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Among the large class of $A$-site ordered perovskites of stoichiometry $A{C}_{3}{B}_{4}{\mathrm{O}}_{12}$, the rare-earth $(R)$ ruthenates $R{\mathrm{Cu}}_{3}{\mathrm{Ru}}_{4}{\mathrm{O}}_{12}$ $(R=\mathrm{La}, \mathrm{Pr}, \mathrm{Nd})$ are interesting compounds due both to $\mathrm{Ru}\text{\ensuremath{-}}4d$-derived electronic correlations and to unconventional crystal-electric-field effects of the $R$ ions. Here we report on detailed investigations of these compounds utilizing x-ray diffraction, neutron scattering, magnetic susceptibility, and electrical resistivity measurements as well as heat capacity and nuclear resonance experiments. A broad range of external parameters is scanned and depending on the specific technique, temperatures range from 100 mK to 730 K in external magnetic fields up to 14 T. In this work ${\mathrm{LaCu}}_{3}{\mathrm{Ru}}_{4}{\mathrm{O}}_{12}$ serves as reference compound with a nonmagnetic $A$ site, characterized in detail recently [S. Riegg et al., Phys. Rev. B 93, 115149 (2016)]. All compounds investigated reveal heavy-fermion behavior with a ${T}^{2}$ dependence of the low-temperature electrical resistivity and significantly enhanced Sommerfeld coefficients. Toward low temperatures, the compounds with $R=\mathrm{Pr}$ and Nd are dominated by the magnetic moments of the $R$ ions, which occupy crystallographic positions with point-group symmetry ${T}_{h}$. The crystal-electric-field effects are clearly visible especially in heat capacity and inelastic neutron scattering data from which the crystal-electric-field parameters are derived. The ground state of the ${\mathrm{Pr}}^{3+}$ ion is identified as a triplet $({\mathrm{\ensuremath{\Gamma}}}_{4}^{(1)})$, whereas for ${\mathrm{Nd}}^{3+}$ it is a quartet $({\mathrm{\ensuremath{\Gamma}}}_{67})$. Evidence for lowering of the ${T}_{h}$ symmetry is observed at the Pr site at temperatures below 10 K, suggesting the formation of orbital order. Moreover, the spin-lattice relaxation derived from $^{63}\mathrm{Cu}$ nuclear quadrupole resonance indicates characteristic temperatures close to 7 K and 350 mK, probably related to orbital and magnetic order, respectively.

We performed inelastic neutron scattering measurements on a polycrystalline sample of a classical kagome antiferromagnet ${\mathrm{NaBa}}_{2}{\mathrm{Mn}}_{3}{\mathrm{F}}_{11}$ to investigate the possibility of a dispersionless zero-energy excitation associated with rotation of spins along the chains. The observed spectra indeed exhibit such an excitation with strong intensity at low energy, as well as dispersive excitations with weak intensity at high energy. Combining the measurements with calculations from linear spin-wave theory reveals that ${\mathrm{NaBa}}_{2}{\mathrm{Mn}}_{3}{\mathrm{F}}_{11}$ is a good realization of the classical kagome antiferromagnet which exhibits a dispersionless mode lifted by the magnetic dipole-dipole interaction.

The Ising triangular lattice remains the classic test-case for frustrated magnetism. Here we report neutron scattering measurements of short range magnetic order in CuMnO$_2$, which consists of a distorted lattice of Mn$^{3+}$ spins with single-ion anisotropy. Physical property measurements on CuMnO$_2$ are consistent with 1D correlations caused by anisotropic orbital occupation. However the diffuse magnetic neutron scattering seen in powder measurements has previously been fitted by 2D Warren-type correlations. Using neutron spectroscopy, we show that paramagnetic fluctuations persist up to $\sim$25 meV above TN= 65 K. This is comparable to the incident energy of typical diffractometers, and results in a smearing of the energy integrated signal, which hence cannot be analysed in the quasi-static approximation. We use low energy XYZ polarised neutron scattering to extract the purely magnetic (quasi)-static signal. This is fitted by reverse Monte Carlo analysis, which reveals that two directions in the triangular layers are perfectly frustrated in the classical spin-liquid phase at 75 K. Strong antiferromagnetic correlations are only found along the b-axis, and our results hence unify the pictures seen by neutron scattering and macroscopic physical property measurements.

The instrumental divergence parameters and resolution for the D7 neutron diffuse scattering spectrometer at the Institut Laue-Langevin, France, are presented. The resolution parameters are calibrated against measurements of powders, single crystals, and the incoherent scattering from vanadium. We find that the powder diffraction resolution is well described by the Cagliotti function, the single crystal resolution function can be parameterized using the Cooper-Nathans formalism, and that in time-of-flight mode the energy resolution is consistent with monochromatic focussing.

Tb2Ti2O7 presents an ongoing conundrum in the study of rare-earth pyrochlores. Despite the expectation that it should be the prototypical unfrustrated noncollinear Ising antiferromagnet on the pyrochlore lattice, it presents a puzzling correlated state that persists to the lowest temperatures. Effects which can reintroduce frustration or fluctuations are therefore sought, and quadrupolar operators have been implicated. One consequence of strong quadrupolar effects is the possible coupling of magnetic and lattice degrees of freedom, and it has previously been shown that a hybrid magnetoelastic mode with both magnetic and phononic character is formed in Tb2Ti2O7 by the interaction of a crystal field excitation with a transverse-acoustic phonon. Here, using polarized and unpolarized inelastic neutron scattering, we present a detailed characterization of the magnetic and phononic branches of this magnetoelastic mode, particularly with respect to their composition, the anisotropy of any magnetic fluctuations, and also the temperature dependence of the different types of fluctuation that are involved. We also examine the dispersion relations of the exciton branches that develop from the crystal field excitation in the same temperature regime that the coupled mode appears, and find three quasidispersionless branches where four are expected, each with a distinctive structure factor indicating that they are nonetheless cooperative excitations. We interpret the overall structure of the spectrum as containing four branches, one hybridized with the phonons and gaining a strong dispersion, and three remaining dispersionless.

