heat, and thermal expansion measurements. In the antiferromagnetically ordered state slightly below TN = 12 K these domains can be rearranged by a magnetic field inducing a relative elongation of the polydomain crystal parallel to the field of 0.6%. At zero field the magnetic structure in K2ReCl6 does not exhibit a weak ferromagnetic component, but at large magnetic field a distinct magnetic structure with a finite weak ferromagnetic component is stabilized. High magnetic fields rearrange the domains in the crystal to align the weak ferromagnetic moment parallel to the field. The altered domain structure with the crystal elongation is abruptly suppressed at lower temperature but persists upon heating to well above TN. However, heating above the lowest structural phase transition and successive cooling restore the initial shape.

From a systematic study of thermal and charge transport in various single crystals of compensated topological insulators we identify the evolution of a large low-temperature thermal Hall effect as a characteristic common feature. In order to separate phononic and electronic contributions in the measured longitudinal and transverse thermal conductivity, the electronic contributions are estimated from corresponding electrical resisivity and Hall effect measurements on the same samples by using the Wiedemann-Franz law. As may be expected for charge-compensated topological insulators the longitudinal thermal conductivity is phonon-dominated in all samples. However, we also find a pronounced field-linear thermal Hall effect that becomes most pronounced in the low-temperature range, where all samples are good electrical insulators. This indicates an underlying phononic mechanism of the thermal Hall effect and in this respect the topological insulators resemble other, mainly ionic, insulators, which have been reported to show a phonon-induced thermal Hall effect, but its underlying phononic mechanism remains to be identified. Our observation of a comparable thermal Hall ratio in topological insulators supports a theoretical scenario that explains a thermal Hall effect through skew scattering on charged impurities.

Mott insulators with spin-orbit entangled j=1/2 moments host intriguing magnetic properties. The j=1/2 wave function requires cubic symmetry, while a noncubic crystal field mixes j=1/2 and 3/2 character. Spectroscopic studies of 5d^5 iridates typically claim noncubic symmetry, e.g., based on a splitting of the excited j=3/2 quartet. A sizable splitting is particularly puzzling in antifluorite-type K_2IrCl_6, a frustrated fcc quantum magnet with global cubic symmetry. It raises the fundamental question about the stability of j=1/2 moments against magneto-elastic coupling. Combining resonant inelastic x-ray scattering with optical spectroscopy, we demonstrate that the multi-peak line shape in K_2IrCl_6 reflects a vibronic character of the j=3/2 states rather than a noncubic crystal field. The quasimolecular crystal structure with well separated IrCl_6 octahedra explains the existence of well-defined sidebands that are usually smeared out in solids. Our results highlight the spin-orbital-lattice entangled character of cubic K_2IrCl_6 with ideal j=1/2 moments.

Mott insulators with spin-orbit entangled j = 1/2 moments host intriguing magnetic properties. The j = 1/2 wave function requires cubic symmetry, while a noncubic crystal field mixes j = 1/2 and 3/2 character. Spectroscopic studies of 5d5 iridates typically claim noncubic symmetry, e.g., based on a splitting of the excited j = 3/2 quartet. A sizable splitting is particularly puzzling in antifluorite-type K2IrCl6, a frustrated fcc quantum magnet with global cubic symmetry. It raises the fundamental question about the stability of j = 1/2 moments against magnetoelastic coupling. Combining resonant inelastic x-ray scattering with optical spectroscopy, we demonstrate that the multi-peak line shape in K2IrCl6 reflects a vibronic character of the j = 3/2 states rather than a noncubic crystal field. The quasimolecular crystal structure with well separated IrCl6 octahedra explains the existence of well-defined sidebands that are usually smeared out in solids. Our results highlight the spin orbital lattice entangled character of cubic K2IrCl6 with ideal j = 1/2 moments.

Stable composite objects, such as hadrons, nuclei, atoms, molecules and superconducting pairs, formed by attractive forces are ubiquitous in nature. By contrast, composite objects stabilized by means of repulsive forces were long thought to be theoretical constructions owing to their fragility in naturally occurring systems. Surprisingly, the formation of bound atom pairs by strong repulsive interactions has been demonstrated experimentally in optical lattices1. Despite this success, repulsively bound particle pairs were believed to have no analogue in condensed matter owing to strong decay channels. Here we present spectroscopic signatures of repulsively bound three-magnon states and bound magnon pairs in the Ising-like chain antiferromagnet BaCo2V2O8. In large transverse fields, below the quantum critical point, we identify repulsively bound magnon states by comparing terahertz spectroscopy measurements to theoretical results for the Heisenberg-Ising chain antiferromagnet, a paradigmatic quantum many-body model2-5. Our experimental results show that these high-energy, repulsively bound magnon states are well separated from continua, exhibit notable dynamical responses and, despite dissipation, are sufficiently long-lived to be identified. As the transport properties in spin chains can be altered by magnon bound states, we envision that such states could serve as resources for magnonics-based quantum information processing technologies6-8.

