Magnetic excitations in the spin-1 anisotropic Heisenberg antiferromagnetic chain system NiCl(2)-4SC(NH(2))(2)

Haldane topological spin-1 chains in a planar metal-organic framework

Haldane topological materials contain unique antiferromagnetic chains with symmetry-protected energy gaps. Such materials have potential applications in spintronics and future quantum computers. Haldane topological solids typically consist of spin-1 chains embedded in extended three-dimensional (3D) crystal structures. Here, we demonstrate that [Ni(μ-4,4'-bipyridine)(μ-oxalate)]n (NiBO) instead adopts a two-dimensional (2D) metal-organic framework (MOF) structure of Ni2+ spin-1 chains weakly linked by 4,4'-bipyridine. NiBO exhibits Haldane topological properties with a gap between the singlet ground state and the triplet excited state. The latter is split by weak axial and rhombic anisotropies. Several experimental probes, including single-crystal X-ray diffraction, variable-temperature powder neutron diffraction (VT-PND), VT inelastic neutron scattering (VT-INS), DC susceptibility and specific heat measurements, high-field electron spin resonance, and unbiased quantum Monte Carlo simulations, provide a detailed, comprehensive characterization of NiBO. Vibrational (also known as phonon) properties of NiBO have been probed by INS and density-functional theory (DFT) calculations, indicating the absence of phonons near magnetic excitations in NiBO, suppressing spin-phonon coupling. The work here demonstrates that NiBO is indeed a rare 2D-MOF Haldane topological material.

All-electron APW+lo calculation of magnetic molecules with the SIRIUS domain-specific package

We report APW+lo (augmented plane wave plus local orbital) density functional theory (DFT) calculations of large molecular systems using the domain specific SIRIUS multi-functional DFT package. The APW and FLAPW (full potential linearized APW) task and data parallelism options and the advanced eigen-system solver provided by SIRIUS can be exploited for performance gains in ground state Kohn-Sham calculations on large systems. This approach is distinct from our prior use of SIRIUS as a library backend to another APW+lo or FLAPW code. We benchmark the code and demonstrate performance on several magnetic molecule and metal organic framework systems. We show that the SIRIUS package in itself is capable of handling systems as large as a several hundred atoms in the unit cell without having to make technical choices that result in the loss of accuracy with respect to that needed for the study of magnetic systems.

High-Angular Momentum Excitations in Collinear Antiferromagnet FePS3

We report on magneto-optical studies of the quasi-two-dimensional van der Waals antiferromagnet FePS₃. Our measurements reveal an excitation that closely resembles the antiferromagnetic resonance mode typical of easy-axis antiferromagnets; nevertheless, it displays an unusual, four-times larger Zeeman splitting in an applied magnetic field. We identify this excitation with an |S_z| = 4 multipolar magnon─a single-ion 4-magnon bound state─that corresponds to a full reversal of a single magnetic moment of the Fe²⁺ ion. We argue that condensation of multipolar magnons in large-spin materials with a strong magnetic anisotropy can produce new exotic states.

Quadrupolar magnetic excitations in an isotropic spin-1 antiferromagnet

The microscopic origins of emergent behaviours in condensed matter systems are encoded in their excitations. In ordinary magnetic materials, single spin-flips give rise to collective dipolar magnetic excitations called magnons. Likewise, multiple spin-flips can give rise to multipolar magnetic excitations in magnetic materials with spin S ≥ 1. Unfortunately, since most experimental probes are governed by dipolar selection rules, collective multipolar excitations have generally remained elusive. For instance, only dipolar magnetic excitations have been observed in isotropic S = 1 Haldane spin systems. Here, we unveil a hidden quadrupolar constituent of the spin dynamics in antiferromagnetic S = 1 Haldane chain material Y₂BaNiO₅ using Ni L₃-edge resonant inelastic x-ray scattering. Our results demonstrate that pure quadrupolar magnetic excitations can be probed without direct interactions with dipolar excitations or anisotropic perturbations. Originating from on-site double spin-flip processes, the quadrupolar magnetic excitations in Y₂BaNiO₅ show a remarkable dual nature of collective dispersion. While one component propagates as non-interacting entities, the other behaves as a bound quadrupolar magnetic wave. This result highlights the rich and largely unexplored physics of higher-order magnetic excitations.