Spin fluctuations are widely believed to play an important role in the superconducting mechanisms of unconventional high-temperature superconductors. Spin fluctuations have been observed in iron-based superconductors as well. However, in some iron-based superconductors such as LaFePO$_{0.9}$, they have not been observed by inelastic neutron scattering (INS). LaFePO$_{0.9}$ is an iron-based superconductor with a low superconducting transition temperature ($T_{\rm c}$= 5 K), where line nodes are observed in the superconducting gap function. The line-node symmetry typically originates from sign reversal of the order parameter in spin-fluctuation-mediated superconductivity. This contradiction has been a long-standing mystery of this superconductor. Herein, spin fluctuations were found at high energies such as 30$-$50 meV with comparable intensities to an optimally doped LaFeAs(O,F). Based on this finding, the line-node symmetry can be explained naturally as spin-fluctuation-mediated superconductivity., 9 pages, 4 figures

The physical characterisation and understanding of molecular magnetic materials is one of the most important steps towards the integration of such systems in hybrid spintronic devices. Amongst the many characterisation techniques employed in such a task, Inelastic Neutron Scattering (INS) stands as one of the most powerful and sensitive tools to investigate their spin dynamics. Herein, the magnetic properties and spin dynamics of two dinuclear complexes, namely [(M(hfacac)$_2$)$_2$(bpym)] (where M = Ni$^{2+}$, Co$^{2+}$, abbreviated in the following as Ni$_2$, Co$_2$) are reported. These are model systems that could constitute fundamental units of future spintronic devices. By exploiting the highly sensitive IN5 Cold INS spectrometer, we are able to gain a deep insight into the spin dynamics of Ni$_2$ and to fully obtain the microscopic spin Hamiltonian parameters; while for Co$_2$, a multitude of INS transitions are observed demonstrating the complexity of the magnetic properties of octahedral cobalt-based systems.

Chemical science 9(14), 3555-3562 (2018). doi:10.1039/C8SC00163D, Published by RSC, Cambridge

The inelastic response of AV2Al20 (with A = Al, Ga and Y) was probed by high-resolution inelastic neutron scattering experiments and density functional theory (DFT) based lattice dynamics calculations (LDC). Features characteristic of the dynamics of Al, Ga and Y are established experimentally in the low-energy range of the compounds. In the stereotype 'Einstein-solid' compound AlV2Al20 we identify a unique spectral density extending up to 10 meV at 1.6 K. Its dominating feature is a peak centred at 2 meV at the base temperature. A very similar spectral distribution is established in GaV2Al20 albeit the strong peak is located at 1 meV at 1.6 K. In YV2Al20 signals characteristic of Y dynamics are located above 8 meV. The spectral distributions are reproduced by the DFT-based LDC and identified as a set of phonons. The response to temperature changes between 1.6 and ∼300 K is studied experimentally and the exceptionally vivid renormalization of the A characteristic modes in AlV2Al20 and GaV2Al20 is quantified by following the energy of the strong peak. At about 300 K it is shifted to higher energies by 300% for A = Al and 450% for A = Ga. The dynamics of A = Y in YV2Al20 show a minor temperature effect. This holds in general for modes located above 10 meV in any of the compounds. They are associated with vibrations of the V2Al20 matrix. Atomic potentials derived through DFT calculations indicate the propensity of A = Al and Ga to a strong positive energy shift upon temperature increase by a high quartic component. The effect of the strong phonon renormalization on thermodynamic observables is computed on grounds of the LDC results. It is shown that through the hybridization of A = Al and Ga with the V2Al20 dynamics the matrix vibrations in the low-energy range follow this renormalization.

We explore the field-temperature phase diagram of the XY pyrochlore antiferromagnet ${\mathrm{Er}}_{2}{\mathrm{Ti}}_{2}{\mathrm{O}}_{7}$ by means of magnetization and neutron diffraction experiments. Depending on the field strength and direction relative to the high symmetry cubic directions $[001],[1\overline{1}0]$, and $[111]$, the refined field-induced magnetic structures are derived from the zero field ${\ensuremath{\psi}}_{2}$ and ${\ensuremath{\psi}}_{3}$ states of the ${\mathrm{\ensuremath{\Gamma}}}_{5}$ irreducible representation which describes the ground state of XY pyrochlore antiferromagnets. At low field, domain selection effects are systematically at play. In addition, for $[001]$, a phase transition is reported towards a ${\ensuremath{\psi}}_{3}$ structure at a characteristic field ${H}_{c}^{001}=43$ mT. For $[1\overline{1}0]$ and $[111]$, the spins are continuously tilted by the field from the ${\ensuremath{\psi}}_{2}$ state, and no phase transition is found while domain selection gives rise to sharp anomalies in the field dependence of the Bragg peaks intensity. For $[1\overline{1}0]$, these results are confirmed by high resolution inelastic neutron scattering experiments, which in addition allow us to determine the field dependence of the spin gap. This study agrees qualitatively with the scenario proposed theoretically by Maryasin et al. [Phys. Rev. B 93, 100406(R) (2016)], yet the strength of the field-induced anisotropies is significantly different from theory.

