Inelastic Neutron Scattering Measurement of the Ground State Tunneling Gap in Tb and Ho Analogues of a Dy Field-Induced Single-Molecule Magnet.

Recent advances in single-molecule magnet (SMM) research have placed great value on interpretation of inelastic neutron scattering (INS) data for rare earth (RE)-containing SMMs. Here, we present the synthesis of several rare earth complexes where combined magnetic and INS studies have been performed, supported by ab initio calculations. The reaction of rare earth nitrate salts with 2,2'-bipyridine (2,2'-bpy) and tetrahalocatecholate (X4Cat2-, X = Br, Cl) ligands in methanol (MeOH) afforded two new families of compounds [RE(2,2'-bpy)2(X4Cat)(X4CatH)(MeOH)] (X = Br and RE = Y, Eu, Gd, Tb, Dy, Ho, Yb for 1-RE; X = Cl and RE = Y, Tb, Dy, Ho, and Yb for 2-RE). Addition of triethylamine (Et3N) to the reaction mixture delivered Et3NH[RE(2,2'-bpy)2(Br4Cat)2] (3-RE, RE = Er and Yb). Interestingly, cerium behaves differently to the rest of the series, generating (2,2'-bpyH)2[Ce(Br4Cat)3(2,2'-bpy)] (4-Ce) with tetravalent Ce(IV) in contrast to the trivalent metal ions in 1-3. The static magnetic properties of 1-RE (RE = Gd, Tb, Dy and Ho) were investigated in conjunction with INS measurements on 1-Y, 1-Tb, and 1-Ho to probe their ground state properties and any crystal field excitations. To facilitate interpretation of the INS spectra and provide insight into the magnetic behavior, ab initio calculations were performed using the single-crystal X-ray diffraction structural data of 1-RE (RE = Tb, Dy and Ho). The ab initio calculations indicate ground doublets dominated by the maximal angular momentum projection states of Kramers type for 1-Dy and Ising type for 1-Tb and 1-Ho. Dynamic magnetic susceptibility measurements indicate that 1-Dy exhibits slow magnetic relaxation in the presence of a small applied magnetic field mainly through Raman pathways. Inelastic neutron scattering spectra exhibit distinct transitions corresponding to crystal field-induced tunneling gaps between the pseudo-doublet ground state components for 1-Tb and 1-Ho, which is one of the first direct experimental measurements with INS of such tunneling transitions in a molecular nanomagnet. The power of high-resolution INS is demonstrated with evidence of two distinct tunneling gaps measurable for the two crystallographically unique Tb coordination environments observed in the single crystal X-ray structure.

Side Chain Dynamics of Poly(norbornene)-g-Poly(propylene oxide) Bottlebrush Polymers.

The segmental dynamics of the side chains of poly(norbornene)-g-poly(propylene oxide) (PNB-g-PPO) bottlebrush polymer in comparison to PPO is studied by quasi-elastic neutron scattering. Having experimental time and length scale information simultaneously allows to extract spatial information in addition to relaxation time. Tethering one end of the PPO side chain onto a stiff PNB backbone slows down the segmental relaxation, over the length and time scales investigated. The power law dependence of the relaxation time on the momentum transfer, Q, indicates a more heterogeneous relaxation pattern for the bottlebrush polymer, whereas the linear PPO has less deviations from a homogenous relaxation. Similar conclusions can be drawn from the time dependent mean square displacement, 〈r2 (t)〉, and the non-Gaussian parameter, α2 (t). Herein, the bottlebrush polymer shows a more restricted dynamics, whereas the linear PPO reaches 〈r2 (t)〉∝t0.5 at the highest temperature. The deviations from Gaussian behavior are evident at the α2 (t). Both samples show a decaying α2 (t). The non-Gaussian parameter supports the results from the power law dependence of the relaxation times, with lower α2 (t) values for PPO compared to those for PNB-g-PPO, pointing to less deviations from Gaussian behavior.

