Resonance from antiferromagnetic spin fluctuations for superconductivity in UTe2.

Superconductivity originates from the formation of bound (Cooper) pairs of electrons that can move through the lattice without resistance below the superconducting transition temperature Tc (ref. 1). Electron Cooper pairs in most superconductors form anti-parallel spin singlets with total spin S = 0 (ref. 2), although they can also form parallel spin-triplet Cooper pairs with S = 1 and an odd parity wavefunction3. Spin-triplet pairing is important because it can host topological states and Majorana fermions relevant for quantum computation4,5. Because spin-triplet pairing is usually mediated by ferromagnetic (FM) spin fluctuations3, uranium-based materials near an FM instability are considered to be ideal candidates for realizing spin-triplet superconductivity6. Indeed, UTe2, which has a Tc ≈ 1.6 K (refs. 7,8), has been identified as a candidate for a chiral spin-triplet topological superconductor near an FM instability7-14, although it also has antiferromagnetic (AF) spin fluctuations15,16. Here we use inelastic neutron scattering (INS) to show that superconductivity in UTe2 is coupled to a sharp magnetic excitation, termed resonance17-23, at the Brillouin zone boundary near AF order. Because the resonance has only been found in spin-singlet unconventional superconductors near an AF instability17-23, its observation in UTe2 suggests that AF spin fluctuations may also induce spin-triplet pairing24 or that electron pairing in UTe2 has a spin-singlet component.

Neutron Instruments for Research in Coordination Chemistry.

Neutron diffraction and spectroscopy offer unique insight into structures and properties of solids and molecular materials. All neutron instruments located at the various neutron sources are distinct, even if their designs are based on similar principles, and thus, they are usually less familiar to the community than commercial X-ray diffractometers and optical spectrometers. Major neutron instruments in the USA, which are open to scientists around the world, and examples of their use in coordination chemistry research are presented here, along with a list of similar instruments at main neutron facilities in other countries. The reader may easily and quickly find from this minireview an appropriate neutron instrument for research. The instruments include single-crystal and powder diffractometers to determine structures, inelastic neutron scattering (INS) spectrometers to probe magnetic and vibrational excitations, and quasielastic neutron scattering (QENS) spectrometers to study molecular dynamics such as methyl rotation on ligands. Key and unique features of the diffraction and neutron spectroscopy that are relevant to inorganic chemistry are reviewed.

Continuous Spin Excitations in the Three-Dimensional Frustrated Magnet K_{2}Ni_{2}(SO_{4})_{3}.

Continuous spin excitations are widely recognized as one of the hallmarks of novel spin states in quantum magnets, such as quantum spin liquids (QSLs). Here, we report the observation of such kind of excitations in K_{2}Ni_{2}(SO_{4})_{3}, which consists of two sets of intersected spin-1 (Ni^{2+}) trillium lattices. Our inelastic neutron scattering measurement on single crystals clearly shows a dominant excitation continuum, which exhibits a distinct temperature-dependent behavior from that of spin waves, and is rooted in strong quantum spin fluctuations. Further using the self-consistent-Gaussian-approximation method, we determine that the fourth- and fifth-nearest-neighbor exchange interactions are dominant. These two bonds together form a unique three-dimensional network of corner-sharing tetrahedra, which we name as a "hypertrillium" lattice. Our results provide direct evidence for the existence of QSL features in K_{2}Ni_{2}(SO_{4})_{3} and highlight the potential for the hypertrillium lattice to host frustrated quantum magnetism.

Freezing of a Disorder Induced Spin Liquid with Strong Quantum Fluctuations.

Sr_{2}CuTe_{0.5}W_{0.5}O_{6} is a square-lattice magnet with superexchange between S=1/2Cu^{2+} spins mediated by randomly distributed Te and W ions. Here, using sub-K temperature and 20 µeV energy resolution neutron scattering experiments we show that this system transits from a gapless disorder-induced spin liquid to a new quantum state below T_{f}=1.7(1) K, exhibiting a weak frozen moment of ⟨S⟩/S∼0.1 and low energy dynamic susceptibility, χ^{''}(ℏω), linear in energy which is surprising for such a weak freezing in this highly fluctuating quantum regime.