${\mathrm{CePd}}_{2}{\mathrm{Al}}_{2\ensuremath{-}x}{\mathrm{Ga}}_{x}$ compounds crystallizing in the tetragonal ${\mathrm{CaBe}}_{2}{\mathrm{Ge}}_{2}$-type structure (space group $P4/nmm$) and undergoing a structural phase transition to an orthorhombic structure ($Cmme$) at low temperatures were studied by means of neutron scattering. The amplitude-modulated magnetic structure of ${\mathrm{CePd}}_{2}{\mathrm{Al}}_{2}$ is described by an incommensurate propagation vector $\stackrel{P\vec}{k}=({\ensuremath{\delta}}_{x},\frac{1}{2}+{\ensuremath{\delta}}_{y},0)$ with ${\ensuremath{\delta}}_{x}=0.06$ and ${\ensuremath{\delta}}_{y}=0.04$. The magnetic moments order antiferromagnetically within the $ab$ planes stacked along the $c$ axis and are arranged along the direction close to the orthorhombic $a$ axis with a maximum value of 1.5(1) ${\ensuremath{\mu}}_{\mathrm{B}}/{\mathrm{Ce}}^{3+}$. ${\mathrm{CePd}}_{2}{\mathrm{Ga}}_{2}$ reveals a magnetic structure composed of two components: the first is described by the propagation vector $\stackrel{P\vec}{{k}_{1}}=(\frac{1}{2},\phantom{\rule{0.16em}{0ex}}\frac{1}{2},\phantom{\rule{0.16em}{0ex}}0)$, and the second one propagates with $\stackrel{P\vec}{{k}_{2}}=(0,\frac{1}{2},0)$. The magnetic moments of both components are aligned along the same direction---the orthorhombic [100] direction---and their total amplitude varies depending on the mutual phase of magnetic moment components on each Ce site. The propagation vectors $\stackrel{P\vec}{{k}_{1}}$ and $\stackrel{P\vec}{{k}_{2}}$ describe also the magnetic structure of substituted ${\mathrm{CePd}}_{2}{\mathrm{Al}}_{2\ensuremath{-}x}{\mathrm{Ga}}_{x}$ compounds, except the one with $x=0.1.\phantom{\rule{0.28em}{0ex}}{\mathrm{CePd}}_{2}{\mathrm{Al}}_{1.9}{\mathrm{Ga}}_{0.1}$ with magnetic structure described by $\stackrel{P\vec}{k}$ and $\stackrel{P\vec}{{k}_{1}}$ stays on the border between pure ${\mathrm{CePd}}_{2}{\mathrm{Al}}_{2}$ and the rest of the series. Determined magnetic structures are compared with other Ce 112 compounds. Inelastic neutron scattering experiments disclosed three nondispersive magnetic excitations in the paramagnetic state of ${\mathrm{CePd}}_{2}{\mathrm{Al}}_{2}$, while only two crystal field (CF) excitations are expected from the splitting of ground state $J=\frac{5}{2}$ of the ${\mathrm{Ce}}^{3+}$ ion in a tetragonal/orthorhombic point symmetry. Three magnetic excitations at 1.4, 7.8, and 15.9 meV are observed in the tetragonal phase of ${\mathrm{CePd}}_{2}{\mathrm{Al}}_{2}$. A structural phase transition to an orthorhombic structure shifts the first excitation up to 3.7 meV, while the other two excitations remain at almost the same energy. The presence of an additional magnetic peak is discussed and described within the Thalmeier-Fulde CF-phonon coupling (i.e., magnetoelastic coupling) model generalized to the tetragonal point symmetry. The second parent compound ${\mathrm{CePd}}_{2}{\mathrm{Ga}}_{2}$ does not display any sign of additional magnetic excitation. The expected two CF excitations were observed. The development of magnetic excitations in the ${\mathrm{CePd}}_{2}{\mathrm{Al}}_{2\ensuremath{-}x}{\mathrm{Ga}}_{x}$ series is discussed and crystal field parameters determined.

We report on the inelastic response of AV2Al20 (with A = Sc, La and Ce) probed by high-resolution inelastic neutron scattering experiments. Intense signals associated with the dynamics of Sc, La and Ce are identified in the low-energy range at 6–14 meV in ScV2Al20 and at 8–16 meV in LaV2Al20 and CeV2Al20. Their response to temperature changes between 2 and 300 K reveals a very weak softening of the modes upon heating in LaV2Al20 and CeV2Al20 and a distinguished blue shift by about 2 meV in ScV2Al20. By means of density functional theory (DFT) and lattice dynamics calculations (LDC) we show that the unusual anharmonicity of the Sc-dominated modes is due to the local potential of Sc featured by a strong quartic term. The vibrational dynamics of ScV2Al20 as well as of LaV2Al20 and CeV2Al20 is reproduced by a set of eigenmodes. To screen the validity of the DFT and LDC results they are confronted with data from X-ray diffraction measurements. The effect of the strong phonon renormalization in ScV2Al20 on thermodynamic observables is computed on grounds of the LDC derived inelastic response. To set the data in a general context of AV2Al20 compounds and their physical properties we report in addition computer and experimental results of the binary V2Al20 compound.

This short overview gives an account on the use of neutron spectroscopy for the examination of molecular nanomagnets, systems constructed by crystalline arrangement of finite size clusters (usually with regular form) of interacting moment carrying atoms – magnetic molecules. Opposed to extended magnetic systems with bands of collective excitations such as spin-waves the molecular nanomagnets are entities with local properties, each magnetic molecule possessing a finite number of energy levels that can be solved exactly for small enough systems. In essence, the number of states remains finite despite growing rapidly with increasing number of magnetic centers and the value of the spin quantum number. Increasingly large numbers of states and more complex exchange networks lead to the need for approximative treatments, the validity of which can be checked with neutron spectroscopy. Molecular nanomagnets provide interesting examples of physics and magnetochemistry, illustrated here with a few examples that highlight the power of neutron spectroscopy for precise investigation of the energy level structure and spatial configuration of the magnetic exchange parameters.

We present an experimental study of the quantum spin ice candidate pyrochlore compound ${\mathrm{Pr}}_{2}{\mathrm{Zr}}_{2}{\mathrm{O}}_{7}$ by means of magnetization measurements, specific heat, and neutron scattering up to 12 T and down to 60 mK. When the field is applied along the $[111]$ and $[1\overline{1}0]$ directions, $\mathbf{k}=0$ field-induced structures settle in. We find that the ordered moment rises slowly, even at very low temperature, in agreement with macroscopic magnetization. Interestingly, for $H\ensuremath{\parallel}[1\overline{1}0]$, the ordered moment appears on the so-called $\ensuremath{\alpha}$ chains only. The spin excitation spectrum is essentially inelastic and consists in a broad flat mode centered at about 0.4 meV with a magnetic structure factor which resembles the spin ice pattern. For $H\ensuremath{\parallel}[1\overline{1}0]$ (at least up to 2.5 T), we find that a well-defined mode forms from this broad response, whose energy increases with $H$, in the same way as the temperature of the specific-heat anomaly. We finally discuss these results in the light of mean field calculations and propose an interpretation where quadrupolar interactions play a major role, overcoming the magnetic exchange. In this picture, the spin ice pattern appears shifted up to finite energy because of those interactions. We then propose a range of acceptable parameters for ${\mathrm{Pr}}_{2}{\mathrm{Zr}}_{2}{\mathrm{O}}_{7}$ that allow to reproduce several experimental features observed under field. With these parameters, the actual ground state of this material would be an antiferroquadrupolar liquid with spin-ice-like excitations.