Anomalous Structural Evolution and Glassy Lattice in Mixed-Halide Hybrid Perovskites.

Hybrid halide perovskites have emerged as highly promising photovoltaic materials because of their exceptional optoelectronic properties, which are often optimized via compositional engineering like mixing halides. It is well established that hybrid perovskites undergo a series of structural phase transitions as temperature varies. In this work, the authors find that phase transitions are substantially suppressed in mixed-halide hybrid perovskite single crystals of MAPbI3-x Brx (MA = CH3 NH3 + and x = 1 or 2) using a complementary suite of diffraction and spectroscopic techniques. Furthermore, as a general behavior, multiple crystallographic phases coexist in mixed-halide perovskites over a wide temperature range, and a slightly distorted monoclinic phase, hitherto unreported for hybrid perovskites, is dominant at temperatures above 100 K. The anomalous structural evolution is correlated with the glassy behavior of organic cations and optical phonons in mixed-halide perovskites. This work demonstrates the complex interplay between composition engineering and lattice dynamics in hybrid perovskites, shedding new light on their unique properties.

Universality of Time-Temperature Scaling Observed by Neutron Spectroscopy on Bottlebrush Polymers.

The understanding of materials requires access to the dynamics over many orders of magnitude in time; however, single analytical techniques are restricted in their respective time ranges. Assuming a functional relationship between time and temperature is one viable tool to overcome these limits. Despite its frequent usage, a breakdown of this assertion at the glass-transition temperature is common. Here, we take advantage of time- and length-scale information in neutron spectroscopy to show that the separation of different processes is the minimum requirement toward a more universal picture at, and even below, the glass transition for our systems. This is illustrated by constructing the full proton mean-square displacement for three bottlebrush polymers from femto- to nanoseconds, with simultaneous information on the partial contributions from segmental relaxation, methyl group rotation, and vibrations. The information can be used for a better analysis of results from numerous techniques and samples, improving the overall understanding of materials properties.

Magnetic Properties of the Distorted Kagomé Lattice Mn3(1,2,4-(O2C)3C6H3)2.

Kagomé lattice types have been of intense interest as idealized examples of extended frustrated spin systems. Here we demonstrate how the use of neutron diffraction and inelastic neutron scattering coupled with spin wave theory calculations can be used to elucidate the complex magnetic interactions of extended spin networks. We show that the magnetic properties of the coordination polymer Mn3(1,2,4-(O2C)3C6H3)2, a highly distorted kagomé lattice, have been erroneously characterized as a canted antiferromagnet in previous works. Our results demonstrate that, although the magnetic structure is ferrimagnetic, with a net magnetic moment, frustration persists in the system. We conclude by showing that the conventions of the Goodenough-Kanamori rules, which are often applied to similar magnetic exchange interactions, are not relevant in this case.

Magnetic Excitations in Polyoxotungstate-Supported Lanthanoid Single-Molecule Magnets: An Inelastic Neutron Scattering and ab Initio Study.

Inelastic neutron scattering (INS) has been used to investigate the crystal field (CF) magnetic excitations of the analogs of the most representative lanthanoid-polyoxometalate single-molecule magnet family: Na9[Ln(W5O18)2] (Ln = Nd, Tb, Ho, Er). Ab initio complete active space self-consistent field/restricted active space state interaction calculations, extended also to the Dy analog, show good agreement with the experimentally determined low-lying CF levels, with accuracy better in most cases than that reported for approaches based only on simultaneous fitting to CF models of magnetic or spectroscopic data for isostructural Ln families. In this work we demonstrate the power of a combined spectroscopic and computational approach. Inelastic neutron scattering has provided direct access to CF levels, which together with the magnetometry data, were employed to benchmark the ab initio results. The ab initio determined wave functions corresponding to the CF levels were in turn employed to assign the INS transitions allowed by selection rules and interpret the observed relative intensities of the INS peaks. Ultimately, we have been able to establish the relationship between the wave function composition of the CF split LnIII ground multiplets and the experimentally measured magnetic and spectroscopic properties for the various analogs of the Na9[Ln(W5O18)2] family.