Decay and renormalization of a longitudinal mode in a quasi-two-dimensional antiferromagnet

An ongoing challenge in the study of quantum materials, is to reveal and explain collective quantum effects in spin systems where interactions between different modes types are important. Here we approach this problem through a combined experimental and theoretical study of interacting transverse and longitudinal modes in an easy-plane quantum magnet near a continuous quantum phase transition. Our inelastic neutron scattering measurements of Ba₂FeSi₂O₇ reveal the emergence, decay, and renormalization of a longitudinal mode throughout the Brillouin zone. The decay of the longitudinal mode is particularly pronounced at the zone center. To account for the many-body effects of the interacting low-energy modes in anisotropic magnets, we generalize the standard spin-wave theory. The measured mode decay and renormalization is reproduced by including all one-loop corrections. The theoretical framework developed here is broadly applicable to quantum magnets with more than one type of low energy mode.

Anisotropic spin S >1/2 quantum magnets can have multiple low energy modes. In this manuscript, the authors study the interaction of such low energy modes in the S = 1 antiferromagnet Ba₂FeSi₂O₇ by combining neutron scattering measurements with an SU(3) generalization of the 1/S expansion.

Tomonaga-Luttinger Liquid Spin Dynamics in the Quasi-One-Dimensional Ising-Like Antiferromagnet BaCo_{2}V_{2}O_{8}

Combining inelastic neutron scattering and numerical simulations, we study the quasi-one-dimensional Ising anisotropic quantum antiferromagnet BaCo_{2}V_{2}O_{8} in a longitudinal magnetic field. This material shows a quantum phase transition from a Néel ordered phase at zero field to a longitudinal incommensurate spin density wave at a critical magnetic field of 3.8 T. Concomitantly, the excitation gap almost closes and a fundamental reconfiguration of the spin dynamics occurs. These experimental results are well described by the universal Tomonaga-Luttinger liquid theory developed for interacting spinless fermions in one dimension. We especially observe the rise of mainly longitudinal excitations, a hallmark of the unconventional low-field regime in Ising-like quantum antiferromagnetic chains.

Detection of a Disorder-Induced Bose-Einstein Condensate in a Quantum Spin Material at High Magnetic Fields

The coupled spin-1 chains material NiCl_{2}-4SC(NH_{2})_{2} (DTN) doped with Br impurities is expected to be a perfect candidate for observing many-body localization at high magnetic field: the so-called "Bose glass," a zero-temperature bosonic fluid, compressible, gapless, incoherent, and short-range correlated. Using nuclear magnetic resonance, we critically address the stability of the Bose glass in doped DTN, and find that it hosts a novel disorder-induced ordered state of matter, where many-body physics leads to an unexpected resurgence of quantum coherence emerging from localized impurity states. An experimental phase diagram of this new "order-from-disorder" phase, established from nuclear magnetic resonance T_{1}^{-1} relaxation rate data in the 13±1% Br-doped DTN, is found to be in excellent agreement with the theoretical prediction from large-scale quantum Monte Carlo simulations.

Auxiliary-Field Monte Carlo Method to Tackle Strong Interactions and Frustration in Lattice Bosons

We introduce a new numerical technique, the bosonic auxiliary-field Monte Carlo method, which allows us to calculate the thermal properties of large lattice-boson systems within a systematically improvable semiclassical approach, and which is virtually applicable to any bosonic model. Our method amounts to a decomposition of the lattice into clusters, and to an ansatz for the density matrix of the system in the form of a cluster-separable state-with nonentangled, yet classically correlated clusters. This approximation eliminates any sign problem, and can be systematically improved upon by using clusters of growing size. Extrapolation in the cluster size allows us to reproduce numerically exact results for the superfluid transition of hard-core bosons on the square lattice, and to provide a solid quantitative prediction for the superfluid and chiral transition of hardcore bosons on the frustrated triangular lattice.