Fractionalised excitations that emerge from a many body system have revealed rich physics and concepts, from composite fermions in two-dimensional electron systems, revealed through the fractional quantum Hall effect, to spinons in antiferromagnetic chains and, more recently, fractionalisation of Dirac electrons in graphene and magnetic monopoles in spin ice. Even more surprising is the fragmentation of the degrees of freedom themselves, leading to coexisting and a priori independent ground states. This puzzling phenomenon was recently put forward in the context of spin ice, in which the magnetic moment field can fragment, resulting in a dual ground state consisting of a fluctuating spin liquid, a so-called Coulomb phase, on top of a magnetic monopole crystal. Here we show, by means of neutron scattering measurements, that such fragmentation occurs in the spin ice candidate Nd$_2$Zr$_2$O$_7$. We observe the spectacular coexistence of an antiferromagnetic order induced by the monopole crystallisation and a fluctuating state with ferromagnetic correlations. Experimentally, this fragmentation manifests itself via the superposition of magnetic Bragg peaks, characteristic of the ordered phase, and a pinch point pattern, characteristic of the Coulomb phase. These results highlight the relevance of the fragmentation concept to describe the physics of systems that are simultaneously ordered and fluctuating., Comment: accepted in Nature Physics

Molecular nanomagnets are among the first examples of finite-size spin systems and have been test beds for addressing several phenomena in quantum dynamics. In fact, for short-enough timescales the spin wavefunctions evolve coherently according to an appropriate spin Hamiltonian, which can be engineered to meet specific requirements. Unfortunately, so far it has been impossible to determine these spin dynamics directly. Here we show that recently developed instrumentation yields the four-dimensional inelastic-neutron scattering function in vast portions of reciprocal space and enables the spin dynamics to be determined directly. We use the Cr 8 antiferromagnetic ring as a benchmark to demonstrate the potential of this approach which allows us, for example, to examine how quantum fluctuations propagate along the ring or to test the degree of validity of the Néel-vector-tunnelling framework. © 2012 Macmillan Publishers Limited. All rights reserved.

The tetrameric Ni(II) spin cluster Ni4Mo12 has been studied by INS. The data were analyzed extensively in terms of a very general spin Hamiltonian, which includes antiferromagnetic Heisenberg interactions, biquadratic 2-spin and 3-spin interactions, a single-ion magnetic anisotropy, and Dzyaloshinsky-Moriya interactions. Some of the experimentally observed features in the INS spectra could be reproduced, however, one feature at 1.65 meV resisted all efforts. This supports the conclusion that the spin Hamiltonian approach is not adequate to describe the magnetism in Ni4Mo12. The isotropic terms in the spin Hamiltonian can be obtained in a strong-coupling expansion of the Hubbard model at half-filling. Therefore detailed theoretical studies of the Hubbard model were undertaken, using analytical as well as numerical techniques. We carefully analyzed its abilities and restrictions in applications to molecular spin clusters. As a main result it was found that the Hubbard model is also unable to appropriately explain the magnetism in Ni4Mo12. Extensions of the model are also discussed., 12 pages, 12 figures

We report the results of neutron diffraction and inelastic neutron scattering on a powder sample of Gd_{3}Ga_{5}O_{12} at high magnetic fields. Analysis of the diffraction data shows that in high fields (B≳1.8 T) the spins are not fully aligned, but are canted slightly as a result of the dipolar interaction. The magnetic phase for fields ≲1.8 T is characterized by antiferromagnetic peaks at (210) and an incommensurate wave vector. The dominant contribution to inelastic scattering at large momentum transfers is from a band of almost dispersionless excitations. We show that these correspond to the spin waves localized on ten site rings, expected on the basis of nearest neighbor exchange interaction, and that the spectrum at high fields B≳1.8 T is well described by a spin wave theory.

We report on the magnetic properties of the tetranuclear metallic cluster [Mn4O2(O2CPh)6(dpm)2]. Using susceptibility, magnetization and inelastic neutron scattering (INS) spectroscopy we have determined the exchange and anisotropy parameters. The four Mn3+ (S=2) form a tetranuclear cluster with butterfly-type geometry. The two core Mn3+ ions are strongly antiferromagnetically coupled with Jb=−4.8±0.1 meV. The outer Mn3+ ions are loosely coupled to the core spins via two different weak interactions, ferromagnetic and antiferromagnetic, respectively: Jw1=+0.1±0.01 meV and Jw2=−0.1±0.01 meV. In addition, the octahedrally coordinated outer Mn3+ ions experience a large single-ion anisotropy DS2z with D=−0.47±0.01 meV due to a strong distortion of the MnO6 octahedra. The Lande g-factor is g=1.94±0.03. Frustration effects and competitive interactions lead to remarkable magnetic properties which cannot be unambiguously interpreted without the additional information from INS.

Examples of materials where an ``order by disorder'' mechanism is at play to select a particular ground state are scarce. It has recently been proposed, however, that the antiferromagnetic XY pyrochlore ${\mathrm{Er}}_{2}{\mathrm{Ti}}_{2}{\mathrm{O}}_{7}$ reveals a most convincing case of this mechanism, with the observation of a spin gap at zone centers having recently been interpreted as a corroboration of this physics. Here we argue, however, that the anisotropy generated by the interaction-induced admixing between the crystal-field ground and excited levels provides for an alternative mechanism. It especially predicts the opening of a spin gap of about 15 $\ensuremath{\mu}\mathrm{eV}$, which is of the same order of magnitude as the one observed experimentally. We report high-resolution inelastic neutron scattering data which can be well understood within this scenario.

Several ${\mathrm{Cu}}^{2+}$ hydroxide minerals have been recently identified as candidate realizations of the $S=1/2$ kagome Heisenberg model. In this context, we have studied the distorted system ${\mathrm{KCu}}_{3}{\mathrm{As}}_{2}{\mathrm{O}}_{7}$(OD)${}_{3}$ using neutron scattering and bulk measurements. Although the distortion favors magnetic order over a spin liquid ground state, refinement of the magnetic diffraction pattern below ${T}_{N1}=7.05(5)$ K yields a complex helical structure with $\mathbf{k}=(0.77,0,0.11)$. This structure, as well as the spin excitation spectrum, are well described by a classical Heisenberg model with ferromagnetic nearest neighbor couplings. Multiferroicity is observed below ${T}_{N1}$, with an unusual crossover between improper and pseudoproper behavior occurring at ${T}_{N2}=5.5$ K. The polarization at $T=2$ K is $P=1.5\phantom{\rule{0.28em}{0ex}}\ensuremath{\mu}$Cm${}^{\ensuremath{-}2}$. The properties of ${\mathrm{KCu}}_{3}{\mathrm{As}}_{2}{\mathrm{O}}_{7}$(OD)${}_{3}$ highlight the variety of physics which arise from the interplay of spin and orbital degrees of freedom in ${\mathrm{Cu}}^{2+}$ kagome systems.