Incommensurate Spin Fluctuations in the Spin-Triplet Superconductor Candidate UTe_{2}.

Spin-triplet superconductors are of extensive current interest because they can host topological state and Majorana fermions important for quantum computation. The uranium-based heavy-fermion superconductor UTe_{2} has been argued as a spin-triplet superconductor similar to UGe_{2}, URhGe, and UCoGe, where the superconducting phase is near (or coexists with) a ferromagnetic (FM) instability and spin-triplet electron pairing is driven by FM spin fluctuations. Here we use neutron scattering to show that, although UTe_{2} exhibits no static magnetic order down to 0.3 K, its magnetism in the [0,K,L] plane is dominated by incommensurate spin fluctuations near an antiferromagnetic ordering wave vector and extends to at least 2.6 meV. We are able to understand the dominant incommensurate spin fluctuations of UTe_{2} in terms of its electronic structure calculated using a combined density-functional and dynamic mean-field theory.

Spectroscopic Studies of the Magnetic Excitation and Spin-Phonon Couplings in a Single-Molecule Magnet.

Large separations between ground and excited magnetic states in single-molecule magnets (SMMs) are desirable to reduce the likelihood of spin reversal in the molecules. Spin-phonon coupling is a process leading to magnetic relaxation. Both the reversal and coupling, making SMMs lose magnetic moments, are undesirable. However, direct determination of large magnetic states separations (>45 cm-1 ) is challenging, and few detailed investigations of the spin-phonon coupling have been conducted. The magnetic separation in [Co(12-crown-4)2 ](I3 )2 (12-crown-4) (1) is determined and its spin-phonon coupling is probed by inelastic neutron scattering (INS) and far-IR spectroscopy. INS, using oriented single crystals, shows a magnetic transition at 49.4(1.0) cm-1 . Far-IR reveals that the magnetic transition and nearby phonons are coupled, a rarely observed phenomenon, with spin-phonon coupling constants of 1.7-2.5 cm-1 . The current work spectroscopically determines the ground-excited magnetic states separation in an SMM and quantifies its spin-phonon coupling, shedding light on the process causing magnetic relaxation.

Quantum Tunneling of Water in Beryl: A New State of the Water Molecule.

Using neutron scattering and ab initio simulations, we document the discovery of a new "quantum tunneling state" of the water molecule confined in 5 Å channels in the mineral beryl, characterized by extended proton and electron delocalization. We observed a number of peaks in the inelastic neutron scattering spectra that were uniquely assigned to water quantum tunneling. In addition, the water proton momentum distribution was measured with deep inelastic neutron scattering, which directly revealed coherent delocalization of the protons in the ground state.

Slow Magnetic Relaxations in Cobalt(II) Tetranitrate Complexes. Studies of Magnetic Anisotropy by Inelastic Neutron Scattering and High-Frequency and High-Field EPR Spectroscopy.

Three mononuclear cobalt(II) tetranitrate complexes (A)2[Co(NO3)4] with different countercations, Ph4P+ (1), MePh3P+ (2), and Ph4As+ (3), have been synthesized and studied by X-ray single-crystal diffraction, magnetic measurements, inelastic neutron scattering (INS), high-frequency and high-field EPR (HF-EPR) spectroscopy, and theoretical calculations. The X-ray diffraction studies reveal that the structure of the tetranitrate cobalt anion varies with the countercation. 1 and 2 exhibit highly irregular seven-coordinate geometries, while the central Co(II) ion of 3 is in a distorted-dodecahedral configuration. The sole magnetic transition observed in the INS spectroscopy of 1-3 corresponds to the zero-field splitting (2(D2 + 3E2)1/2) from 22.5(2) cm-1 in 1 to 26.6(3) cm-1 in 2 and 11.1(5) cm-1 in 3. The positive sign of the D value, and hence the easy-plane magnetic anisotropy, was demonstrated for 1 by INS studies under magnetic fields and HF-EPR spectroscopy. The combined analyses of INS and HF-EPR data yield the D values as +10.90(3), +12.74(3), and +4.50(3) cm-1 for 1-3, respectively. Frequency- and temperature-dependent alternating-current magnetic susceptibility measurements reveal the slow magnetization relaxation in 1 and 2 at an applied dc field of 600 Oe, which is a characteristic of field-induced single-molecule magnets (SMMs). The electronic structures and the origin of magnetic anisotropy of 1-3 were revealed by calculations at the CASPT2/NEVPT2 level.