Carbonate-Bridged Lanthanoid Triangles: Single-Molecule Magnet Behavior, Inelastic Neutron Scattering, and Ab Initio Studies.

Optimization of literature synthetic procedures has afforded, in moderate yield, homogeneous and crystalline samples of the five analogues Na11[{RE(OH2)}3CO3(PW9O34)2] (1-RE; RE = Y, Tb, Dy, Ho, and Er). Phase-transfer methods have allowed isolation of the mixed salts (Et4N)9Na2[{RE(OH2)}3CO3(PW9O34)2] (2-RE; RE = Y and Er). The isostructural polyanions in these compounds are comprised of a triangular arrangement of trivalent rare-earth ions bridged by a µ3-carbonate ligand and sandwiched between two trilacunary Keggin {PW9O34} polyoxometalate ligands. Alternating-current (ac) magnetic susceptibility studies of 1-Dy, 1-Er, and 2-Er reveal the onset of frequency dependence for the out-of-phase susceptibility in the presence of an applied magnetic field at the lowest measured temperatures. Inelastic neutron scattering (INS) spectra of 1-Ho and 1-Er exhibit transitions between the lowest-lying crystal-field (CF) split states of the respective J = 8 and (15)/2 ground-state spin-orbit multiplets of the Ho(III) and Er(III) ions. Complementary ab initio calculations performed for these two analogues allow excellent reproduction of the experimental magnetic susceptibility and low-temperature magnetization data and are in reasonable agreement with the experimental INS data. The ab initio calculations reveal that the slight difference in coordination environments of the three Ln(III) ions in each complex gives rise to differences in the CF splitting that are not insignificant. This theoretical result is consistent with the observation of multiple relaxation processes by ac magnetic susceptibility and the broadness of the measured INS peaks. The ab initio calculations also indicate substantial mixing of the MJ contributions to the CF split energy levels of each Ln(III) ion. Calculations indicate that the CF ground states of the Ho(III) centers in 1-Ho are predominantly comprised of contributions from small MJ, while those of the Er(III) centers in 1-Er are predominantly comprised of contributions from large MJ, giving rise to slow magnetic relaxation. Although no direct evidence for intramolecular RE···RE magnetic coupling is observed in either magnetic or INS studies, on the basis of the ab initio calculations, we find noncollinear magnetic axes in 1-Er that are coplanar with the erbium triangle and radially arranged with respect to the triangle's centroid; thus, we argue that the absence of magnetic coupling in this system arises from dipolar and antiferromagnetic superexchange interactions that cancel each other out.

Energy and temperature dependence of rigid unit modes in AlPO4-5.

For structures that can be treated as networks of rigid, corner-connected polyhedra, the dominant distortion modes can be described by so-called rigid unit modes that are close to zero frequency. This type of behaviour is common in zeolitic/zeotypic materials such as the AlPO4 family of compounds and has been suggested by some authors to play a significant role in molecular diffusion within the pores of such compounds. We explore the energy and temperature dependence of these modes in AlPO4-5 using inelastic neutron scattering and heat capacity measurements. Ab initio based computational modelling is also used to assign the observed dynamic behaviour to rigid unit modes. We observe that these rigid unit modes persist down to very low temperatures and show no signs of freezing out.

What difference does a methyl group make: pentamethylbenzene?

The crystal structure of pentamethylbenzene has been obtained for the first time with the use of synchrotron radiation, whilst the low-energy spectrum of lattice dynamics, dominated by the methyl group torsions, was obtained using inelastic neutron scattering. The effect of symmetry lowering by the removal of a single methyl group relative to hexamethylbenzene has been investigated, including the role that this plays in the charge-transfer characteristics of complexes formed with tetracyanoethylene.

