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Y${}_{0.5}$Ca${}_{0.5}$BaCo${}_{4}$O${}_{7}$ was recently introduced as a possible candidate for capturing some of the predicted classical spin kagome ground-state features. Stimulated by this conjecture, we have taken up a more complete study of the spin correlations in this compound with neutron scattering methods on a powder sample characterized with high-resolution neutron diffraction and the temperature dependence of magnetic susceptibility and specific heat. We have found that the frustrated near-neighbor magnetic correlations involve not only the kagome planes but concern the full Co sublattice, as evidenced by the analysis of the wave-vector dependence of the short-range order. We conclude from our results that the magnetic moments are located on the Co sublattice as a whole and that correlations extend beyond the two-dimensional kagome planes. We identify intriguing dynamical properties, observing high-frequency fluctuations with a Lorentzian linewidth $\ensuremath{\Gamma}\ensuremath{\leqslant}20$ meV at ambient temperature. On cooling a low-frequency ($~$1 meV) dynamical component develops alongside the high-frequency fluctuations, which eventually becomes static at temperatures below $T\ensuremath{\approx}50$ K. The high-frequency response with an overall linewidth of $~$10 meV prevails at $T\ensuremath{\leqslant}2$ K, coincident with a fully elastic short-range-ordered contribution.

The low-temperature magnetic properties of ${\text{Tb}}_{2}{\text{Mo}}_{2}{\text{O}}_{7}$ have been studied with bulk susceptibility measurements and with elastic and high-resolution inelastic neutron scattering. This system is a spin glass with a freezing temperature ${T}_{g}\ensuremath{\sim}25\text{ }\text{K}$. A reverse Monte Carlo simulation of the neutron diffraction data shows weak ferromagnetic near-neighbor spatial correlations that do not extend beyond $\ensuremath{\lesssim}10\text{ }\text{\AA{}}$. Neutron measurements of the spin dynamics reveal a slowing down with decreasing temperature without an anomaly at the glass transition. A low-lying $Q$-independent mode is seen at $\ensuremath{\hbar}{\ensuremath{\omega}}_{0}\ensuremath{\sim}0.28\text{ }\text{meV}$. This dispersionless crystal electric field transition is measurable up to 60 K.

The critical helix fluctuations in the cubic noncentrosymmetric helimagnet MnSi have been studied by means of neutron small angle scattering and spin echo spectroscopy. To interpret the data, analytical formulas for the susceptibility in real space were obtained for the first time. The calculations presented here are based on the theory introduced in S. V. Grigoriev et al., Phys. Rev. B 72, 134420 (2005). According to this theory the temperature in the critical region can be divided into three parts with different types of chiral fluctuations: (i) ferromagnetic like; (ii) isotropic helical; and (iii) anisotropic helical ones. The fluctuations increase in amplitude with a randomly oriented but left-skewed pitch $\mathbf{k}$ upon approaching ${T}_{c}=29\text{ }\text{K}$. The scaling law of the inverse correlation length $\ensuremath{\kappa}$ exhibits a crossover at $\ensuremath{\kappa}\ensuremath{\approx}k$. The value of the critical exponent $\ensuremath{\nu}$ is changed from ${\ensuremath{\nu}}_{1}=0.40(6)$ in the vicinity of ${T}_{c}$ to ${\ensuremath{\nu}}_{2}=0.68(1)$ at high temperatures. The critical behavior of the relaxation rate $\ensuremath{\Gamma}$ along the easy direction obeys the dynamical scaling $\ensuremath{\Gamma}\ensuremath{\sim}{\ensuremath{\kappa}}^{Z}\ensuremath{\sim}{\ensuremath{\tau}}^{Z\ensuremath{\nu}}$ with a crossover at the temperature where $\ensuremath{\kappa}\ensuremath{\approx}k$ with ${Z}_{1}=2.5(1)$ for the high temperatures and ${Z}_{2}=1.10(3)$ close to ${T}_{c}$. Fluctuations become 100% left handed at the crossover point. The observed crossover is associated with the dominating influence of the Dzyaloshinskii-Moria interaction near ${T}_{c}$, responsible for the chiral ordering.

The spin dynamics of substituted colossal magnetoresistive (CMR) manganites of general formula ${\mathrm{La}}_{0.7}{\mathrm{Pb}}_{0.3}({\mathrm{Mn}}_{1\ensuremath{-}x}{\mathrm{Fe}}_{x}){\mathrm{O}}_{3}$, $0\ensuremath{\leqslant}x\ensuremath{\leqslant}0.2$ is investigated by means of neutron spin-echo measurements. Substitution of Mn by Fe leads to a strong decrease of the temperature of macroscopic magnetic long-range ordering with a concomitant enhancement of the CMR effect. For $x=0.2$, a long-range-ordered state is not achieved as a result of the increase in antiferromagnetic interactions brought forward by ${\mathrm{Fe}}^{+3}$-Mn couplings. The results display two relaxations having well separated decay constants. A fast process with a relaxation time of about $10\phantom{\rule{0.3em}{0ex}}\mathrm{ps}$ within the paramagnetic phase is found for all compositions. It shows a remarkably strong dependence with temperature and sample composition as the apparent activation energy for spin diffusion as well as the preexponential term exemplify. The physical origin of such a fast relaxation is assigned to heavily damped or overdamped spin waves (spin diffusion) on the basis of some signatures of excitations having finite frequencies found for the parent compound ${\mathrm{La}}_{0.7}{\mathrm{Pb}}_{0.3}\mathrm{Mn}{\mathrm{O}}_{3}$ at temperatures just below ${T}_{c}$, together with preliminary data on the effect of Fe doping on the stiffness constant. A slower relaxation is present for all compositions. Its temperature dependence follows the behavior of the macroscopic magnetization, and its intensity grows within the ordered ferromagnetic state. Its physical origin is ascribed to collective reorientation of nanoscale ferromagnetic domains on the basis of the wave-vector dependence of its relaxation rate and amplitude.