Pressure Effect on the Boson Peak in Deeply Cooled Confined Water: Evidence of a Liquid-Liquid Transition.

The boson peak in deeply cooled water confined in nanopores is studied to examine the liquid-liquid transition (LLT). Below ∼180 K, the boson peaks at pressures P higher than ∼3.5 kbar are evidently distinct from those at low pressures by higher mean frequencies and lower heights. Moreover, the higher-P boson peaks can be rescaled to a master curve while the lower-P boson peaks can be rescaled to a different one. These phenomena agree with the existence of two liquid phases with different densities and local structures and the associated LLT in the measured (P, T) region. In addition, the P dependence of the librational band also agrees with the above conclusion.

Magnetic Transitions in Iron Porphyrin Halides by Inelastic Neutron Scattering and Ab Initio Studies of Zero-Field Splittings.

Zero-field splitting (ZFS) parameters of nondeuterated metalloporphyrins [Fe(TPP)X] (X = F, Br, I; H2TPP = tetraphenylporphyrin) have been directly determined by inelastic neutron scattering (INS). The ZFS values are D = 4.49(9) cm⁻¹ for tetragonal polycrystalline [Fe(TPP)F], and D = 8.8(2) cm⁻¹, E = 0.1(2) cm⁻¹ and D = 13.4(6) cm⁻¹, E = 0.3(6) cm⁻¹ for monoclinic polycrystalline [Fe(TPP)Br] and [Fe(TPP)I], respectively. Along with our recent report of the ZFS value of D = 6.33(8) cm⁻¹ for tetragonal polycrystalline [Fe(TPP)Cl], these data provide a rare, complete determination of ZFS parameters in a metalloporphyrin halide series. The electronic structure of [Fe(TPP)X] (X = F, Cl, Br, I) has been studied by multireference ab initio methods: the complete active space self-consistent field (CASSCF) and the N-electron valence perturbation theory (NEVPT2) with the aim of exploring the origin of the large and positive zero-field splitting D of the 6A1 ground state. D was calculated from wave functions of the electronic multiplets spanned by the d5 configuration of Fe(III) along with spin­orbit coupling accounted for by quasi degenerate perturbation theory. Results reproduce trends of D from inelastic neutron scattering data increasing in the order from F, Cl, Br, to I. A mapping of energy eigenvalues and eigenfunctions of the S = 3/2 excited states on ligand field theory was used to characterize the σ- and π-antibonding effects decreasing from F to I. This is in agreement with similar results deduced from ab initio calculations on CrX6³â» complexes and also with the spectrochemical series showing a decrease of the ligand field in the same directions. A correlation is found between the increase of D and decrease of the π- and σ-antibonding energies e(λ)(X) (λ = σ, π) in the series from X = F to I. Analysis of this correlation using second-order perturbation theory expressions in terms of angular overlap parameters rationalizes the experimentally deduced trend. D parameters from CASSCF and NEVPT2 results have been calibrated against those from the INS data, yielding a predictive power of these approaches. Methods to improve the quantitative agreement between ab initio calculated and experimental D and spectroscopic transitions for high-spin Fe(III) complexes are proposed.

Boson peak in deeply cooled confined water: a possible way to explore the existence of the liquid-to-liquid transition in water.