Nuclear Magnetic Resonance Reveals Disordered Level-Crossing Physics in the Bose-Glass Regime of the Br-Doped Ni(Cl_{1-x}Br_{x})_{2}-4SC(NH_{2})_{2} Compound at a High Magnetic Field

By measuring the nuclear magnetic resonance (NMR) T_{1}^{-1} relaxation rate in the Br (bond) doped DTN compound, Ni(Cl_{1-x}Br_{x})_{2}-4SC(NH_{2})_{2}(DTNX), we show that the low-energy spin dynamics of its high magnetic field "Bose-glass" regime is dominated by a strong peak of spin fluctuations found at the nearly doping-independent position H^{*}≅13.6  T. From its temperature and field dependence, we conclude that this corresponds to a level crossing of the energy levels related to the doping-induced impurity states. Observation of the local NMR signal from the spin adjacent to the doped Br allowed us to fully characterize this impurity state. We have thus quantified a microscopic theoretical model that paves the way to better understanding of the Bose-glass physics in DTNX, as revealed in the related theoretical study [M. Dupont, S. Capponi, and N. Laflorencie, Phys. Rev. Lett. 118, 067204 (2017).PRLTAO0031-900710.1103/PhysRevLett.118.067204].

Frustrated magnets in high magnetic fields-selected examples

An indispensable parameter to study strongly correlated electron systems is the magnetic field. Application of high magnetic fields allows the investigation, modification and control of different states of matter. Specifically for magnetic materials experimental tools applied in such fields are essential for understanding their fundamental properties. Here, we focus on selected high-field studies of frustrated magnetic materials that have been shown to host a broad range of fascinating new and exotic phases. We will give brief insights into the influence of geometrical frustration on the critical behavior of triangular-lattice antiferromagnets, the accurate determination of exchange constants in the high-field saturated state by use of electron spin resonance measurements, and the coupling of magnetic degrees of freedom to the lattice evidenced by ultrasound experiments. The latter technique as well allowed new, partially metastable phases in strong magnetic fields to be revealed.

Antiferromagnetism in a Family of S = 1 Square Lattice Coordination Polymers NiX2(pyz)2 (X = Cl, Br, I, NCS; pyz = Pyrazine)

The crystal structures of NiX2(pyz)2 (X = Cl (1), Br (2), I (3), and NCS (4)) were determined by synchrotron X-ray powder diffraction. All four compounds consist of two-dimensional (2D) square arrays self-assembled from octahedral NiN4X2 units that are bridged by pyz ligands. The 2D layered motifs displayed by 1-4 are relevant to bifluoride-bridged [Ni(HF2)(pyz)2]EF6 (E = P, Sb), which also possess the same 2D layers. In contrast, terminal X ligands occupy axial positions in 1-4 and cause a staggered packing of adjacent layers. Long-range antiferromagnetic (AFM) order occurs below 1.5 (Cl), 1.9 (Br and NCS), and 2.5 K (I) as determined by heat capacity and muon-spin relaxation. The single-ion anisotropy and g factor of 2, 3, and 4 were measured by electron-spin resonance with no evidence for zero-field splitting (ZFS) being observed. The magnetism of 1-4 spans the spectrum from quasi-two-dimensional (2D) to three-dimensional (3D) antiferromagnetism. Nearly identical results and thermodynamic features were obtained for 2 and 4 as shown by pulsed-field magnetization, magnetic susceptibility, as well as their Néel temperatures. Magnetization curves for 2 and 4 calculated by quantum Monte Carlo simulation also show excellent agreement with the pulsed-field data. Compound 3 is characterized as a 3D AFM with the interlayer interaction (J⊥) being slightly stronger than the intralayer interaction along Ni-pyz-Ni segments (J(pyz)) within the two-dimensional [Ni(pyz)2](2+) square planes. Regardless of X, J(pyz) is similar for the four compounds and is roughly 1 K.

Direct determination of exchange parameters in Cs2CuBr4 and Cs2CuCl4: high-field electron-spin-resonance studies

Spin-1/2 Heisenberg antiferromagnets Cs2CuCl4 and Cs2CuBr4 with distorted triangular-lattice structures are studied by means of electron spin resonance spectroscopy in magnetic fields up to the saturation field and above. In the magnetically saturated phase, quantum fluctuations are fully suppressed, and the spin dynamics is defined by ordinary magnons. This allows us to accurately describe the magnetic excitation spectra in both materials and, using the harmonic spin-wave theory, to determine their exchange parameters. The viability of the proposed method was proven by applying it to Cs2CuCl4, yielding J/kB=4.7(2)  K, J'/kB=1.42(7)  K, [J'/J≃0.30] and revealing good agreement with inelastic neutron-scattering results. For the isostructural Cs2CuBr4, we obtain J/kB=14.9(7)  K, J'/kB=6.1(3)  K, [J'/J≃0.41], providing exact and conclusive information on the exchange couplings in this frustrated spin system.