At low temperatures, Tb2Ti2O7 enters a spin liquid state, despite expectations of magnetic order and/or a structural distortion. Using neutron scattering, we have discovered that in this spin liquid state an excited crystal field level is coupled to a transverse acoustic phonon, forming a hybrid excitation. Magnetic and phononlike branches with identical dispersion relations can be identified, and the hybridization vanishes in the paramagnetic state. We suggest that Tb2Ti2O7 is aptly named a "magnetoelastic spin liquid" and that the hybridization of the excitations suppresses both magnetic ordering and the structural distortion. The spin liquid phase of Tb2Ti2O7 can now be regarded as a Coulomb phase with propagating bosonic spin excitations.

The concept of ‘rattling modes’ has been brought up in the context of several recent studies concerning thermoelectric materials as well as a new class of oxide superconductors. We have initiated projects for the study of such phenomena, with the aim of better understanding of the ‘rattling mode’ scenario and its role in the physical properties in question. The experiments using Time-of-Flight (T-o-F) investigation of polycrystalline samples with optimized resolution are complemented with ab-initio -based phonon calculations, including the powder averaged coherent inelastic response. Accordingly, we can follow the wave-vector transfer dependence of intensities, in consequence the phase coherence of the motion between particular atomic species. The results we have obtained point out the power of the Powder Averaged Lattice Dynamics (PALD) approach using T-o-F experiments. Detailed modeling for this type of study is especially interesting for materials in polycrystalline form and, therefore, well suitable for material science investigations.

We report on spin dynamics in the highly hole doped quasi-one-dimensional cuprate ${\mathrm{Sr}}_{0.73}{\mathrm{CuO}}_{2}$ measured by inelastic neutron scattering. An excitation mode with peaks at $E=10$ and 17.5 meV is observed in the spectrum. Additional magnetic scattering remains present up to $E\ensuremath{\sim}25\mathrm{meV}.$ These features are due to excitations of dimerized antiferromagnetic chains; the two peaks are associated with the dispersion of the lowest-lying magnon branch, whereas the scattering in the region up to $E\ensuremath{\sim}25\mathrm{meV}$ is consistent with an excitation continuum. The spin excitation gap $\ensuremath{\Delta}\ensuremath{\sim}10\mathrm{meV}$ remains present below the long-range magnetic ordering temperature ${T}_{\mathrm{AF}}\ensuremath{\sim}10\mathrm{K},$ indicating coexistence of the quantum-mechanical singlet ground state and the classical N\'eel ordered state. This result shows that such coexistence is not restricted to the doped spin-Peierls system ${\mathrm{CuGeO}}_{3}.$

The temperature dependence of the relaxation rate of crystal-field excitations in the slightly underdoped HoBa2Cu4O8 and Er2Ba4Cu7O14.92 high-temperature superconductors has been investigated by means of neutron scattering measurements. Our data show clear evidence for the opening of an electronic gap in the normal state at T* ≈ 200 K far above Tc. The temperature evolution of the relaxation rate appears to be extremely dependent upon the energy at which the susceptibility is being probed. This points to a strongly anisotropic gap function which is tentatively modelled to be of the form s + id3, with Δs/Δd ≈ 0.2.

The dynamical magnetic correlations in ${\mathrm{Tb}}_{2}{\mathrm{Ti}}_{2}{\mathrm{O}}_{7}$ have been investigated using polarized inelastic neutron scattering. Dispersive excitations are observed, emerging from pinch points in reciprocal space and characterized by an anisotropic spectral weight. Anomalies in the crystal field and phonon excitation spectrum at Brillouin zone centers are also reported. These findings suggest that Coulomb phases, although they present a disordered ground state with dipolar correlations, allow the propagation of collective excitations. They also point out a strong spin-lattice coupling, which likely drives effective interactions between the $4f$ quadrupolar moments.

We have measured the generalized phonon-DOS of the La and Ce filled skutterudites LaFe4Sb12 and CeFe4Sb12 that are interesting materials for thermoelectric applications. We conclude that a single peak at ℏω≈7 meV corresponds to a localized mode of La-atoms in the LaFe4Sb12 compound. Our results agree with the phenomenological theory proposed earlier, based on the high value of atomic displacement parameter of this filling atom in diffraction data. Moreover, we find agreement with the recent INS results of Hermann et al. (Phys. Rev. Lett. 90 (2003) 135505), who observed a localized mode of the Tl-filling atoms in TlxCoSb4.

Structurally, the two mixed-valence manganese disks Mn${}_{7}$-11 and Mn${}_{7}$-16 differ only in the peripheral ligand but, as a result of a subtle interplay of intramolecular exchange interactions, differ strongly in their magnetic properties, e.g., Mn${}_{7}$-11 possesses a ground-state spin of $S=11$ and Mn${}_{7}$-16 of $S=16$. The exchange interactions in the disks were studied by inelastic neutron scattering. The analysis of the $Q$ dependence of the observed magnetic transition intensities reveals that ferromagnetic cluster spin-wave excitations were observed. In this framework, it was possible to successfully model the experimental data and provide a physical understanding of the magnetism in the two disks.

SrYb${}_{2}$O${}_{4}$ is a geometrically frustrated rare-earth magnet, which presents a variety of interrelated magnetic phenomena. The magnetic Yb${}^{3+}$ ions ($J=7/2$) form potentially frustrated ``zigzag'' chains along the $c$ axis, arranged in a honeycomb fashion in the $ab$ plane. Heat capacity reveals a magnetic phase transition at ${T}_{\mathrm{N}}=0.9$ K. The magnetic structure was solved by polarized neutron diffraction and found to be noncollinear with a reduction of the ordered spin moment from the full ionic moment. The low-energy excitations, which were measured by inelastic neutron scattering reveal diffuse scattering both above and below ${T}_{\mathrm{N}}$. Heat capacity and magnetocaloric effect were performed to map out the magnetic phase diagram as a function of magnetic field and temperature and show a complicated series of states. Altogether, the results suggest that the magnetic interactions in SrYb${}_{2}$O${}_{4}$ compete with each other and with the single-ion anisotropy to produce a highly degenerate ground state manifold that suppresses the magnetic order, broadens the excitations and gives rise to a complex phase diagram.

