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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.

The low lattice thermal conductivity in inorganic clathrates has been shown recently to be related to the low-energy range of optical phonons dominated by motions of guest atoms trapped in a network of host covalent cages. A promising route to further reduce the heat conduction, and increase the material efficiency for thermoelectric heat waste conversion, is then to lower the energy of these guest-weighted optical phonons. In the present work, the effect of the host cage geometry is explored. The lattice dynamics of the binary type-IX clathrate, Ba24Si100, has been investigated experimentally by means of inelastic neutron scattering as a function of temperature between 5 K and 280 K, and computed by ab-initio density functional techniques. It is compared with the lattice dynamics of Ba8Si46, the simplest representative of the well-known type-I clathrate structure. The binary Ba8Si46 and Ba24Si100 materials have both a cubic unit cell made of different Si cages. The energies, the degree of anharmonicity as well as the anisotropy of the optical phonon modes weighted by Ba motions are found to depend strongly on 2 the size and shape of the cages. The lowest optical phonon energies in Ba24Si100 are found around 2.5-4 meV, while those in Ba8Si46 have higher energies around 7-9 meV. The low-lying optical phonons in Ba24Si100 are mainly weighted by the motion of Ba in the opened Si20 cage, which doesn't exist in Ba8Si46. Moreover, the Ba vibrations within the opened Si20 cages are found intrinsically anisotropic, strongly dispersionless in some directions and exhibit a significant anharmonicity, which is not observed for any optical phonon modes in Ba8Si46.

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.

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.

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 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.

A magnetic insulator, LiInCr${}_{4}$O${}_{8}$ realizes a so-called ``breathing'' pyrochlore lattice of $S=3/2$ spins on corner-sharing tetrahedra that alternate in size. In this manuscript, a collaboration of researchers from Institut Laue-Langevin in Grenoble and Institute for Solid State Physics in Tokyo present a detailed neutron scattering study that elucidates the sequence of structural and magnetic phase transitions that occur at low temperatures in this material.

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.

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 ${\mathrm{CuGeO}}_{3}.$

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.

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.

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.

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 report a detailed study of specific heat, electrical resistivity, and thermal expansion in combination with inelastic neutron and inelastic x-ray scattering to investigate the origin of superconductivity in the two silicon clathrate superconductors Ba8Si46 and Ba24Si100. Both compounds have a similar structure based on encaged barium atoms in oversized silicon cages. However, the transition temperatures are rather different: 8 and 1.5 K, respectively. By extracting the superconducting properties, phonon density of states, electron-phonon coupling function, and phonon anharmonicity from these measurements, we discuss the important factors governing Tc and explain the difference between the two compounds.

The Cu4 OCl6 daca4 system composed of isolated Cu2+ S=1/2 tetrahedra with antiferromagnetic exchange should exhibit the properties of a frustrated quantum spin system. Ab initio density functional theory calculations for electronic structure and molecular dynamics computations suggest a complex interplay between magnetic exchange, electron delocalization, and molecular vibrations. Yet, extensive experimental characterization of Cu4 OCl6 daca4 by means of synchrotron x-ray diffraction, magnetization, specific heat, and inelastic neutron scattering reveal that properties of the real material can be only partly explained by proposed theoretical models as the low-temperature properties seem to be governed by a manifold of molecular configurations coexisting at high temperatures. © 2008 The American Physical Society.

The low-lying magnetic excitations in the dimers of single-molecule magnets [Mn{sub 4}O{sub 3}Cl{sub 4}(O{sub 2}CEt){sub 3}(py){sub 3}]{sub 2}, or (Mn{sub 4}){sub 2}, are studied by inelastic neutron scattering as a function of hydrostatic pressure. The anisotropy parameters D and B{sub 0}{sup 4}, which describe each Mn{sub 4} subunit, are essentially pressure independent, while the antiferromagnetic exchange coupling J between the two Mn{sub 4} subunits strongly depends on pressure, with an increase of 42% at 17 kbar. Additional pressure-dependent powder x-ray measurements allow a structural interpretation of the findings.

The $A$-site spinel compound $\mathrm{Mn}{\mathrm{Sc}}_{2}{\mathrm{S}}_{4}$ exhibits strong frustration effects with a low ordering temperature $({T}_{N}=2.3\phantom{\rule{0.3em}{0ex}}\mathrm{K})$. Detailed neutron-scattering investigations have been performed to study the magnetic ordering process and the associated magnetic excitations. The magnetic structure found at $T=1.5\phantom{\rule{0.3em}{0ex}}\mathrm{K}$ is a spiral within the $a\text{\ensuremath{-}}b$ plane characterized by a propagation vector of $\mathbf{q}=(3∕4,3∕4,0)$. The magnetic ordering process is spectroscopically reflected by a change from a purely quasielastic to an inelastic response. The quasielastic line width corresponds to a magnetic energy scale of $\ensuremath{\approx}1\phantom{\rule{0.3em}{0ex}}\mathrm{meV}$ which is consistent with the spin wave stiffness as determined from the magnon dispersion at low temperatures.

