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Fe$_{1+x}$Te is a two dimensional van der Waals antiferromagnet that becomes superconducting on anion substitution on the Te site. The parent phase of Fe$_{1+x}$Te is sensitive to the amount of interstitial iron situated between the iron-tellurium layers displaying collinear magnetic order coexisting with low temperature metallic resistivity for small concentrations of interstitial iron $x$ and helical magnetic order for large values of $x$. While this phase diagram has been established through scattering [see for example E. E. Rodriguez $\textit{et al.}$ Phys. Rev. B ${\bf{84}}$, 064403 (2011) and S. R\"ossler $\textit{et al.}$ Phys. Rev. B ${\bf{84}}$, 174506 (2011)], recent scanning tunnelling microscopy measurements [C. Trainer $\textit{et al.}$ Sci. Adv. ${\bf{5}}$, eaav3478 (2019)] have observed a different magnetic structure for small interstitial iron concentrations $x$ with a significant canting of the magnetic moments along the crystallographic $c$ axis of $\theta$=28 $\pm$ 3$^{\circ}$. In this paper, we revisit the magnetic structure of Fe$_{1.09}$Te using spherical neutron polarimetry and scanning tunnelling microscopy to search for this canting in the bulk phase and compare surface and bulk magnetism. The results show that the bulk magnetic structure of Fe$_{1.09}$Te is consistent with collinear in-plane order ($\theta=0$ with an error of $\sim$ 5$^{\circ}$). Comparison with scanning tunnelling microscopy on a series of Fe$_{1+x}$Te samples reveals that the surface exhibits a magnetic surface reconstruction with a canting angle of the spins of $\theta=29.8^{\circ}$. We suggest that this is a consequence of structural relaxation of the surface layer resulting in an out-of-plane magnetocrystalline anisotropy. The magnetism in Fe$_{1+x}$Te displays different properties at the surface when the symmetry constraints of the bulk are removed., Comment: 11 pages, 6 figures, to be Published in Phys. Rev. B

We apply neutron spectroscopy to measure the magnetic dynamics in the $S=3/2$ magnet $\ensuremath{\beta}\text{\ensuremath{-}}{\mathrm{CaCr}}_{2}{\mathrm{O}}_{4}$ (${\mathrm{T}}_{N}=21\text{ }\text{ }\mathrm{K}$). The low-energy fluctuations, in the ordered state, resemble large-$S$ linear spin waves from the incommensurate ground state. However, at higher energy transfers, these semiclassical and harmonic dynamics are replaced by an energy and momentum broadened continuum of excitations. Applying kinematic constraints required for energy and momentum conservation, sum rules of neutron scattering, and comparison against exact diagonalization calculations, we show that the dynamics at high-energy transfers resemble low-$S$ one-dimensional quantum fluctuations. $\ensuremath{\beta}\text{\ensuremath{-}}{\mathrm{CaCr}}_{2}{\mathrm{O}}_{4}$ represents an example of a magnet at the border between classical N\'eel and quantum phases, displaying dual characteristics.

VI$_{3}$ is a ferromagnet with planar honeycomb sheets of bonded V$^{3+}$ ions held together by van der Waals forces. We apply neutron spectroscopy to measure the two dimensional ($J/J_{c} \approx 17$) magnetic excitations in the ferromagnetic phase, finding two energetically gapped ($\Delta \approx k_{B} T_{c} \approx$ 55 K) and dispersive excitations. We apply a multi-level spin wave formalism to describe the spectra in terms of two coexisting domains hosting differing V$^{3+}$ orbital ground states built from contrasting distorted octahedral environments. This analysis fits a common nearest neighbor in-plane exchange coupling ($J$=-8.6 $\pm$ 0.3 meV) between V$^{3+}$ sites. The distorted local crystalline electric field combined with spin-orbit coupling provides the needed magnetic anisotropy for spatially long-ranged two-dimensional ferromagnetism in VI$_{3}$., Comment: (main text - 7 pages, 4 figures; supplementary information - 13 pages, 9 figures, to be published in Phys. Rev. B)