Novel magnetism of Ir5+(5d4) Ions in the double perovskite Sr2YIrO6

We synthesize and study single crystals of a new double-perovskite Sr2YIrO6. Despite two strongly unfavorable conditions for magnetic order, namely, pentavalent Ir5+(5d4) ions which are anticipated to have Jeff=0 singlet ground states in the strong spin-orbit coupling (SOC) limit and geometric frustration in a face-centered cubic structure formed by the Ir5+ ions, we observe this iridate to undergo a novel magnetic transition at temperatures below 1.3 K. We provide compelling experimental and theoretical evidence that the origin of magnetism is in an unusual interplay between strong noncubic crystal fields, local exchange interactions, and "intermediate-strength" SOC. Sr2YIrO6 provides a rare example of the failed dominance of SOC in the iridates.

Neutron study of the magnetism in NiCl2·4SC(NH2)2

We study the strongly anisotropic quasi-one-dimensional S = 1 quantum magnet NiCl2·4SC(NH2)2 using elastic and inelastic neutron scattering. We demonstrate that a magnetic field splits the excited doublet state and drives the lower doublet state to zero energy at a critical field Hc1. For Hc1 < H < Hc2, where Hc2 indicates the transition to a fully magnetized state, three-dimensional magnetic order is established with the AF moment perpendicular to the magnetic field. We mapped the temperature/magnetic field phase diagram, and we find that the total ordered magnetic moment reaches m(tot) = 2.1 μB at the field μ(0)H = 6 T and is thus close to the saturation value of the fully ordered moment. We study the magnetic spin dynamics in the fully magnetized state for H > Hc2, and we demonstrate the presence of an AF interaction between Ni(2+) on the two interpenetrating sublattices. In the antiferromagnetically ordered phase, the spin-waves that develop from the lower-energy doublet are split into two modes. This is most likely the result of the presence of the AF interaction between the interpenetrating lattices.

Quantum-critical spin dynamics in quasi-one-dimensional antiferromagnets

By means of nuclear spin-lattice relaxation rate T(1)(-1), we follow the spin dynamics as a function of the applied magnetic field in two gapped quasi-one-dimensional quantum antiferromagnets: the anisotropic spin-chain system NiCl(2)-4SC(NH(2))(2) and the spin-ladder system (C(5)H(12)N)(2)CuBr(4). In both systems, spin excitations are confirmed to evolve from magnons in the gapped state to spinons in the gapless Tomonaga-Luttinger-liquid state. In between, T(1)(-1) exhibits a pronounced, continuous variation, which is shown to scale in accordance with quantum criticality. We extract the critical exponent for T(1)(-1), compare it to the theory, and show that this behavior is identical in both studied systems, thus demonstrating the universality of quantum-critical behavior.

Antiferromagnet with two coupled antiferromagnetic sublattices in a magnetic field

We discuss the magnon spectrum of an antiferromagnet (AF) in a magnetic field h consisting of two interpenetrating AF sublattices coupled by the exchange interaction at T = 0. One-ion easy-plane anisotropy is also taken into account. We calculate using the 1/S expansion the gap in the spectrum which is a manifestation of the order-by-disorder effect in this system and the optical magnon mode splitting. Both of these phenomena originate from the inter-sublattice interaction. We also calculate the gap value at h≈h(c) in the leading order of the small parameter (h(c) - h)/h(c) using the magnon Bose-Einstein condensation treatment, where h(c) is the saturation field. By comparing results obtained within these two approaches we conclude that the 1/S expansion gives a qualitatively correct result at h ~ h(c) even at large one-ion anisotropy but it overestimates the gap value. The application is discussed of these results to the actively studied AF of the considered type NiCl₂-4SC(NH₂)₂(DTN).

Thermal transport and strong mass renormalization in NiCl2-4SC(NH2)2

Several quantum paramagnets exhibit magnetic-field-induced quantum phase transitions to an antiferromagnetic state that exists for H c1 ≤ H ≤ H c2. For some of these compounds, there is a significant asymmetry between the low- and high-field transitions. We present specific heat and thermal conductivity measurements in NiCl2-4SC(NH2)2, together with calculations which show that the asymmetry is caused by a strong mass renormalization due to quantum fluctuations for H ≤ H c1 that are absent for H ≥ H c2. We argue that the enigmatic lack of asymmetry in thermal conductivity is due to a concomitant renormalization of the impurity scattering.