Position-Dependent Segmental Relaxation in Bottlebrush Polymers.

Segmental dynamics of specifically labeled poly(propylene oxide), PPO, based bottlebrush polymers, PNB-g-PPO, were studied using quasi-elastic neutron scattering. The focus was set to different parts of the side chains to investigate the hypothetical gradual relaxation behavior within the side chains of a bottlebrush polymer. Different sections of the side chains were highlighted for QENS via sequential polymerization of protonated and deuterated monomers to allow the study of the relaxation behavior of the inner and outer parts of the side chain separately. A comparison of these two parts reveals a slowdown due to the grafting process happening across the different regions. This is seen for the segmental relaxation time as well as on the time-dependent mean-square displacement. Additionally, the non-Gaussian parameter, α, shows a decreasing difference from Gaussian behavior with the distance to the backbone. Altogether, this leads to the conclusion that gradual relaxation behavior exists.

On the temperature dependence of the density of states of liquids at low energies.

We report neutron-scattering measurements of the density of states (DOS) of water and liquid Fomblin in a wide range of temperatures. In the liquid phase, we confirm the presence of a universal low-energy linear scaling of the experimental DOS as a function of the frequency, g ( ω ) = a ( T ) ω , which persists at all temperatures. The low-frequency scaling of the DOS exhibits a sharp jump at the melting point of water, below which the standard Debye's law, g ( ω ) ∝ ω 2 , is recovered. On the contrary, in Fomblin, we observe a continuous transition between the two exponents reflecting its glassy dynamics, which is confirmed by structure measurements. More importantly, in both systems, we find that the slope a(T) grows with temperature following an exponential Arrhenius-like form, a ( T ) ∝ exp ( - ⟨ E ⟩ / T ) . We confirm this experimental trend using molecular dynamics simulations and show that the prediction of instantaneous normal mode (INM) theory for a(T) is in qualitative agreement with the experimental data.

Ab initio-based determination of lanthanoid-radical exchange as visualised by inelastic neutron scattering.

Magnetic exchange coupling can modulate the slow magnetic relaxation in single-molecule magnets. Despite this, elucidation of exchange coupling remains a significant challenge for the lanthanoid(iii) ions, both experimentally and computationally. In this work, the crystal field splitting and 4f-π exchange coupling in the erbium-semiquinonate complex [ErTp2dbsq] (Er-dbsq; Tp- = hydro-tris(1-pyrazolyl)borate, dbsqH2 = 3,5-di-tert-butyl-1,2-semiquinone) have been determined by inelastic neutron scattering (INS), magnetometry, and CASSCF-SO ab initio calculations. A related complex with a diamagnetic ligand, [ErTp2trop] (Er-trop; tropH = tropolone), has been used as a model for the crystal field splitting in the absence of coupling. Magnetic and INS data indicate antiferromagnetic exchange for Er-dbsq with a coupling constant of Jex = -0.23 meV (-1.8 cm-1) (-2Jex formalism) and good agreement is found between theory and experiment, with the low energy magnetic and spectroscopic properties well modelled. Most notable is the ability of the ab initio modelling to reproduce the signature of interference between localised 4f states and delocalised π-radical states that is evident in the Q-dependence of the exchange excitation. This work highlights the power of combining INS with EPR and magnetometry for determination of ground state properties, as well as the enhanced capability of CASSCF-SO ab initio calculations and purposely developed ab initio-based theoretical models. We deliver an unprecedentedly detailed representation of the entangled character of 4f-π exchange states, which is obtained via an accurate image of the spin-orbital transition density between the 4f-π exchange coupled wavefunctions.

Switchable magnetism: neutron diffraction studies of the desolvated coordination polymer Co3(OH)2(C4O4)2.

