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The crystal structure and magnetic correlations in triangular antiferromagnet $\mathrm{Fe}\mathrm{Ga}{}_{2}\mathrm{S}{}_{4}$ are studied by x-ray diffraction, magnetic susceptibility, neutron diffraction, and neutron inelastic scattering. We report significant mixing at the cation sites and disentangle magnetic properties dominated by major and minor magnetic sites. The magnetic short-range correlations at $0.77\phantom{\rule{0.28em}{0ex}}{\AA{}}^{\ensuremath{-}1}$ correspond to the major sites and being static at base temperature they evolve into dynamic correlations around 30--50 K. The minor sites contribute to the magnetic peak at $0.6\phantom{\rule{0.28em}{0ex}}{\AA{}}^{\ensuremath{-}1}$, which vanishes at 5.5 K. Our analytical studies of triangular lattice models with bilinear and biquadratic terms provide the ratios between exchanges for the proposed ordering vectors. The modeling of the inelastic neutron spectrum within linear spin-wave theory results in the set of exchange couplings ${J}_{1}=1.7,\phantom{\rule{0.28em}{0ex}}{J}_{2}=0.9,\phantom{\rule{0.28em}{0ex}}{J}_{3}=0.8\phantom{\rule{0.28em}{0ex}}\mathrm{meV}$ for the bilinear Heisenberg Hamiltonian. However, not all features of the excitation spectrum are explained with this model.

We report a comprehensive investigation of the triple perovskite iridate ${\mathrm{Ba}}_{3}\mathrm{Co}{\mathrm{Ir}}_{2}{\mathrm{O}}_{9}$. Stabilizing in the hexagonal $P{6}_{3}/mmc$ symmetry at room temperature, this system transforms to a monoclinic $C2/c$ symmetry at the magnetic phase transition. On further reduction in temperature, the system partially distorts to an even lower symmetry ($P2/c$), with both these structurally disparate phases coexisting down to the lowest measured temperatures. The magnetic structure as determined from neutron diffraction data indicates a weakly canted antiferromagnetic structure, which is also supported by first-principles calculations. Theory indicates that the ${\mathrm{Ir}}^{5+}$ carries a finite magnetic moment, which is also consistent with the neutron data. This suggests that the putative $J=0$ state is avoided. Measurements of heat capacity, electrical resistance noise, and dielectric susceptibility all point toward the stabilization of a highly correlated ground state in the ${\mathrm{Ba}}_{3}\mathrm{Co}{\mathrm{Ir}}_{2}{\mathrm{O}}_{9}$ system.

Terbium gallium garnet (TGG), ${\mathrm{Tb}}_{3}{\mathrm{Ga}}_{5}{\mathrm{O}}_{12}$, is well known for its applications in laser optics but also exhibits complex low-temperature magnetism that is not yet fully understood. Its low-temperature magnetic order is determined by means of time-of-flight neutron powder diffraction. It is found to be a multiaxial antiferromagnet with magnetic ${\mathrm{Tb}}^{3+}$ ions forming six sublattices of magnetic moments aligned parallel and antiparallel to the $\ensuremath{\langle}100\ensuremath{\rangle}$ crystallographic directions of the cubic unit cell. The structure displays strong easy-axis anisotropy with respect to a twofold axis of symmetry in the local orthorhombic environment of the ${\mathrm{Tb}}^{3+}$ sites. The crystal-field splitting within the single-ion ground-state manifold is investigated by inelastic neutron scattering on powder samples. A strong temperature dependence of the quasidoublet ground state is observed and revised parameters of the crystal-field Hamiltonian are given. The results of bulk magnetic susceptibility and magnetization measurements are in good agreement with values based on the crystal-field model down to 20 K, where the onset of magnetic correlations is observed.