Terahertz-range free-electron laser electron spin resonance spectroscopy: techniques and applications in high magnetic fields

The successful use of picosecond-pulse free-electron-laser (FEL) radiation for the continuous-wave terahertz-range electron spin resonance (ESR) spectroscopy has been demonstrated. The combination of two linac-based FELs (covering the wavelength range of 4-250 microm) with pulsed magnetic fields up to 70 T allows for multifrequency ESR spectroscopy in a frequency range of 1.2-75 THz with a spectral resolution better than 1%. The performance of the spectrometer is illustrated with ESR spectra obtained in the 2,2-diphenyl-1-picrylhydrazyl and the low-dimensional organic material (C6H9N2)CuCl3.

Low-temperature heat transport in the low-dimensional quantum magnet NiCl2-4SC(NH2)2

We report a study of the low-temperature thermal conductivity of NiCl2-4SC(NH2)_{2}, which is a spin-1 chain system exhibiting the magnon Bose-Einstein condensation (BEC) in a magnetic field. It is found that the low-T thermal conductivity along the spin-chain direction shows strong anomalies at the lower and upper critical fields of the magnon BEC state. In this state, magnons act mainly as phonon scatterers at relatively high temperature, but change their role to heat carriers upon temperature approaching zero. The result demonstrates a large thermal conductivity in the magnon BEC state and points to a direct analog between the magnon BEC and the conventional one.

Critical properties at the field-induced Bose-Einstein condensation in NiCl(2)-4SC(NH2)2

We report new magnetization measurements on the spin-gap compound NiCl(2)-4SC(NH2)2 at the low-field boundary of the magnetic field-induced ordering. The critical density of the magnetization is analyzed in terms of a Bose-Einstein condensation of bosonic quasiparticles. The analysis of the magnetization at the transition leads to the conclusion for the preservation of the U(1) symmetry, as required for Bose-Einstein condensation. The experimental data are well described by quantum Monte Carlo simulations.

Direct measurement of the Bose-Einstein condensation universality class in NiCl2-4SC(NH2)2 at ultralow temperatures

In this work, we demonstrate field-induced Bose-Einstein condensation (BEC) in the organic compound NiCl2-4SC(NH2)_{2} using ac susceptibility measurements down to 1 mK. The Ni S=1 spins exhibit 3D XY antiferromagnetism between a lower critical field H_{c1} approximately 2 T and a upper critical field H_{c2} approximately 12 T. The results show a power-law temperature dependence of the phase transition line H_{c1}(T)-H_{c1}(0)=aT;{alpha} with alpha=1.47+/-0.10 and H_{c1}(0)=2.053 T, consistent with the 3D BEC universality class. Near H_{c2}, a kink was found in the phase boundary at approximately 150 mK.

Unusual magneto-optical phenomenon reveals low energy spin dispersion in the spin-1 anisotropic Heisenberg antiferromagnetic chain system NiCl2-4SC(NH2)_{2}

Electron paramagnetic resonance measurements of NiCl2-4SC(NH2)_{2} reveal the low-energy spin dispersion, including a magnetic-field interval in which the two-magnon continuum is within k_{B}T of the ground state, allowing a continuum of excitations over a range of k states, rather than only the k=0 single-magnon excitations. This produces a novel Y shape in the frequency-field EPR spectrum measured at T > or = 1.5 K. Since the interchain coupling J_{ perpendicular}<<k_{B}T, this shape can be reproduced by a single S=1 antiferromagnetic Heisenberg chain with a strong easy-plane single-ion anisotropy. Importantly, the combination of experiment and modeling we report herein demonstrates a powerful approach to probing spin dispersion in a wide range of interacting magnetic systems without the stringent sample requirements and complications associated with inelastic scattering experiments.

Diverging thermal expansion of the spin-ladder system (C5H12N)2CuBr4

We present high-resolution measurements of the c(*)-axis thermal expansion and magnetostriction of piperidinium copper bromide (C5H12N)2CuBr4. The experimental data at low temperatures are well accounted for by a two-leg spin-ladder Hamiltonian. The thermal expansion shows a complex behavior with various sign changes and approaches a 1/square root T divergence at the critical fields. All low-temperature features are semiquantitatively explained within a free-fermion model; full quantitative agreement is obtained with quantum Monte Carlo simulations.