Neutron scattering experiments on a polycrystalline sample of the frustrated pyrochlore magnet Tb2Ti2O7, which does not show any magnetic order down to 50 mK, have revealed that it shows condensation behavior below 0.4 K from a thermally fluctuating
paramagnetic state to a spin-liquid ground-state with quantum spin fluctuations. Energy spectra change from quasielastic scattering to a continuum with a double-peak structure at energies of 0 and 0.8 K in the spin-liquid state. Specific heat shows an anomaly at the crossover temperature.
We have performed magnetic susceptibility and neutron scattering measurements on polycrystalline Ag-In-RE (RE: rare-earth) 1/1 approximants. In the magnetic susceptibility measurements, for most of the RE elements, inverse susceptibility shows linear
behaviour in a wide temperature range, confirming well localized isotropic moments for the RE$^{3+}$ ions. Exceptionally for the light RE elements, such as Ce and Pr, non-linear behaviour was observed, possibly due to significant crystalline field splitting or valence fluctuation. For RE = Tb, the susceptibility measurement clearly shows a bifurcation of the field-cooled and zero-field-cooled susceptibility at $T_{rm f} = 3.7$~K, suggesting a spin-glass-like freezing. On the other hand, neutron scattering measurements detect significant development of short-range antiferromagnetic spin correlations in elastic channel, which accompanied by a broad peak at $hbaromega = 4$~meV in inelastic scattering spectrum. These features have striking similarity to those in the Zn-Mg-Tb quasicrystals, suggesting that the short-range spin freezing behaviour is due to local high symmetry clusters commonly seen in both the systems.
Quantum-critical behavior of the itinerant electron antiferromagnet (V0.9Ti0.1)2O3 has been studied by single-crystal neutron scattering. By directly observing antiferromagnetic spin fluctuations in the paramagnetic phase, we have shown that the char
acteristic energy depends on temperature as c_1 + c_2 T^{3/2}, where c_1 and c_2 are constants. This T^{3/2} dependence demonstrates that the present strongly correlated d-electron antiferromagnet clearly shows the criticality of the spin-density-wave quantum phase transition in three space dimensions.
Spin correlations and fluctuations in the 3d-transition-metal-based icosahedral quasicrystal Zn-Fe-Sc have been investigated by neutron scattering using polycrystalline samples. Magnetic diffuse scattering has been observed in the elastic experiment
at low temperatures, indicating development of static short-range-spin correlations. In addition, the inelastic scattering experiment detects a $Q$-independent quasielastic signal ascribed to single-site relaxational spin fluctuations. Above the macroscopic freezing temperature $T_{rm f} simeq 7$ K, the spin relaxation rate shows Arrhenius-type behavior, indicating thermally activated relaxation process. In contrast, the relaxation rate remains finite even at the lowest temperature, suggesting a certain quantum origin for the spin fluctuations below $T_{rm f}$.