International audience; [(iC3H7)2NH2][Cr8NiF9(O2CCMe)18], or Cr8Ni, is a prominent example of an odd-membered antiferromagnetic "wheel." A detailed characterization of the magnetic properties of Cr8Ni has been conducted. Inelastic neutron scattering (INS) is used to investigate the energy and momentum transfer dependence of the low-lying spin excitations, including excited states inaccessible by other experimental techniques. The richness of the INS data, in conjunction with microscopic spin Hamiltonian simulations, enables an accurate characterization of the magnetic properties of Cr8Ni. Nearest-neighbor exchange constants of JCrCr = 1.31 meV and JCrNi = 3.22 meV are determined, and clear evidence of axial single-ion anisotropy is found. The parameters determined by INS are shown to fit magnetic susceptibility. The spectroscopic identification of several successive S=1 excited total spin states and lowest spin band excitations show that the rotational band picture, valid for bipartite AFM wheels, breaks down for this odd-numbered wheel. The exchange constants determined here differ from previous efforts based on bulk measurements, and possible reasons are discussed. The large JCrNi/JCrCr ratio in Cr8Ni puts this wheel into a regime with strong quantum fluctuations in which the ground state can be described with a valence bond solid state picture.

The low-temperature elementary spin excitations in the AFM molecular wheel Fe18 were studied experimentally by inelastic neutron scattering and theoretically by modern numerical methods, such as dynamical density matrix renormalization group or quantum Monte Carlo techniques, and analytical spin-wave theory calculations. Fe18 involves eighteen spin-5/2 Fe(III) ions with a Hilbert space dimension of 10^14, constituting a physical system that is situated in a region between microscopic and macroscopic. The combined experimental and theoretical approach allowed us to characterize and discuss the magnetic properties of Fe18 in great detail. It is demonstrated that physical concepts such as the rotational-band or L&E-band concepts developed for smaller rings are still applicable. In particular, the higher-lying low-temperature elementary spin excitations in Fe18 or AFM wheels in general are of discrete antiferromagnetic spin-wave character., 16 pages, 10 figures

Inelastic neutron scattering experiments have been carried out in the ``ordered spin ice'' Tb${}_{2}$Sn${}_{2}$O${}_{7}$, aiming at a detailed understanding of the low-energy magnetic excitations in this highly frustrated magnet. Besides the crystal-field transition lines, we report on a well-defined low-energy line that develops in the ordered phase. We show that the intensity of this transition cannot be understood within the trigonal crystal-field scheme and argue that an interaction, which involves the spin lattice coupling through a low-temperature distortion of the trigonal crystal field, is necessary to explain the data. Based on random-phase approximation spin-dynamics calculations, taking into account the actual crystal-field scheme as well as this distortion, we successfully describe the neutron data, quantitatively consistent with the experimental observations.

Non-collinear local configurations with null total moment are expected to be a hallmark of geometrically frustrated antiferromagnets. We attempt an experimental verification of such ideas in SrCr9xGa12-9xO19 (SCGO), using the reverse Monte Carlo (RMC) analysis, recently adapted to the investigation of the magnetic correlations starting from total scattering powder data. The microscopic spin configurations obtained by RMC were used to calculate the spin nematic correlation function proposed to be of importance for classical spins on the kagome lattice. In the low-temperature range our analysis shows a strong deviation from the behaviour of classical spins on the SCGO lattice obtained with our standard Monte Carlo simulations.

We report a combination of physical property and neutron scattering measurements for polycrystalline samples of the one-dimensional spin-chain compound CoV2O6. Heat capacity measurements show that an effective S = 1/2 state is found at low temperatures and that magnetic fluctuations persist up to similar to 6T(N). Above T-N = 6.3 K, measurements of the magnetic susceptibility as a function of T and H show that the nearest-neighbor exchange is ferromagnetic. In the ordered state, we have discovered a crossover from a metamagnet with strong fluctuations between 5 K and T-N to a state with a 1/3 magnetization plateau at 2 < T < 5 K. We use neutron powder diffraction measurements to show that the antiferromagnetic state has incommensurate long-range order and inelastic time-of-flight neutron scattering to examine the magnetic fluctuations as a function of temperature. Above T-N, we find two broad bands between 3.5 and 5 meV and thermally activated low-energy features which correspond to transitions within these bands. These features show that the excitations are deconfined solitons rather than the static spin reversals predicted for a uniform ferromagnetic Ising spin chain. Below T-N, we find a ladder of states due to the confining effect of the internal field. A region of weak confinement below T-N, but above 5 K, is identified which may correspond to a crossover between two- and three-dimensional magnetic ordering. (Less)

The vibrational dynamics of the ternary Ca${}_{1\ensuremath{-}x}$Fe${}_{4}$Sb${}_{12}$, Ba${}_{1\ensuremath{-}x}$Fe${}_{4}$Sb${}_{12}$, Sr${}_{1\ensuremath{-}x}$Fe${}_{4}$Sb${}_{12}$, and Yb${}_{1\ensuremath{-}x}$Fe${}_{4}$Sb${}_{12}$ compounds is studied for its temperature dependence, dispersion relations, and material properties by experiments and ab initio powder-averaged lattice-dynamics (PALD) calculations. The experimental techniques used are high-resolution inelastic neutron scattering (INS) and inelastic x-ray scattering (IXS). Vibrational properties of polycrystalline material have been mapped out in an extensive energy-momentum phase space facilitating the study of powder-averaged phonon-dispersion relations within the first and second Brillouin zones. Qualitatively, the experimental dynamic structure factor $S(Q,\ensuremath{\omega})$ matches, to a high degree, PALD calculations allowing different schemes of collective vibrational eigenmodes to be evaluated. From the PALD calculations, quantitative values of velocity of sound, Debye temperatures, and elastic, bulk, and Young's moduli are computed. The variation of the generalized density of states $G(\ensuremath{\omega})$ with temperature is studied experimentally in the range from 2 to 600 K. No particular anomalies in the collective dynamics are observed apart from a global softening of $G(\ensuremath{\omega})$ upon heating.