${\mathrm{Co}}^{2+}$ ions in an octahedral crystal field stabilize a ${j}_{\mathrm{eff}}=1/2$ ground state with an orbital degree of freedom and have been recently put forward for realizing Kitaev interactions, a prediction we have tested by investigating spin dynamics in two cobalt honeycomb lattice compounds, ${\mathrm{Na}}_{2}{\mathrm{Co}}_{2}{\mathrm{TeO}}_{6}$ and ${\mathrm{Na}}_{3}{\mathrm{Co}}_{2}{\mathrm{SbO}}_{6}$, using inelastic neutron scattering. We used linear spin wave theory to show that the magnetic spectra can be reproduced with a spin Hamiltonian including a dominant Kitaev nearest-neighbor interaction, weaker Heisenberg interactions up to the third neighbor, and bond-dependent off-diagonal exchange interactions. Beyond the Kitaev interaction that alone would induce a quantum spin liquid state, the presence of these additional couplings is responsible for the zigzag-type long-range magnetic ordering observed at low temperature in both compounds. These results provide evidence for the realization of Kitaev-type coupling in cobalt-based materials, despite hosting a weaker spin-orbit coupling than their $4d$ and $5d$ counterparts.

$\ensuremath{\alpha}\ensuremath{-}\mathrm{Co}{\mathrm{V}}_{2}{\mathrm{O}}_{6}$ consists of ${j}_{\mathrm{eff}}=\frac{1}{2}$ Ising spins located on an anisotropic triangular motif with magnetization plateaus in an applied field. We combine neutron diffraction with low temperature magnetization to investigate the magnetic periodicity in the vicinity of these plateaus. We find these steps to be characterized by metastable and spatially short-range ($\ensuremath{\xi}\ensuremath{\sim}10$ \AA{}) magnetic correlations with antiphase boundaries defining a local periodicity of $\ensuremath{\langle}{\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{T}}^{2}\ensuremath{\rangle}=\phantom{\rule{4pt}{0ex}}\ensuremath{\uparrow}\ensuremath{\downarrow}$ to $\ensuremath{\langle}{\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{T}}^{3}\ensuremath{\rangle}=\phantom{\rule{4pt}{0ex}}\ensuremath{\uparrow}\ensuremath{\uparrow}\ensuremath{\downarrow}$ and $\ensuremath{\langle}{\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{T}}^{4}\ensuremath{\rangle}=\phantom{\rule{4pt}{0ex}}\ensuremath{\uparrow}\ensuremath{\uparrow}\ensuremath{\downarrow}\ensuremath{\downarrow}$ or $\ensuremath{\uparrow}\ensuremath{\uparrow}\ensuremath{\uparrow}\ensuremath{\downarrow}$ spin arrangements. This shows the presence of spatially short range and metastable/hysteretic, commensurate magnetism in Ising magnetization steps.

Materials based on the cubic perovskite unit cell continue to provide the basis for technologically important materials with two notable recent examples being lead-based relaxor piezoelectrics and lead-based organic-inorganic halide photovoltaics. These materials carry considerable disorder, arising from site substitution in relaxors and molecular vibrations in the organic-inorganics, yet much of our understanding of these systems derives from the initial classic work of Prof. Roger A. Cowley, who applied both theory and neutron scattering methods while at Chalk River Laboratories to the study of lattice vibrations in SrTiO$_{3}$. Neutron scattering continues to play a vital role in characterizing lattice vibrations in perovskites owing to the simple cross section and the wide range of energy resolutions achievable with current neutron instrumentation. We discuss the dynamics that drive the phase transitions in the relaxors and organic-inorganic lead-halides in terms of neutron scattering and compare them to those in phase transitions associated with a ``central peak" and also a soft mode. We review some of the past experimental work on these materials and present new data from high-resolution time-of-flight backscattering spectroscopy taken on organic-inorganic perovskites. We will show that the structural transitions in disordered lead-based perovskites are driven by a broad frequency band of excitations., 23 pages, 9 figures, submitted as part of a special issue of JPCM on X-ray and Neutron Scattering and dedicated to the memory of Prof. R. A. Cowley