Motivated by several claims of spin-orbit-driven spin-liquid physics in hexagonal Ba_{3}Ti_{3−x}Ir_{x}O_{9} hosting Ir_{2}O_{9} dimers, we report on resonant inelastic x-ray scattering (RIXS) at the Ir L_{3} edge for different x. We demonstrate that magnetism in Ba_{3}Ti_{3−x}Ir_{x}O_{9} is governed by an unconventional realization of strong disorder, where cation disorder affects the character of the local moments. RIXS interferometry, studying the RIXS intensity over a broad range of transferred momentum q, is ideally suited to assign different excitations to different Ir sites. We find pronounced Ir-Ti site mixing. Both ions are distributed over two crystallographically inequivalent sites, giving rise to a coexistence of quasimolecular singlet states on Ir_{2}O_{9} dimers and spin-orbit-entangled j=1/2 moments of 5d^{5}Ir^{4+} ions. RIXS reveals different kinds of strong magnetic couplings for different bonding geometries, highlighting the role of cation disorder for the suppression of long-range magnetic order in this family of compounds.

We investigate the electronic structure of LaCoO3 across the gradual spin-state and insulator-to-metal transitions using bulk-sensitive hard x-ray photoelectron and soft x-ray absorption spectroscopies. The spectra exhibit strong variations with temperature. The energy gap is reduced by about 0.6 eV in going from 80 to 650 K but the near Fermi level intensity remains small, classifying LaCoO3 as a bad metal even in the metallic phase. We are able to explain the spectra in terms of incoherent sums of low-spin and high-spin Co3+ spectra. We also find that the energy parameters for the two Co sites are very different, revealing that paramagnetic LaCoO3 is a highly inhomogeneous system with local lattice relaxations that are spin-state-specific. This, in turn, provides a natural explanation for the much-debated temperature dependence of the activation energy for the transitions.

We demonstrate that the cubic antifluorite-type halides K2OsCl6, K2OsBr6, and Rb2OsBr6 are excellent realizations of nonmagnetic J = 0 compounds. The magnetic susceptibility shows the corresponding Van Vleck type of behavior and no sign of defects. We investigate the electronic excitations with two complementary techniques, resonant inelastic x-ray scattering and optical spectroscopy. This powerful combination allows us to thoroughly study, e.g., on-site intra-t2g excitations and t2g-to-eg excitations as well as intersite excitations across the Mott gap and an exciton below the gap. In this way, we determine the electronic parameters with high accuracy, altogether yielding a comprehensive picture. In K2OsCl6, we find the spin-orbit coupling constant zeta = 0.34 eV, Hund's coupling JH = 0.43 eV, the onset of excitations across the Mott gap at A = 2.2 eV, the cubic crystal-field splitting 10Dq = 3.3 eV, and the charge-transfer energy ACT = 4.6 eV. With JH/zeta = 1.3, K2OsCl6 is in the intermediate-coupling regime. In a t2g-only Kanamori picture, the above values correspond to zeta eff = 0.41 eV and Jeff H = 0.28 eV, which is very close to results reported for related 5d4 iridates. In the tetragonal phase at 5 K, the noncubic crystal field causes a peak splitting of the J = 1 state as small as 4 meV. Compared to K2OsCl6, the bromides K2OsBr6 and Rb2OsBr6 show about 12-14% smaller values of 10Dq and ACT, while the spin-orbit entangled intra-t2g excitations below 2 eV and hence zeta and JH are reduced by less than 4%. Furthermore, the Mott gap in K2OsBr6 is reduced to about 1.8 eV.

We study the excitation spectrum of the one-dimensional spin -21 XXZ chain with antiferromagnetic Ising anisotropy across a magnetic quantum phase transition induced by the application of a site-dependent transverse magnetic field. Motivated by the chain antiferromagnet BaCo2V2O8, we consider a situation where the transverse magnetic field has a strong uniform component and a weaker staggered part. To determine the nature of the excitations giving rise to the spin dynamical structure factor, we use a combination of analytical approaches and the numerically exact time-dependent matrix product state method. We identify below the quantum phase transition high-energy many-body two-magnon and three-magnon repulsively bound states which are clearly visible due to the staggered component of the magnetic field. At high magnetic fields and low temperature, single magnons dominate the dynamics. Our theory results are in very good agreement with terahertz spectroscopy experimental results.