The boson peak in deeply cooled water confined in nanopores is studied with inelastic neutron scattering. We show that in the (P, T) plane, the locus of the emergence of the boson peak is nearly parallel to the Widom line below ∼ 1600 bar. Above 1600 bar, the situation is different and from this difference the end pressure of the Widom line is estimated. The frequency and width of the boson peak correlate with the density of water, which suggests a method to distinguish the hypothetical "low-density liquid" and "high-density liquid" phases in deeply cooled water.

Magnetic excitations in metalloporphyrins by inelastic neutron scattering: determination of zero-field splittings in iron, manganese, and chromium complexes.

Zero field splitting (ZFS) parameters of several nondeuterated metalloporphyrins [M(TPP)Cl] and [Mn(TPP)] (H2TPP = tetraphenylporphyrin) have been directly determined by inelastic neutron scattering (INS). The ZFS values are the following: D = 6.33(8) cm(-1) for [Fe(TPP)Cl], -2.24(3) cm(-1) for [Mn(TPP)Cl], 0.79(2) cm(-1) for [Mn(TPP)], and |D|= 0.234(12) cm(-1) for [Cr(TPP)Cl]. The work shows that compounds with magnetic excitations below ∼30 cm(-1) could be determined using nondeuterated samples.

Kinetically inhibited order in a diamond-lattice antiferromagnet.

Frustrated magnetic systems exhibit highly degenerate ground states and strong fluctuations, often leading to new physics. An intriguing example of current interest is the antiferromagnet on a diamond lattice, realized physically in A-site spinel materials. This is a prototypical system in three dimensions where frustration arises from competing interactions rather than purely geometric constraints, and theory suggests the possibility of unusual magnetic order at low temperature. Here, we present a comprehensive single-crystal neutron scattering study of CoAl(2)O(4), a highly frustrated A-site spinel. We observe strong diffuse scattering that peaks at wavevectors associated with Néel ordering. Below the temperature T(∗) = 6.5 K, there is a dramatic change in the elastic scattering lineshape accompanied by the emergence of well-defined spin-wave excitations. T(∗) had previously been associated with the onset of glassy behavior. Our new results suggest instead that T(∗) signifies a first-order phase transition, but with true long-range order inhibited by the kinetic freezing of domain walls. This scenario might be expected to occur widely in frustrated systems containing first-order phase transitions and is a natural explanation for existing reports of anomalous glassy behavior in other materials.

Probing spin waves in Co3O4 nanoparticles for magnonics applications.

The magnetic properties of spinel nanoparticles can be controlled by synthesizing particles of a specific shape and size. The synthesized nanorods, nanodots and cubic nanoparticles have different crystal planes selectively exposed on the surface. The surface effects on the static magnetic properties are well documented, while their influence on spin waves dispersion is still being debated. Our ability to manipulate spin waves using surface and defect engineering in magnetic nanoparticles is the key to designing magnonic devices. We synthesized cubic and spherical nanoparticles of a classical antiferromagnetic material Co3O4 to study the shape and size effects on their static and dynamic magnetic proprieties. Using a combination of experimental methods, we probed the magnetic and crystal structures of our samples and directly measured spin wave dispersions using inelastic neutron scattering. We found a weak, but unquestionable, increase in exchange interactions for the cubic nanoparticles as compared to spherical nanoparticle and bulk powder reference samples. Interestingly, the exchange interactions in spherical nanoparticles have bulk-like properties, despite a ferromagnetic contribution from canted surface spins.

Diffusive excitonic bands from frustrated triangular sublattice in a singlet-ground-state system.

Magnetic order in most materials occurs when magnetic ions with finite moments arrange in a particular pattern below the ordering temperature. Intriguingly, if the crystal electric field (CEF) effect results in a spin-singlet ground state, a magnetic order can still occur due to the exchange interactions between neighboring ions admixing the excited CEF levels. The magnetic excitations in such a state are spin excitons generally dispersionless in reciprocal space. Here we use neutron scattering to study stoichiometric Ni2Mo3O8, where Ni2+ ions form a bipartite honeycomb lattice comprised of two triangular lattices, with ions subject to the tetrahedral and octahedral crystalline environment, respectively. We find that in both types of ions, the CEF excitations have nonmagnetic singlet ground states, yet the material has magnetic order. Furthermore, CEF spin excitons from the tetrahedral sites form a dispersive diffusive pattern around the Brillouin zone boundary, likely due to spin entanglement and geometric frustrations.