A high resolution inelastic neutron scattering (INS) study of fully deuterated Mn$_{12}$-acetate provides the most accurate spin Hamiltonian parameters for this prototype single molecule magnet so far. The Mn$_{12}$-clusters deviate from axial symmetry, a non-zero rhombic term in the model Hamiltonian leading to excellent agreement with observed positions and intensities of the INS peaks. The following parameter set provides the best agreement with the experimental data: $D=-0.0570(1)$ meV, $B_{4}^0=-2.78(7)\cdot 10^{-6}$ meV, $B_{4}^4=-3.2(6)\cdot 10^{-6}$ meV and $\mid$\textit{E}$\mid =6.8(15)\cdot 10^{-4}$ meV. Crystal dislocations are not the likely cause of the symmetry lowering. Rather, this study lends strong support to a recently proposed model, which is based on the presence of several molecular isomers with distinct spin Hamiltonian parameters., 4 pages, 4 figures

The anisotropy splitting in the ground state of the single-molecule magnet ${\mathrm{Mn}}_{4}{\mathrm{O}}_{3}\mathrm{Br}{(\mathrm{O}\mathrm{Ac})}_{3}{(\mathrm{dbm})}_{3}$ is studied by inelastic neutron scattering as a function of hydrostatic pressure. This allows a tuning of the anisotropy and thus the energy barrier for slow magnetization relaxation at low temperatures. The value of the negative axial anisotropy parameter ${D}_{\text{cluster}}$ changes from $\ensuremath{-}0.0627(1)\phantom{\rule{0.3em}{0ex}}\mathrm{meV}$ at ambient to $\ensuremath{-}0.0603(3)\phantom{\rule{0.3em}{0ex}}\mathrm{meV}$ at $12\phantom{\rule{0.3em}{0ex}}\mathrm{kbar}$ pressure, and in the same pressure range the height of the energy barrier between up and down spins is reduced from $1.260(5)\phantom{\rule{0.3em}{0ex}}\mathrm{meV}\phantom{\rule{0.5em}{0ex}}\text{to}\phantom{\rule{0.5em}{0ex}}1.213(9)\phantom{\rule{0.3em}{0ex}}\mathrm{meV}$. Since the $\mathrm{Mn}\mathrm{Br}$ bond is significantly softer and thus more compressible than the $\mathrm{Mn}\mathrm{O}$ bonds, pressure induces a tilt of the single ion ${\mathrm{Mn}}^{3+}$ anisotropy axes, resulting in the net reduction of the axial cluster anisotropy.

The oxygen and copper isotope effects on the relaxation rate of crystal-field excitations in the optimally doped high-temperature superconductor ${\mathrm{La}}_{1.81}{\mathrm{Ho}}_{0.04}{\mathrm{Sr}}_{0.15}{\mathrm{CuO}}_{4}$ have been investigated by means of inelastic neutron scattering. For the ${}^{16}\mathrm{O}$ compound there is clear evidence for the opening of an electronic pseudogap in the normal state at ${T}^{*}\ensuremath{\approx}60\mathrm{K},$ far above ${T}_{c}\ensuremath{\approx}32\mathrm{K}.$ Upon substituting ${}^{16}\mathrm{O}$ by ${}^{18}\mathrm{O},$ ${T}^{*}$ is shifted to about 70 K. On the other hand, no shift is found for the copper isotope substitution, i.e., ${T}^{*}{(}^{63}\mathrm{Cu})\ensuremath{\approx}{T}^{*}{(}^{65}\mathrm{Cu})\ensuremath{\approx}60\mathrm{K}.$ These results, together with the large oxygen and copper isotope effects on ${T}^{*}$ for ${\mathrm{HoBa}}_{2}{\mathrm{Cu}}_{4}{\mathrm{O}}_{8},$ give evidence that the pseudogap formation in the single-layer LSCO and bilayer YBCO type compounds is governed by an additional local mode in the latter.

Elementary excitations in valence bond magnets have a finite spin gap $\ensuremath{\Delta}=g{\ensuremath{\mu}}_{B}{H}_{c}$ to well-defined triplet states. The degeneracy of the triplet states is lifted in the presence of an external field, according to the Zeeman interaction term. The energy and intensity of the excitation spectra in $S=1/2$ valence bond ${\mathrm{KCuCl}}_{3}$ and ${\mathrm{TlCuCl}}_{3}$ are investigated by inelastic neutron scattering at finite external fields. Experimental observations along representative directions of reciprocal space are addressed up to ${H/H}_{c}\ensuremath{\sim}0.6$ and ${H/H}_{c}\ensuremath{\sim}0.9,$ respectively. A comprehensive analysis of the split Zeeman modes is reported, which shows excellent agreement with first principles. The obtained results extend former characterizations at $H=0$ and are of importance in the context of the field-driven quantum criticality realized in the sister compounds ${\mathrm{KCuCl}}_{3}$ and ${\mathrm{TlCuCl}}_{3}.$