We study magnetic behavior of the ${\mathrm{Yb}}^{3+}$ ions on a frustrated pyrochlore lattice in the spinel ${\mathrm{CdYb}}_{2}{\mathrm{Se}}_{4}$. The crystal-electric-field parameters deduced from high-energy inelastic neutron scattering reveal a well-isolated ytterbium ground-state doublet with a weakly Ising character. Magnetic order studied by powder neutron diffraction evolves from the XY-type antiferromagnetic ${\mathrm{\ensuremath{\Gamma}}}_{5}$ state to a splayed icelike ferromagnet (both with $\mathbf{k}=0$) in applied magnetic field with ${B}_{c}=3\phantom{\rule{0.28em}{0ex}}\mathrm{T}$. Low-energy inelastic neutron scattering identifies weakly dispersive magnetic bands around 0.72 meV starting at $|\mathbf{Q}|=1.1\phantom{\rule{4pt}{0ex}}{\AA{}}^{\ensuremath{-}1}$ at zero field, which diminish with field and vanish above 3 T. We explain the observed magnetic behavior in framework of the nearest-neighbor anisotropic exchange model for effective $S=\frac{1}{2}$ Kramers doublets on the pyrochlore lattice. The estimated exchanges position the ${\mathrm{CdYb}}_{2}{\mathrm{Se}}_{4}$ spinel close to the phase boundary between the ${\mathrm{\ensuremath{\Gamma}}}_{5}$ and splayed ferromagnet states, similar to the Yb pyrochlores, suggesting an important role of the competition between these phases.

In spinels ACr2O4 (A=Mg, Zn), realization of the classical pyrochlore Heisenberg antiferromagnet model is complicated by a strong spin-lattice coupling: the extensive degeneracy of the ground state is lifted by a magneto-structural transition at TN = 12.5 K. We study the resulting low-temperature low-symmetry crystal structure by synchrotron x-ray diffraction. The consistent features of x-ray low-temperature patterns are explained by the tetragonal model of Ehrenberg et al. [Pow. Diff. 17, 230 (2002)], while other features depend on sample or cooling protocol. A complex, partially ordered magnetic state is studied by neutron diffraction and spherical neutron polarimetry. Multiple magnetic domains of configuration arms of the propagation vectors k1 = (1/2 1/2 0), k2 = (1 0 1/2 ) appear. The ordered moment reaches 1.94(3) μB/Cr3+ for k1 and 2.08(3) μB/Cr3+ for k2, if equal amount of the k1 and k2 phases is assumed. The magnetic arrangements have the dominant components along the [110] and [1−10] diagonals and a smaller c component.We use inelastic neutron scattering to investigate the spin excitations, which comprise a mixture of dispersive spin waves propagating from the magnetic Bragg peaks and resonance modes centered at equal energy steps of 4.5 meV.We interpret these as acoustic and optical spin wave branches, but show that the neutron scattering cross sections of transitions within a unit of two corner-sharing tetrahedra match the observed intensity distribution of the resonances. The distinctive fingerprint of clusterlike excitations in the optical spin wave branches suggests that propagating excitations are localized by the complex crystal structure and magnetic orders.

We present a model of the lattice dynamics of the rare-earth titanate pyrochlores R2Ti2O7 (R=Tb,Dy,Ho), which are important materials in the study of frustrated magnetism. The phonon modes are obtained by density functional calculations, and these predictions are verified by comparison with scattering experiments. Single crystal inelastic neutron scattering is used to measure acoustic phonons along high symmetry directions for R=Tb, Ho; single crystal inelastic x-ray scattering is used to measure numerous optical modes throughout the Brillouin zone for R=Ho; and powder inelastic neutron scattering is used to estimate the phonon density of states for R=Tb, Dy, Ho. Good agreement between the calculations and all measurements is obtained, allowing confident assignment of the energies and symmetries of the phonons in these materials under ambient conditions. Knowledge of the phonon spectrum is important for understanding spin-lattice interactions, and can be expected to be transferred readily to other members of the series to guide the search for unconventional magnetic excitations.

Recent experimental results have emphasized two aspects of Tb2Ti2O7 which have not been taken into account in previous attempts to construct theories of Tb2Ti2O7: the role of small levels of quenched structural disorder, which appears to control the formation of a long-range ordered state of as yet unknown nature; and the importance of strong coupling between spin and lattice degrees of freedom, which results in the hybridization of crystal field excitons and transverse acoustic phonons. In this work we examine the juncture of these two phenomena and show that samples with strongly contrasting behavior vis-a-vis the quenched disorder (i.e. with and without the transition to the ordered state), have identical magnetoelastic coupling. We also show that the comparison between single crystal and powder samples is more complicated than previously thought - the correlation between lattice parameter (as a measure of superstoichiometric Tb3+) and the existence of a specific heat peak, as observed in powder samples, does not hold for single crystals.