We apply neutron spectroscopy to measure the magnetic dynamics in the S=3/2 magnet β-CaCr_{2}O_{4} (T_{N}=21 K). The low-energy fluctuations, in the ordered state, resemble large-S linear spin waves from the incommensurate ground state. However, at higher energy transfers, these semiclassical and harmonic dynamics are replaced by an energy and momentum broadened continuum of excitations. Applying kinematic constraints required for energy and momentum conservation, sum rules of neutron scattering, and comparison against exact diagonalization calculations, we show that the dynamics at high-energy transfers resemble low-S one-dimensional quantum fluctuations. β-CaCr_{2}O_{4} represents an example of a magnet at the border between classical Néel and quantum phases, displaying dual characteristics.

Polycrystalline $\mathrm{CaF}{\mathrm{e}}_{2}{\mathrm{O}}_{4}$ and $\mathrm{CaC}{\mathrm{r}}_{0.5}\mathrm{F}{\mathrm{e}}_{1.5}{\mathrm{O}}_{4}$ have been investigated by elastic and inelastic neutron scattering. In agreement with previous reports, $\mathrm{CaF}{\mathrm{e}}_{2}{\mathrm{O}}_{4}$ undergoes two magnetic transitions, first to a $B$ phase, below ${T}_{\mathrm{NB}}=200\phantom{\rule{0.16em}{0ex}}\mathrm{K}$, then to an $A$ phase, below ${T}_{\mathrm{NA}}=175\phantom{\rule{0.16em}{0ex}}\mathrm{K}$, while substituted $\mathrm{CaC}{\mathrm{r}}_{0.5}\mathrm{F}{\mathrm{e}}_{1.5}{\mathrm{O}}_{4}$ undergoes a magnetic transition to the $B$ phase only, at ${T}_{\mathrm{N}}=125\phantom{\rule{0.16em}{0ex}}\mathrm{K}$. Each phase corresponds to staggered antiferromagnetic chains coupled either ferromagnetically $(A$ phase) or antiferromagnetically $(B$ phase). In the $A$ phase of $\mathrm{CaF}{\mathrm{e}}_{2}{\mathrm{O}}_{4}$, inelastic scattering measurements show clearly defined gapped spin waves, which can be modeled with classical calculations, based on a simple exchange Hamiltonian following the topology of the crystal structure. In contrast, in the $B$ phase of both compounds, the interpretation of the excitation spectrum evades completely the classical approach, even at low temperature. These results are interpreted based on an interchain exchange close to the threshold between ferromagnetic and antiferromagnetic bonding geometry. This induces random interchain coupling, thus creating magnetic exchange disorder whose dominating effect is to blur out the magnetic excitation spectrum of the $B$ phase. A magnetoelastic effect, through which the interchain coupling becomes sizably ferromagnetic, and which is not observed in $\mathrm{CaC}{\mathrm{r}}_{0.5}\mathrm{F}{\mathrm{e}}_{1.5}{\mathrm{O}}_{4}$, stabilizes the $A$ phase at low temperature in $\mathrm{CaF}{\mathrm{e}}_{2}{\mathrm{O}}_{4}$.

The organic-inorganic lead-halide perovskites are composed of organic molecules imbedded in an inorganic framework. The compounds with general formula ${\mathrm{CH}}_{3}{\mathrm{NH}}_{3}\mathrm{Pb}{X}_{3}$ ($\mathrm{MAPb}{X}_{3}$) display large photovoltaic efficiencies for halogens $X=\mathrm{Cl}$, Br, and I in a wide variety of sample geometries and preparation methods. The organic cation and inorganic framework are bound by hydrogen bonds that tether the molecules to the halide anions, and this has been suggested to be important to the optoelectronic properties. We have studied the effects of this bonding using time-of-flight neutron spectroscopy to measure the molecular dynamics in ${\mathrm{CH}}_{3}{\mathrm{NH}}_{3}{\mathrm{PbCl}}_{3}$ (${\mathrm{MAPbCl}}_{3}$). Low-energy/high-resolution neutron backscattering reveals thermally activated molecular dynamics with a characteristic temperature of $\ensuremath{\sim}95$ K. At this same temperature, higher-energy neutron spectroscopy indicates the presence of an anomalous broadening in energy (reduced lifetime) associated with the molecular vibrations. By contrast, neutron powder diffraction shows that a spatially long-range structural phase transitions occurs at 178 K (cubic $\ensuremath{\rightarrow}$ tetragonal) and 173 K (tetragonal $\ensuremath{\rightarrow}$ orthorhombic). The large difference between these two temperature scales suggests that the molecular and inorganic lattice dynamics in ${\mathrm{MAPbCl}}_{3}$ are actually decoupled. With the assumption that underlying physical mechanisms do not change with differing halogens in the organic-inorganic perovskites, we speculate that the energy scale most relevant to the photovoltaic properties of the lead-halogen perovskites is set by the lead-halide bond, not by the hydrogen bond.