We report the magnetic structure of the two magnetically ordered phases of Co3(OH)2(C4O4)2, a coordination polymer that consists of a triangular framework decorated with anisotropic Co(II) ions. Neutron diffraction experiments allow us to confirm that the magnetic behavior changes upon dehydration and reveal the complex phase behavior of this system, relative to the hydrated compound Co3(OH)2(C4O4)2·3H2O. One phase is shown to display spin idle behavior, where only a fraction of the moments order at intermediate temperatures, while at the lowest temperatures the system orders fully, in this case with a net magnetic moment. This novel magnetic behavior is discussed within the framework of a simple Hamiltonian and representational analysis and rationalizes this multiphase behavior by considering the combination of frustration and anisotropy. The change in behavior on dehydration is also rationalized with respect to the changes in the single-ion anisotropy of the cobalt.

Proline induced disruption of the structure and dynamics of water.

We use quasi-elastic neutron scattering spectroscopy to study the diffusive motion of water molecules at ambient temperature as a function of the solute molar fraction of the amino acid, proline. We validate molecular dynamics simulations against experimental quasielastic neutron scattering data and then use the simulations to reveal, and understand, a strong dependence of the translational self-diffusion coefficient of water on the distance to the amino acid molecule. An analysis based on the juxtaposition of water molecules in the simulation shows that the rigidity of proline imposes itself on the local water structure, which disrupts the hydrogen-bond network of water leading to an increase in the mean lifetime of hydrogen bonds. The net effect is some distortion of the proline molecule and a slowing down of the water mobility.

Direct observation of magnetoelastic coupling in a molecular spin qubit: new insights from crystal field neutron scattering data.

Single-molecule magnets are promising candidates for data storage and quantum computing applications. A major barrier to their use is rapid magnetic relaxation and quantum decoherence due to thermal vibrations. Here we report a reanalysis of inelastic neutron scattering (INS) data of the candidate qubit Na9[Ho(W5O18)2]·35D2O, wherein we demonstrate for the first time that magnetic relaxation times and mechanisms can be directly observed as crystal field (CF) peak broadening in INS spectra of a lanthanoid molecular system. The magnetoelastic coupling between the lower energy CF states and phonons (lattice vibrations) is determined by the simultaneous measurement of CF excitations and the phonon density of states, encoded within the same INS experiment. This directly results in the determination of relaxation coupling pathways that occur in this molecule. Such information is invaluable for the further advancement of SMMs and to date has only been obtained from techniques performed in external magnetic fields. Additionally, we determine a relaxation rate of quantum-tunnelling of magnetisation that is consistent with previously measured EPR spectroscopy data.

Modulation of Slow Magnetic Relaxation in Gd(III)-Tetrahalosemiquinonate Complexes.

Incorporating lanthanoid(III)-radical magnetic exchange coupling is a possible route to improving the performance of lanthanoid (Ln) single-molecule magnets (SMMs), molecular materials that exhibit slow relaxation and low temperature quantum tunnelling of the magnetization. Complexes of Gd(III) can conveniently be used as model systems to study the Ln-radical exchange coupling, thanks to the absence of the orbital angular momentum that is present for many Ln(III) ions. Two new Gd(III)-radical compounds of formula [Gd(18-c-6)X4 SQ(NO3 )].I3 (18-c-6=18-crown-6, X4 SQ⋅- =tetrahalo-1,2-semiquinonate, 1: X=Cl, 2: X=Br) have been synthesized, and the presence of the dioxolene ligand in its semiquinonate form confirmed by X-ray crystallography, UV-Visible-NIR spectroscopy and voltammetry. Static magnetometry and EPR spectroscopy indicate differences in the low temperature magnetic properties of the two compounds, with antiferromagnetic exchange coupling of JGd-SQ ∼-2.0 cm-1 (Hex =-2JGd-SQ (SGd SSQ )) determined by data fitting. Interestingly, compound 1 exhibits slow magnetic relaxation in applied magnetic fields while 2 relaxes much faster, pointing to the major role of packing effects in modulating slow relaxation of the magnetization.