We investigated the crystal structure and lattice excitations of the ternary intermetallic stannide Ca3Ir4Sn13 using neutron and x-ray scattering techniques. For T > T* ~ 38 K the x-ray diffraction data can be satisfactorily refined using the space group Pm-3n. Below T* the crystal structure is modulated with a propagation vector of q = (1/2, 1/2, 0). This may arise from a merohedral twinning in which three tetragonal domains overlap to mimic a higher symmetry, or from a doubling of the cubic unit cell. Neutron diffraction and neutron spectroscopy results show that the structural transition at T* is of a second-order, and that it is well described by mean-field theory. Inelastic neutron scattering data point towards a displacive structural transition at T* arising from the softening of a low-energy phonon mode with an energy gap of Delta(120 K) = 1.05 meV. Using density functional theory the soft phonon mode is identified as a 'breathing' mode of the Sn12 icosahedra and is consistent with the thermal ellipsoids of the Sn2 atoms found by single crystal diffraction data.

${\mathrm{CoAl}}_{2}{\mathrm{O}}_{4}$ spinel with magnetic ${\mathrm{Co}}^{2+}$ ions on the diamond lattice is known to be magnetically frustrated. We compare neutron single-crystal diffraction patterns measured in zero and applied magnetic fields with the ones obtained from classical Monte Carlo models. In simulations we test the influence of various parameters on diffraction patterns: the ratio of nearest-, ${J}_{1}$, and next-nearest-, ${J}_{2}$, neighbor interactions, magnetic field applied along the principal crystallographic directions, and random disorder on the $A({\mathrm{Co}}^{2+})$ and $B({\mathrm{Al}}^{3+})$ sites. We conclude that the models considered so far explain the broadening of magnetic Bragg peaks in zero magnetic field and their anisotropic response to applied magnetic field only partly. As bulk properties of our single crystal are isotropic, we suggest that its microstructure, specifically $\ensuremath{\langle}111\ensuremath{\rangle}$-twin boundaries, could be a reason for the nonconventional magnetic order in ${\mathrm{CoAl}}_{2}{\mathrm{O}}_{4}$.

A quite unusual diffuse scattering phenomenology was observed in the single-crystal X-ray diffraction pattern of cubic perovskite BMT ($\mathrm{BaMg}_{1/3}\mathrm{Ta}_{2/3}\mathrm{O}_3$). The intensity of the scattering is parametrized as a set of cube-like objects located at the centers of reciprocal space unit cells, resembling very broad and cubic-shaped (1/2,1/2,1/2)-satellites. BMT belongs to perovskites of formula AB$'_{1/3}$B$"_{2/3}$O$_{3}$ (A=Mg, B$'=$Ta, B$"=$Mg). The cubes of the intensity can be attributed to the partial correlations of the occupancies of the B site. The pair correlation function is the Fourier transform of the diffuse scattering intensity and the latter's idealized form yields the unusual property of a power-law correlation decay with distance. Up to now this is observed only in a few exotic instances of magnetic order or nematic crystals. Therefore it cannot be classified as a short-range order phenomenon, as in most situations originating diffuse scattering. A Monte-Carlo search in configuration space yielded solutions that reproduce faithfully the observed diffuse scattering. Analysis of the results in terms of the electrostatic energy and the entropy point to this phase of BMT as a metastable state, kinetically locked, which could be the equilibrium state just below the melting point.

To clarify the reason for the coexistence of long-range antiferromagnetic order and metallic conductivity for ${\text{NaV}}_{2}{\text{O}}_{4}$, in which the V ions form quasi-one-dimensional zigzag chains along the $b$ axis, we have performed a neutron-scattering experiment using a powder sample down to 20 K. The analysis of the magnetic powder diffractogram below ${T}_{\text{N}}=140\text{ }\text{K}$ demonstrates the formation of an incommensurate spin-density-wave order with $\mathbit{k}=(0,0.191,0)$; the ordered moment was estimated as $(0,0,0.77{\ensuremath{\mu}}_{\text{B}})$ at 20 K.