We study the excitation spectrum of the one-dimensional spin-1/2 XXZ chain with antiferromagnetic Ising anisotropy across a magnetic quantum phase transition induced by the application of a site-dependent transverse magnetic field. Motivated by the chain antiferromagnet BaCo_2V_2O_8, we consider a situation where the transverse magnetic field has a strong uniform component and a weaker staggered part. To determine the nature of the excitations giving rise to the spin dynamical structure factor, we use a combination of analytical approaches and the numerically exact time-dependent matrix product state method. We identify below the quantum phase transition high-energy many-body two-magnon and three-magnon repulsively bound states which are clearly visible due to the staggered component of the magnetic field. At high magnetic fields and low temperature, single magnons dominate the dynamics. Our theory results are in very good agreement with terahertz spectroscopy experimental results presented in [Wang et al., Nature 631, 760 (2024)].

We present a study of high-quality BaCo2(PO4)(2) single crystals via magnetization, heat-capacity, thermalexpansion, and magnetostriction measurements. Sharp anomalies in the thermodynamic properties at T-N = 3.4 K reveal a long-range antiferromagnetic order in these single-crystalline samples, which is absent in polycrystalline BaCo2(PO4)(2). The temperature dependent magnetic susceptibilities for in-plane and out-of-plane magnetic fields are strongly anisotropic and reveal a pronounced easy-plane anisotropy. A Curie-Weiss analysis implies strong orbital magnetism, as it is known from the sister compound BaCo2(AsO4)(2) that is discussed as a potential Kitaev spin-liquid material. When applying in-plane magnetic fields at low temperature, BaCo2(PO4)(2) is driven to another ordered phase at a critical field mu H-0(C1) approximate to 0.11 T and then undergoes a further field-induced transition to a highly polarized paramagnetic phase at mu H-0(C2) approximate to 0.3 T, which is again similar to the case of BaCo2(AsO4)(2). In addition, our lowest-temperature data reveal that the field-induced transitions in BaCo2(PO4)(2) become dominated by thermally assisted domain-wall motion.

We demonstrate that the cubic antifluorite-type halides K_2OsCl_6, K_2OsBr_6, and Rb_2OsBr_6 are excellent realizations of non-magnetic J=0 compounds. The magnetic susceptibility shows the corresponding Van-Vleck type behavior and no sign of defects. We investigate the electronic excitations with two complementary techniques, resonant inelastic x-ray scattering (RIXS) and optical spectroscopy. This powerful combination allows us to thoroughly study, e.g., on-site intra-t_2g excitations and t_2g-to-e_g excitations as well as inter-site excitations across the Mott gap and an exciton below the gap. In this way, we determine the electronic parameters with high accuracy, altogether yielding a comprehensive picture. In K_2OsCl_6, we find the spin-orbit coupling constant ζ=0.34 eV, Hund's coupling J_H=0.43 eV, the onset of excitations across the Mott gap at Δ=2.2 eV, the cubic crystal-field splitting 10Dq=3.3 eV, and the charge-transfer energy Δ_CT=4.6 eV. With J_H/ζ=1.3, K_2OsCl_6 is in the intermediate-coupling regime. In a t_2g-only Kanamori picture, the above values correspond to ζ^eff=0.41 eV and J_H^eff=0.28 eV, which is very close to results reported for related 5d^4 iridates. In the tetragonal phase at 5 K, the non-cubic crystal field causes a peak splitting of the J=1 state as small as 4 meV. Compared to K_2OsCl_6, the bromides K_2OsBr_6 and Rb_2OsBr_6 show about 12-14 while the spin-orbit-entangled intra-t_2g excitations below 2 eV and hence ζ and J_H are reduced by less than 4 K_2OsBr_6 is reduced to about 1.8 eV.

Crystals and glasses differ by the amplitude and the temperature dependence of their thermal conductivity. However, there are crystals known to display glass-like thermal conductivity. Here, we show that EuTiO$_3$, a quantum paraelectric known to order antiferromagnetically at 5.5 K, is one such system. The temperature dependence of resistivity and Seebeck coefficient yield an insulating band gap of $\sim 0.22$ eV. Thermal conductivity is drastically reduced. Its amplitude and temperature dependence are akin to what is seen in amorphous silica. Comparison with non-magnetic perovskite solids, SrTiO$_3$, KTaO$_3$, and EuCoO$_3$, shows that what impedes heat transport are $4f$ spins at Eu$^{2+}$ sites, which couple to phonons well above the ordering temperature. Thus, in this case, superexchange and valence fluctuations, not magnetic frustration, are the drivers of the glass-like thermal conductivity.