Two stage magnetic ordering and spin idle behavior of the coordination polymer Co3(OH)2(C4O4)2·3H2O determined using neutron diffraction.

We report the magnetic structure of two of the magnetically ordered phases of Co(3)(OH)(2)(C(4)O(4))(2)·3H(2)O, a coordination polymer that consists of a triangular framework decorated with anisotropic Co(II) ions. The combination of neutron diffraction experiments and magnetic susceptibility data allows us to identify one phase as displaying spin idle behavior, where only a fraction of the moments order at intermediate temperatures, while at the lowest temperatures the system orders fully. This novel magnetic behavior is discussed within the framework of a simple Hamiltonian and representational analysis and rationalizes this multiphase behavior by considering the combination of frustration and anisotropy.

Mixed alkali metal/transition metal coordination polymers with the mellitic acid hexaanion: 2-dimensional hexagonal magnetic nets.

The hexaanion of mellitic acid, mel = (C(6)(CO(2))(6))(6-), links metal ions into extensively connected magnetic coordination polymers. Reaction of alkali metal mellitate salts, M(6)(mel) (M = K, Rb), with M'Cl(2) precursors (M' = Mn, Co, Ni) under mild (473 K) hydrothermal conditions yields an extensive family of isostructural 3-dimensional mixed alkali metal/transition metal polymers of general formula M(2)[M'(2)(mel)(OH(2))(2)] (M/M' = K/Mn (1a); K/Co (1b); K/Ni (1c); Rb/Mn (2a); Rb/Co (2b); Rb/Ni (2c)). These materials incorporate distorted 2-dimensional magnetic hexagonal nets with a honeycomb topology that are exclusively based on metal-carboxylate-metal bridging interactions. A further isostructural alkali metal-free Co(2+) material with NH(4)(+) cations, (NH(4))(2)[Co(2)(mel)(OH(2))(2)] (3), produced by reaction of H(6)mel with [Co(NH(3))(6)]Cl(3) is also presented. The magnetic susceptibility data for 1a-c, 2a-c, and 3 are presented. The susceptibility data for the Mn(II)- and Ni(II)-containing phases have been analyzed using a simple Mean Field Theory approach, and have been modeled using a high temperature series expansion. The comparative magnetism of the Co(II) phases is also presented, and is more complicated because of significant spin-orbit coupling effects.

Short-Time Dynamics of PDMS-g-PDMS Bottlebrush Polymer Melts Investigated by Quasi-Elastic Neutron Scattering.

We have studied the short-time dynamical behavior of polydimethylsiloxane (PDMS) bottlebrush polymers, PDMS-g-PDMS. The samples have similar backbone lengths but different side-chain lengths, resulting in a shape transition. Quasi-elastic neutron scattering was used to observe the dynamical changes inherent to these structural changes. The combination of data from three spectrometers enabled to follow the dynamics over broad frequency and temperature ranges, which included segmental relaxations and more localized motions. The latter, identified as the methyl group rotation, is described by a threefold jump model and shows higher activation energies compared to linear PDMS. The segmental relaxation times, τs, decrease with increasing molecular weight of the side chains but increase with momentum transfer, Q, following a power law, which suggests a non-Gaussian behavior for bottlebrush polymers.

Non-classical behaviour in an S = 5/2 chain with next nearest neighbour interactions observed from the inelastic neutron scattering of Mn(2)(OD)(2)(C(4)O(4)).

Low-dimensional and frustrated magnetic systems often show interesting quantum phenomena. The use of large moments such as S = 5/2 within such materials is uncommon, partly due to the evidence that the large manifold of states associated with these centres results in pseudo-classical behaviour. Here we report on the inelastic neutron scattering of Mn(2)(OD)(2)(C(4)O(4)), a well-isolated chain with next nearest neighbour interactions. We observe a magnetic excitation spectrum below 30 K whose characteristics resemble those of quantum spin singlets. Inelastic neutron scattering from a powdered sample is shown to yield a great deal of information about the nature of these effects.