${\mathrm{Ba}}_{3}{\mathrm{NbFe}}_{3}{\mathrm{Si}}_{2}{\mathrm{O}}_{14}$ (langasite) is structurally and magnetically single-domain chiral with the magnetic helicity induced through competing symmetric exchange interactions. Using neutron scattering, we show that the spin waves in antiferromagnetic langasite display directional anisotropy. On applying a time-reversal symmetry breaking magnetic field along the $c$ axis, the spin-wave energies differ when the sign is reversed for either the momentum transfer $\ifmmode\pm\else\textpm\fi{}\stackrel{P\vec}{Q}$ or applied magnetic field $\ifmmode\pm\else\textpm\fi{}{\ensuremath{\mu}}_{0}\mathrm{H}$. When the field is applied within the crystallographic $ab$ plane, the spin-wave dispersion is directionally isotropic and symmetric in $\ifmmode\pm\else\textpm\fi{}{\ensuremath{\mu}}_{0}\mathrm{H}$. However, a directional anisotropy is observed in the spin-wave intensity. We discuss this directional anisotropy in the dispersion in langasite in terms of a field-induced precession of the dynamic unit cell staggered magnetization resulting from a broken twofold symmetry. Directional anisotropy, often referred to as nonreciprocal responses, can occur in antiferromagnetic phases in the absence of the Dzyaloshinskii-Moriya interaction or other effects resulting from spin-orbit coupling.

The acoustic phonons in the organic-inorganic lead halide perovskites have been reported to have anomalously short lifetimes over a large part of the Brillouin zone. The resulting shortened mean free paths of the phonons have been implicated as the origin of the low thermal conductivity. We apply neutron spectroscopy to show that the same acoustic phonon energy linewidth broadening (corresponding to shortened lifetimes) occurs in the fully inorganic ${\mathrm{CsPbBr}}_{3}$ by comparing the results on the organic-inorganic ${\mathrm{CH}}_{3}{\mathrm{NH}}_{3}{\mathrm{PbCl}}_{3}$. We investigate the critical dynamics near the three zone boundaries of the cubic $Pm\overline{3}m$ Brillouin zone of ${\mathrm{CsPbBr}}_{3}$ and find energy and momentum broadened dynamics at momentum points where the Cs-site ($A$-site) motions contribute to the cross section. Neutron diffraction is used to confirm that both the Cs and Br sites have unusually large thermal displacements with an anisotropy that mirrors the low temperature structural distortions. The presence of an organic molecule is not necessary to disrupt the low-energy acoustic phonons at momentum transfers located away from the zone center in the lead halide perovskites and such damping may be driven by the large displacements or possibly disorder on the $A$ site.