Using neutron powder diffraction and Monte-Carlo simulations we show that a spin-liquid regime emerges at $all compositions in the diamond-lattice antiferromagnets Co(Al1-xCox)2O4. This spin-liquid regime induced by frustration due to the second-neighbour exchange coupling J2, is gradually superseded by antiferromagnetic collinear long-range order (k=0) at low temperatures. Upon substitution of Al3+ by Co3+ in the octahedral B-site the temperature range occupied by the spin-liquid regime narrows and TN increases. To explain the experimental observations we considered magnetic anisotropy D or third-neighbour exchange coupling J3 as degeneracy-breaking perturbations. We conclude that Co(Al1-xCox)2O4 is below the theoretical critical point J2/J1=1/8, and that magnetic anisotropy assists in selecting a collinear long-range ordered ground state, which becomes more stable with increasing x due to a higher efficiency of O-Co3+-O as an interaction path compared to O-Al3+-O.

We have studied the superconducting and magnetic properties of ${\text{Fe}}_{1+y}{\text{Se}}_{x}{\text{Te}}_{1\ensuremath{-}x}$ single crystals $(0\ensuremath{\le}x\ensuremath{\le}0.5)$ by magnetic susceptibility, muon-spin rotation, and neutron diffraction. We find three regimes of behavior: (i) commensurate magnetic order for $x\ensuremath{\lesssim}0.1$, (ii) bulk superconductivity for $x\ensuremath{\sim}0.5$, and (iii) a range $x\ensuremath{\approx}0.25--0.45$ in which superconductivity coexists with incommensurate magnetic order. The results are qualitatively consistent with two-band mean-field models in which itinerant magnetism and extended $s$-wave superconductivity are competing order parameters.

In ${\text{Cu}}_{2}{\text{CdB}}_{2}{\text{O}}_{6}$, a quantum-mechanical 1/2 magnetization plateau and classical antiferromagnetic long-range order (AF-LRO) appear. Two crystallographic Cu sites (Cu1 and Cu2) exist and have spin-1/2. It was speculated previously that spins on the Cu1 sites were in a nearly singlet state and that spins on the Cu2 sites formed the long-range order in weak magnetic fields and were almost saturated in fields of the magnetization plateau. As described herein, we report the magnetic structure of ${\text{Cu}}_{2}{^{114}\text{C}\text{d}}^{11}{\text{B}}_{2}{\text{O}}_{6}$ as determined using neutron powder-diffraction measurements. Contrary to that previous speculation, both the Cu1 and Cu2 spins have large magnetic moments in the ordered state. We discuss the mechanism which causes the magnetization plateau and AF-LRO.

We report a study of the triangular-lattice Heisenberg magnet $\mathrm{Ni}{\mathrm{Ga}}_{2}{\mathrm{S}}_{4}$ by the positive muon spin relaxation technique. We unravel three temperature regimes: (i) below ${T}_{c}=9.2(2)\phantom{\rule{0.3em}{0ex}}\mathrm{K}$, a spontaneous static magnetic field at the muon site is observed and the spin dynamics is appreciable: the time scale of the modes we probe is $\ensuremath{\simeq}7\phantom{\rule{0.3em}{0ex}}\mathrm{ns}$; (ii) an unconventional stretched exponential relaxation function is found for ${T}_{c}lTl{T}_{\text{cross}}$, where ${T}_{\text{cross}}=12.6\phantom{\rule{0.3em}{0ex}}\mathrm{K}$, which is a signature of a multichannel relaxation for this temperature range; and (iii) above ${T}_{\text{cross}}$, the relaxation is exponential as expected for a conventional compound. The transition at ${T}_{c}$ is of the continuous type. It occurs at a temperature slightly smaller than the temperature at which the specific heat displays a maximum at low temperature. This is reminiscent of the behavior expected for the Berezinskii--Kosterlitz--Thouless transition. We argue that these results reflect the presence of topological defects above ${T}_{c}$.

The increasing scientific and technological interest in nanoparticles has raised the need for fast, efficient and precise characterization techniques. Powder diffraction is a very efficient experimental method, as it is straightforward and non-destructive. However, its use for extracting information regarding very small particles brings some common crystallographic approximations to and beyond their limits of validity. Powder pattern diffraction calculation methods are critically discussed, with special focus on spherical particles with log-normal distribution, with the target of determining size distribution parameters. A 20-nm CeO$_{2}$ sample is analyzed as example., Comment: 10 pages, 4 figures; submitted to Phys. Rev. B