We present neutron inelastic-scattering results on the low-temperature magnetic state of the frustrated-hyperkagome compound Gd3Ga5O12 gadolinium gallium garnet (GGG). Our neutron-scattering studies reveal a remarkable range of time scales. Short-range spatial correlations appear static within the instrumental resolution (50 mu eV). Three distinct inelastic modes are found at 0.04(1), 0.12(2), and 0.58(3) meV at 0.06 K. The lowest and highest energy excitations show spatial dependencies indicative of dimerized short-range antiferromagnetic correlations that survive to high temperatures, comparable to the nearest-neighbor exchange interactions. Our results suggest that the ground state of a three-dimensional hyperkagome compound differs distinctly from its frustrated counterparts on a pyrochlore lattice and reveal a juxtaposition of co-operative paramagnetism and strong-dimerized coupling. These results are surprising since GGG is often classified as a strongly frustrated system with a manifold of connected states for which one would expect a continuum of gapless excitations.

We investigate the magnetic properties of three Mn6 single-molecule magnets by means of inelastic neutron scattering and frequency domain magnetic resonance spectroscopy. The experimental data reveal that small structural distortions of the molecular geometry produce a significant effect on the energy-level diagram and therefore on the magnetic properties of the molecule. We show that the giant spin model completely fails to describe the spin-level structure of the ground spin multiplets. We analyze theoretically the spin Hamiltonian for the low-spin Mn6 molecule S =4 and we show that the excited S multiplets play a key role in determining the effective energy barrier for the magnetization reversal, in analogy to what was previously found for the two high spin Mn6 S =1 2 molecules S. Carretta et al., Phys. Rev. Lett. 100, 157203 2008.

First-principles density-functional theory and lattice-dynamics calculations were performed to study the vibrational dynamics and related observables of the ternary compounds ${\text{Ca}}_{1\ensuremath{-}x}{\text{Fe}}_{4}{\text{Sb}}_{12}$, ${\text{Sr}}_{1\ensuremath{-}x}{\text{Fe}}_{4}{\text{Sb}}_{12}$, ${\text{Ba}}_{1\ensuremath{-}x}{\text{Fe}}_{4}{\text{Sb}}_{12}$. and ${\text{Yb}}_{1\ensuremath{-}x}{\text{Fe}}_{4}{\text{Sb}}_{12}$. The calculation results are supported by experimental data, which were obtained from neutron inelastic scattering, neutron-diffraction, and heat-capacity measurements. Within the calculation approach based on the theory of harmonic solids all observables are linked to the phonon density of states $Z(\ensuremath{\omega})$. The good agreement with experimental data shows that the vibrational dynamics of the ternary skutterudite structures can be described by a set of normal modes. Features in the experimentally obtained density of states $G(\ensuremath{\omega})$ reflecting the variation in properties (mass, ionic radius) of the cations Ca, Sr, Ba, and Yb are reproduced by the calculations. The quality of the inelastic neutron experiments enables the detection of at least two mode peaks at 4.9 and 5.7 meV with a pronounced spectral weight of ytterbium.

We are interested in the phonon response in the frustrated magnets ${\text{SrCr}}_{9x}{\text{Ga}}_{12\ensuremath{-}9x}{\text{O}}_{19}$ (SCGO) and ${\text{Ba}}_{2}{\text{Sn}}_{2}{\text{ZnCr}}_{7x}{\text{Ga}}_{10\ensuremath{-}7x}{\text{O}}_{22}$ (BSZCGO). The motivation of the study is the recently discovered, phonon-driven, magnetic relaxation in the SCGO compound [Mutka et al., Phys. Rev. Lett. 97, 047203 (2006)] pointing out the importance of a low-energy $(\ensuremath{\hbar}\ensuremath{\omega}\ensuremath{\sim}7\text{ }\text{meV})$ phonon mode. In neutron-scattering experiments on these compounds, the phonon signal is partly masked by the magnetic signal from the Cr moments and we have therefore examined in detail the nonmagnetic isostructural counterparts ${\text{SrGa}}_{12}{\text{O}}_{19}$ (SGO) and ${\text{Ba}}_{2}{\text{Sn}}_{2}{\text{ZnGa}}_{10}{\text{O}}_{22}$ (BSZGO). Our ab initio lattice-dynamics calculations on SGO reveal a peak in the vibrational density of states matching with the neutron observations on SGO and SCGO. A strong contribution in the vibrational density of states comes from the partial contribution of the Ga atoms on the $2b$ and $12k$ sites, involving modes at the M point of the hexagonal system. These modes comprise dynamics of the Kagom\'e planes of the pyrochlore slab magnetic sublattice, $12k$ sites, and therefore can drive magnetic relaxation via spin-phonon coupling. Both BSZCGO and BSZGO show a similar low-energy Raman peak but no corresponding peak in the neutron-determined density of states of BSZGO is seen. However, a strong non-Debye enhancement of low-energy phonon response is observed. We attribute this particular feature to the Zn/Ga disorder on the $2d$ site, already evoked earlier to affect the magnetic properties of BSZCGO. We propose that this disorder-induced phonon response explains the absence of a characteristic energy scale and the much faster magnetic relaxation observed in BSZCGO.

Detailed knowledge of the dynamical spin–spin correlation function S(κ, ω) turns out to be a necessity in characterizing unconventional quantum spin systems — in particular if a finite spin excitation gap separates a singlet ground state from excited states. Basic predictions relying on a Heisenberg dimer model are presented in the context of neutron scattering investigations on the S= 1 2 Cu 2+ compound KCuCl3. Expressions concerning dispersion relation, intensity and field dependence of the observed singlet–triplet modes above the gap are derived and compared to the experimental results. The agreement between theory and experiment is found to be remarkably good, supporting the characterization of KCuCl3 as a quantum spin liquid near to the dimer limit.

International audience; Inelastic neutron scattering has been used to determine the microscopic Hamiltonian describing two high-spin variants of the high-anisotropy Mn-6 nanomagnet. The energy spectrum of both systems is characterized by the presence of several excited total-spin multiplets partially overlapping the S = 12 ground multiplet. This implies that the relaxation processes of these molecules are different from those occurring in prototype giant-spin nanomagnets. In particular, we show that both the height of the energy barrier and resonant tunnelling processes are greatly influenced by low-lying excited total-spin multiplets.