CoO has an odd number of electrons in its unit cell, and therefore is expected to be metallic. Yet, CoO is strongly insulating owing to significant electronic correlations, thus classifying it as a Mott insulator. We investigate the magnetic fluctuations in CoO using neutron spectroscopy. The strong and spatially far-reaching exchange constants reported in [Sarte et al. Phys. Rev. B 98 024415 (2018)], combined with the single-ion spin-orbit coupling of similar magnitude [Cowley et al. Phys. Rev. B 88, 205117 (2013)] results in significant mixing between $j_{eff}$ spin-orbit levels in the low temperature magnetically ordered phase. The high degree of entanglement, combined with the structural domains originating from the Jahn-Teller structural distortion at $\sim$ 300 K, make the magnetic excitation spectrum highly structured in both energy and momentum. We extend previous theoretical work on PrTl$_{3}$ [Buyers et al. Phys. Rev. B 11, 266 (1975)] to construct a mean-field and multi-level spin exciton model employing the aforementioned spin exchange and spin-orbit coupling parameters for coupled Co$^{2+}$ ions on a rocksalt lattice. This parameterization, based on a tetragonally distorted type-II antiferromagnetic unit cell, captures both the sharp low energy excitations at the magnetic zone center, and the energy broadened peaks at the zone boundary. However, the model fails to describe the momentum dependence of the excitations at high energy transfers, where the neutron response decays faster with momentum than the Co$^{2+}$ form factor. We discuss such a failure in terms of a possible breakdown of localized spin-orbit excitons at high energy transfers., (main text - 21 pages, 12 figures; supplementary information - 15 pages, 3 figures, to be published in Phys. Rev. B)

CeRhSi$_{3}$ is a superconductor under pressure coexisting with a weakly antiferromagnetic phase characterized by a Bragg peak at $\vec{q}_{0}$=($\sim$ 0.2, 0, 0.5) (N. Aso et al. J. Magn. Magn. Mater. 310, 602 (2007)). The compound is also a heavy fermion material with a large specific heat coefficient $\gamma$=110 mJ $\cdot$ mol$^{-1}$ $\cdot$ K$^{-2}$ and a high Kondo temperature of $T_{K}$=50 K indicative that CeRhSi$_{3}$ is in a strongly Kondo screened state. We apply high resolution neutron spectroscopy to investigate the magnetic fluctuations in the normal phase, at ambient pressures, and at low temperatures. We measure a commensurate dynamic response centered around the $\vec{Q}$=(0, 0, 2) position that gradually evolves to H$\sim$ 0.2 with decreasing temperature and/or energy transfers. The response is broadened both in momentum and energy and not reminiscent of sharp spin wave excitations found in insulating magnets where the electrons are localized. We parameterize the excitation spectrum and temperature dependence using a heuristic model utilizing the random phase approximation to couple relaxing Ce$^{3+}$ ground state Kramers doublets with a Kondo-like dynamic response. With a Ruderman-Kittel-Kasuya-Yosida (RKKY) exchange interaction within the $ab$ plane and an increasing single site susceptibility, we can qualitatively reproduce the neutron spectroscopic results in CeRhSi$_{3}$ and namely the trade-off between scattering at commensurate and incommensurate positions. We suggest that the antiferromagnetic phase in CeRhSi$_{3}$ is driven by weakly correlated relaxing localized Kramers doublets and that CeRhSi$_{3}$ at ambient pressures is on the border between a Rudderman-Kittel-Yosida antiferromagnetic state and a Kondo screened phase where static magnetism is predominately absent., Comment: (11 pages, 8 figures, to be published in Physical Review B)

The antiferromagnetic mixed valence ternary oxide α-CoV3O8 displays disorder on the Co 2+ site that is inherent to the Ibam space group resulting in a local selection rule requiring one Co 2+ and one V 4+ reside next to each other, thus giving rise to an intrinsically disordered magnet without the need for any external influences such as chemical dopants or porous media. The zero field structural and dynamic properties of α-CoV3O8 have been investigated using a combination of neutron and x-ray diffraction, DC susceptibility, and neutron spectroscopy. The low temperature magnetic and structural properties are consistent with a random macroscopic distribution of Co 2+ over the 16k metal sites. However, by applying the sum rules of neutron scattering we observe the collective magnetic excitations are parameterized with an ordered Co 2+ arrangement and critical scattering consistent with a three dimensional Ising universality class. The low energy spectrum is well-described by Co 2+ cations coupled via a three dimensional network composed of competing ferromagnetic and stronger antiferromagnetic superexchange within the ab plane and along c, respectively. While the extrapolated Weiss temperature is near zero, the 3D dimensionality results in long range antiferromagnetic order at T N ∼ 19 K. A crystal field analysis finds two bands of excitations separated in energy at ω ∼ 5 meV and 25 meV, consistent with a j eff = 1 2 ground state with little mixing between spin-orbit split Kramers doublets. A comparison of our results to the random 3D Ising magnets and other compounds where spin-orbit coupling is present indicate that the presence of an orbital degree of freedom, in combination with strong crystal field effects and well-separated j eff manifolds may play a key role in making the dynamics largely insensitive to disorder.