Evidence for pressure induced unconventional quantum criticality in the coupled spin ladder antiferromagnet C9H18N2CuBr4.

Quantum phase transitions in quantum matter occur at zero temperature between distinct ground states by tuning a nonthermal control parameter. Often, they can be accurately described within the Landau theory of phase transitions, similarly to conventional thermal phase transitions. However, this picture can break down under certain circumstances. Here, we present a comprehensive study of the effect of hydrostatic pressure on the magnetic structure and spin dynamics of the spin-1/2 ladder compound C9H18N2CuBr4. Single-crystal heat capacity and neutron diffraction measurements reveal that the Néel-ordered phase breaks down beyond a critical pressure of Pc ∼ 1.0 GPa through a continuous quantum phase transition. Estimates of the critical exponents suggest that this transition may fall outside the traditional Landau paradigm. The inelastic neutron scattering spectra at 1.3 GPa are characterized by two well-separated gapped modes, including one continuum-like and another resolution-limited excitation in distinct scattering channels, which further indicates an exotic quantum-disordered phase above Pc.

Effect of Hydration on the Molecular Dynamics of Hydroxychloroquine Sulfate.

Chloroquine and its derivative hydroxychloroquine are primarily known as antimalaria drugs. Here, we investigate the influence of hydration water on the molecular dynamics in hydroxychloroquine sulfate, a commonly used solubilized drug form. When hydration, even at a low level, results in a disordered structure, as opposed to the highly ordered structure of dry hydroxychloroquine sulfate, the activation barriers for the rotation of methyl groups in the drug molecules become randomized and, on average, significantly reduced. The facilitated stochastic motions of the methyl groups may benefit the biomolecular activity due to the more efficient sampling of the energy landscape in the disordered hydration environment experienced by the drug molecules in vivo.

Strong anisotropic dynamics of ultra-confined water.

Dynamics of water confined in ∼5 Å diameter channels of beryl and cordierite single crystals were studied by using inelastic (INS) and quasielastic (QENS) neutron scattering. The INS spectra for both samples were similar and showed that there are no hydrogen bonds acting on water molecule, which experiences strong anisotropic potential, steep along the channels and very soft perpendicular to it. The high-resolution (3.4 µeV) QENS data revealed gradual freezing out of the water molecule dynamics for both minerals at temperatures below about 80 K when the scattering momentum transfer was parallel to the channels, but not when it was perpendicular to the channels. The QENS study with medium energy resolution (0.25 meV) of the beryl with the scattering momentum transfer along the channels showed gradual freezing out of water molecule dynamics at temperatures below about 200 K, whereas at higher temperatures the data could be described as 2-fold rotational jumps about the axis coinciding with the direction of the dipole moment (that is, perpendicular to the channels), with a residence time of 5.5 ps at 225 K. The energy resolution dependence of the apparent dynamics freezing temperature suggests gradual slowing down of the rotational jumps as the temperature is decreased, until the associated QENS broadening can no longer be detected, rather than actual freezing.

Dipolar antiferromagnetism and quantum criticality in LiErF4.

Magnetism has been predicted to occur in systems in which dipolar interactions dominate exchange. We present neutron scattering, specific heat, and magnetic susceptibility data for LiErF(4), establishing it as a model dipolar-coupled antiferromagnet with planar spin-anisotropy and a quantum phase transition in applied field H(c|| = 4.0 ± 0.1 kilo-oersteds. We discovered non-mean-field critical scaling for the classical phase transition at the antiferromagnetic transition temperature that is consistent with the two-dimensional XY/h(4) universality class; in accord with this, the quantum phase transition at H(c) exhibits three-dimensional classical behavior. The effective dimensional reduction may be a consequence of the intrinsic frustrated nature of the dipolar interaction, which strengthens the role of fluctuations.