Electronic inhomogeneity appears to be an inherent characteristic of the enigmatic cuprate superconductors. Here we report the observation of charge-density-wave correlations in the model cuprate superconductor HgBa2CuO(4+δ) (T(c)=72 K) via bulk Cu L3-edge-resonant X-ray scattering. At the measured hole-doping level, both the short-range charge modulations and Fermi-liquid transport appear below the same temperature of about 200 K. Our result points to a unifying picture in which these two phenomena are preceded at the higher pseudogap temperature by q=0 magnetic order and the build-up of significant dynamic antiferromagnetic correlations. The magnitude of the charge modulation wave vector is consistent with the size of the electron pocket implied by quantum oscillation and Hall effect measurements for HgBa2CuO(4+δ) and with corresponding results for YBa2Cu3O(6+δ), which indicates that charge-density-wave correlations are universally responsible for the low-temperature quantum oscillation phenomenon.

We report detailed measurements of the low temperature magnetic phase diagram of Er2Ti2O7. Heat capacity and time-of-flight neutron scattering studies of single crystals reveal unconventional low-energy states. Er3+ magnetic ions reside on a pyrochlore lattice in Er2Ti2O7, where local XY anisotropy and antiferromagnetic interactions give rise to a unique frustrated system. In zero field, the ground state exhibits coexisting short and long-range order, accompanied by soft collective spin excitations previously believed to be absent. The application of finite magnetic fields tunes the ground state continuously through a landscape of noncollinear phases, divided by a zero temperature phase transition at micro{0}H{c} approximately 1.5 T. The characteristic energy scale for spin fluctuations is seen to vanish at the critical point, as expected for a second order quantum phase transition driven by quantum fluctuations.

Polarized small-angle neutron scattering studies of single-crystalline multiferroic BiFeO(3) reveal a long-wavelength spin density wave generated by ∼1° spin canting of the spins out of the rotation plane of the antiferromagnetic cycloidal order. This signifies weak ferromagnetism within mesoscopic regions of dimension 0.03 microns along [110], to several microns along [111], confirming a long-standing theoretical prediction. The average local magnetization is 0.06 μ(B)/Fe. Our results provide an indication of the intrinsic macroscopic magnetization to be expected in ferroelectric BiFeO(3) thin films under strain, where the magnetic cycloid is suppressed.

Examples of stable binary icosahedral quasicrystals are relatively rare, and at present there are no known examples featuring localized magnetic moments. These would represent an ideal model system for attaining a deeper understanding of the nature of magnetic interactions in aperiodic lattices. Here we report the discovery of a family of at least seven rare earth icosahedral binary quasicrystals, i-R-Cd (R  =  Gd to Tm, Y), six of which bear localized magnetic moments. Our work highlights the importance of carefully motivated searches through phase space and supports the proposal that, like icosahedral Sc12Zn88 (ref. ), binary quasicrystalline phases may well exist nearby known crystalline approximants, perhaps as peritectically forming compounds with very limited liquidus surfaces, offering very limited ranges of composition/temperature for primary solidification.