Lead halide hybrid perovskites consist of an inorganic framework hosting a molecular cation located in the interstitial space. These compounds have been extensively studied as they have been identified as promising materials for photovoltaic applications. In particular, the interaction between the molecular cation and the inorganic framework has been suggested to influence the electronic properties. CH$_3$NH$_3$PbCl$_3$ undergoes several structural transitions associated with both distortion of the octahedra and orientational ordering of the CH$_3$NH$_3$ cation. We have measured the low-frequency lattice dynamics using neutron spectroscopy. We report an anomaly in the acoustic phonon linewidth towards the high-symmetry point $\textbf{Q}_X=(2,\frac{1}{2}, 0)$ when approaching the transitions, and a hardening of the entire phonon branch with decreasing temperature. Measurements at the Brillouin zone edges $\textbf{Q}_X=(2,\frac{1}{2}, 0)$, $\textbf{Q}_M=(\frac{3}{2},\frac{1}{2}, 0)$, and $\textbf{Q}_R=(\frac{3}{2},\frac{3}{2}, \frac{5}{2})$ show central peaks appearing at the lower temperature transition. We discuss the presence of both central peaks and acoustic phonon instabilities as evidence of a strong coupling between the inorganic framework and the molecular cation.

${\mathrm{RbFe}}^{2+}{\mathrm{Fe}}^{3+}{\mathrm{F}}_{6}$ is an example of a charge ordered antiferromagnet where iron sites, with differing valences, are structurally separated into two interpenetrating sublattices. The low temperature magnetically ordered ${\mathrm{Fe}}^{2+}$ ($S=2$) and ${\mathrm{Fe}}^{3+}$ ($S=5/2$) moments form a noncollinear orthogonal structure with the ${\mathrm{Fe}}^{3+}$ site displaying a reduced static ordered moment. Neutron spectroscopy on single crystals finds two distinct spin wave branches with a dominant coupling along the ${\mathrm{Fe}}^{3+}$ chain axis ($b$ axis). High resolution spectroscopic measurements find an intense energy and momentum broadened magnetic band of scattering bracketing a momentum-energy region where two magnon processes are kinematically allowed. These anharmonic excitations are enhanced in this noncollinear magnet owing to the orthogonal spin arrangement.

Neutron spectroscopy was applied to study the magnetic interactions of orbitally degenerate Co2+ on a host MgO rocksalt lattice where no long-range spin or orbital order exists. The paramagnetic nature of the substituted monoxide Co0.03Mg0.97O allows for the disentanglement of spin exchange and spin-orbit interactions. By considering the prevalent excitations from Co2+ spin pairs, we extract seven exchange constants out to the fourth coordination shell. An antiferromagnetic next-nearest-neighbor 180◦ exchange interaction is dominant; however, dual ferromagnetic and antiferromagnetic interactions are observed for pairings with other pathways. These interactions can be understood in terms of a combination of orbital degeneracy in the t2g channel and the Goodenough-Kanamori-Anderson rules. Our work suggest that such a hierarchy of exchange interactions exists in transition-metal-based oxides with a t2g orbital degeneracy.

RbFe^{2+}Fe^{3+}F_{6} is an example of a charge ordered antiferromagnet where iron sites, with differing valences, are structurally separated into two interpenetrating sublattices. The low temperature magnetically ordered Fe^{2+} (S=2) and Fe^{3+} (S=5/2) moments form a noncollinear orthogonal structure with the Fe^{3+} site displaying a reduced static ordered moment. Neutron spectroscopy on single crystals finds two distinct spin wave branches with a dominant coupling along the Fe^{3+} chain axis (b axis). High resolution spectroscopic measurements find an intense energy and momentum broadened magnetic band of scattering bracketing a momentum-energy region where two magnon processes are kinematically allowed. These anharmonic excitations are enhanced in this noncollinear magnet owing to the orthogonal spin arrangement.