The antiferromagnetic molecular wheel Fe18 of eighteen exchange-coupled Fe(III) ions has been studied by measurements of the magnetic torque, the magnetization, and the inelastic neutron scattering spectra. The combined data show that the low-temperature magnetism of Fe18 is very accurately described by the Neel-vector tunneling (NVT) scenario, as unfolded by semiclassical theory. In addition, the magnetic torque as a function of applied field exhibits oscillations that reflect the oscillations in the NVT tunnel splitting with field due to quantum phase interference., Comment: 5 pages, 4 figures, REVTEX4, to appear in PRL

We have studied magnetically frustrated ${\text{Tb}}_{2}{\text{Sn}}_{2}{\text{O}}_{7}$ by neutron diffraction and high-resolution energy-resolved neutron scattering. At 0.1 K, we observed short-range magnetic correlations with a typical scale of $4\text{ }\text{\AA{}}$, close to the near-neighbor distance between ${\text{Tb}}^{3+}$ ions. This short-range order coexists with ferromagnetic correlations and long-range spin ice order at the scales of 18 and $190\text{ }\text{\AA{}}$, respectively. Spin dynamics was investigated at a time scale down to ${10}^{\ensuremath{-}9}\text{ }\text{s}$ by energy-resolved experiments on a backscattering spectrometer. We observed a freezing of the spin dynamics for all length scales with a strong slowing down of the spin fluctuations when long-range order settles in. We discuss the spin fluctuations remaining in the ground state, in comparison with previous data obtained by muon spectroscopy.

Inelastic neutron scattering on powder samples has been employed to investigate the lattice dynamics of alkali-metal osmates. We have obtained the neutron weighted generalized phonon density-of-states from momentum-transfer averaged coherent inelastic response. We have paid special attention to the low-energy modes that have been assigned to the Einstein term of the lattice specific heat and from which a ``rattling'' behavior of the alkali atoms has been inferred. In all of the three compounds our results reveal a split band with two prominent peaks in the low-energy range associated with the vibrational modes of $A$ atoms. The temperature dependence of these bands has been followed in the range from $1.5\text{ }\text{K}lTl300\text{ }\text{K}$. The strongest temperature effect is visible in the case of ${\text{KOs}}_{2}{\text{O}}_{6}$, the split band peaking at $\ensuremath{\hbar}\ensuremath{\omega}\ensuremath{\approx}5.5\text{ }\text{meV}$, and 6.8 meV at $T=300\text{ }\text{K}$ softens on cooling resulting in a main band at about $\ensuremath{\hbar}\ensuremath{\omega}\ensuremath{\approx}3.4\text{ }\text{meV}$ at $T\ensuremath{\lesssim}50\text{ }\text{K}$, while a smaller softening of $\ensuremath{\Delta}(\ensuremath{\hbar}\ensuremath{\omega})l1\text{ }\text{meV}$ is seen in the other two compounds. In agreement with earlier work the temperature dependent modifications of the phonon spectrum can be attributed to the weak potential felt by the $A$ atom in the oversized cage where it is located. At low $T$ the characteristic energies for each of the compounds are well correlated with the specific-heat observations published earlier. The powder averaged phonon response shows $Q$ dependence indicating coherent coupling of the alkali atom vibrations with the rest of the lattice.

We follow the evolution of the elementary excitations of the quantum antiferromagnet TlCuCl3 through the pressure-induced quantum critical point, which separates a dimer-based quantum disordered phase from a phase of long-ranged magnetic order. We demonstrate by neutron spectroscopy the continuous emergence in the weakly ordered state of a low-lying but massive excitation corresponding to longitudinal fluctuations of the magnetic moment. This mode is not present in a classical description of ordered magnets, but is a direct consequence of the quantum critical point., 4 pages, 4 figures

We study the spin dynamics in two variants of the high-anisotropy Mn-6 nanomagnet by inelastic neutron scattering, magnetic resonance spectroscopy and magnetometry. We show that a giant-spin picture is completely inadequate for these systems and that excited S multiplets play a key role in determining the effective energy barrier for the magnetization reversal. Moreover, we demonstrate the occurrence of tunneling processes involving pair of states having different total spin.

A field-dependent inelastic neutron scattering (INS) experiment on an array of oriented single crystals of Mn12-acetate is reported. The experimental results provide clear evidence that the minority species observed in the INS spectra is the fast-relaxing species observed in, for instance, AC-susceptibility measurements.

The antiferromagnetic molecular finite chain Cr6 was studied by inelastic neutron scattering. The observed magnetic excitations at 2.6 and 4.3 meV correspond, due to the open boundaries of a finite chain, to standing spin waves. The determined energy spectrum revealed an essentially classical spin structure. Hence, various spin-wave theories were investigated in order to assess their potential for describing the elementary excitations of finite spin systems., Comment: 6 pages, 6 figures, accepted for publication in Europhysics Letters

The Q dependence of the inelastic neutron scattering (INS) intensity of transitions within the ground-state spin multiplet of single-molecule magnets (SMMs) is considered. For these transitions, the Q dependence is related to the spin density map in the ground state, which in turn is governed by the Heisenberg exchange interactions in the cluster. This provides the possibility to infer the exchange-coupling constants from the Q dependence of the INS transitions within the spin ground state. The potential of this strategy is explored for the M = +-10 -> +- 9 transition within the S = 10 multiplet of the molecule Mn12 as an example. The Q dependence is calculated for powder as well as single-crystal Mn12 samples for various exchange-coupling situations discussed in the literature. The results are compared to literature data on a powder sample of Mn12 and to measurements on an oriented array of about 500 single-crystals of Mn12. The calculated Q dependence exhibits significant variation with the exchange-coupling constants, in particular for a single-crystal sample, but the experimental findings did not permit an unambiguous determination. However, although challenging, suitable experiments are within the reach of today's instruments., 11 pages, 6 figures, REVTEX4, to appear in PRB

International audience; This paper aims at showing the complementarity between time-of-flight and triple-axis neutron scattering experiments, on the basis of two topical examples in the field of geometrical magnetic frustration. Rare earth pyrochlore magnets R 2 Ti 2 O 7 (R is a rare earth) play a prominent role in this field, as they form model systems showing a rich variety of ground states, depending on the balance between dipolar, exchange interactions and crystal field. We first review the case of the XY antiferromagnet Er 2 Ti 2 O 7. Here a transition towards a Néel state is observed, possibly induced by an order-by-disorder mechanism. Effective exchange parameters can be extracted from S(Q, ω). We then examine the case of the spin liquid Tb 2 Ti 2 O 7. Recent experiments reveal a complex ground state characterized by " pinch points " and supporting a low energy excitation. These studies demonstrate the existence of a coupling between crystal field transitions and a transverse acoustic phonon mode.