The spin dynamics in the distorted triangular lattice antiferromagnet $\ensuremath{\alpha}\ensuremath{-}{\mathrm{SrCr}}_{2}{\mathrm{O}}_{4}$ has been investigated by inelastic neutron scattering on a single crystal. The spin wave dispersion has been mapped out in the $(0\phantom{\rule{4pt}{0ex}}k\phantom{\rule{4pt}{0ex}}l)$ and $(h\phantom{\rule{4pt}{0ex}}k\phantom{\rule{4pt}{0ex}}0)$ planes, and modeled by spin wave calculations, in order to determine the intraplane and interplane exchange couplings. Comparison with $\ensuremath{\alpha}\ensuremath{-}{\mathrm{CaCr}}_{2}{\mathrm{O}}_{4}$ shows that, despite the smaller lattice distortion of $\ensuremath{\alpha}\ensuremath{-}{\mathrm{SrCr}}_{2}{\mathrm{O}}_{4}$, the deviation from a perfect triangular lattice still affects the spin dynamics of the Sr compound, with a soft mode, similar to the one observed in the Ca counterpart, being observed in (020). Although $\ensuremath{\alpha}\ensuremath{-}{\mathrm{SrCr}}_{2}{\mathrm{O}}_{4}$ is further away from a magnetic phase boundary than its Ca counterpart, its dynamic magnetic properties still show intriguing features, which are discussed as quantum fluctuations arising from a two-magnon continuum.

We have studied the magnetic properties of ${\mathrm{Na}}_{2}{\mathrm{Co}}_{2}{\mathrm{TeO}}_{6}$, which features a honeycomb lattice of magnetic ${\mathrm{Co}}^{2+}$ ions, through macroscopic characterization and neutron diffraction on a powder sample. We have shown that this material orders in a zigzag antiferromagnetic structure. In addition to allowing a linear magnetoelectric coupling, this magnetic arrangement displays very peculiar spatial magnetic correlations, larger in the honeycomb planes than between the planes, which do not evolve with the temperature. We have investigated this behavior by classical Monte Carlo calculations using the ${J}_{1}\text{\ensuremath{-}}{J}_{2}\text{\ensuremath{-}}{J}_{3}$ model on a honeycomb lattice with a small interplane interaction. Our model reproduces the experimental neutron structure factor, although its absence of temperature evolution must be due to additional ingredients, such as chemical disorder or quantum fluctuations enhanced by the proximity to a phase boundary.

Random dilution effects in the magnetic zigzag ladder (${J}_{1}\ensuremath{-}{J}_{2}$ chain) $\ensuremath{\beta}\text{\ensuremath{-}}\mathrm{CaC}{\mathrm{r}}_{2\ensuremath{-}x}\mathrm{S}{\mathrm{c}}_{x}{\mathrm{O}}_{4}$ have been investigated combining magnetic susceptibility, specific heat measurements, and neutron scattering. The pseudogapped magnetic excitations observed above ${T}_{\mathrm{N}}$ in $\ensuremath{\beta}\text{\ensuremath{-}}\mathrm{CaC}{\mathrm{r}}_{2}{\mathrm{O}}_{4} (x=0)$ persist up to $x=0.3$ with an increasing characteristic frequency ${E}_{0}$ but vanish for $x=0.5$ for which a quasielastic signal extending up to $8\phantom{\rule{0.16em}{0ex}}\mathrm{meV}$ becomes the characteristic feature of the magnetic spectrum. Magnetic ordering is seen up to $x=0.3$ with decreased ordering temperature ${T}_{\mathrm{N}}$ and correlation length. The results are interpreted in terms of the progressive confinement of one-dimensional excitations within shorter chains as $x$ increases and emphasize the crucial role of ${J}_{2}$ in propagating magnetic excitations. For an average chain length $l$ smaller than \ensuremath{\sim}16 magnetic atoms, the system breaks apart into a set of disconnected units with the dynamical properties of a spin glass.