The elucidation of the pseudogap phenomenon of the cuprates, a set of anomalous physical properties below the characteristic temperature T * and above the superconducting transition temperature T c , has been a major challenge in condensed matter physics for the past two decades [1]. Following initial indications of broken time-reversal symmetry in photoemission experiments [2], recent polarized neutron diffraction work demonstrated the universal existence of an unusual magnetic order below T * [3,4]. These findings have the profound implication that the pseudogap regime constitutes a genuine new phase of matter rather than a mere crossover phenomenon. They are furthermore consistent with a particular type of order involving circulating orbital currents, and with the notion that the phase diagram is controlled by a quantum critical point [5]. Here we report inelastic neutron scattering results for HgBa 2 CuO 4+δ (Hg1201) that reveal a fundamental collective magnetic mode associated with the unusual order, and that further support this picture. The mode's intensity rises below the same temperature T * and its dispersion is weak, as expected for an Ising-like order parameter [6]. Its energy of 52-56 meV and its enormous integrated spectral weight render it a new candidate for the hitherto unexplained ubiquitous electron-boson coupling features observed in spectroscopic studies [7][8][9][10].Inelastic neutron scattering (INS) is the most direct probe of magnetic excitations in solids. In the present work, we employed both spin-polarized and unpolarized INS measurements. The use of spin-polarized neutrons was crucial to unambiguously identify the magnetic response reported here, because such neutrons are separately collected according to whether their spins have or have not been flipped in the scattering process, which renders magnetic and nuclear scattering clearly distinguishable (Supplementary Information Section 1). Our measurements were carried out on three samples made of co-aligned crystals, which were grown by a self-flux method [11] and free from substantial macroscopic impurity phases and inhomogeneity (SI Section 2). Hg1201 exhibits the highest value of T c of all cuprates with one copper-oxygen plane per unit cell, has a simple tetragonal structure, and is furthermore thought to be relatively free of disorder effects [12,13]. The scattering wave vector is quoted as Q = Ha* + Kb* + Lc* ≡ (H,K,L) in reciprocal lattice units (r.l.u.). Neutron intensities are presented in normalized units in most figures to facilitate a direct comparison of the intensity among the measurements (SI Section 3).Spin-polarized INS data ( Fig. 1) demonstrate the existence of a magnetic excitation throughout the two-dimensional (2D) Brillouin zone in a nearly-optimally-doped sample (T c = 94.5 ± 2 K, denoted as OP95). Energy scans in the spin-flip channel reveal a resolution-limited feature at low temperatures, with a weak dispersion and a maximum of 56 meV at the 2D zone-corner q AF (H = K = 0.5). The feature cannot be due to a p...

Inelastic neutron-scattering measurements of single-CuO 2 -layer HgBa 2 CuO 4+␦ reveal an antiferromagnetic resonance with energy r =56 meV ͑Ϸ6.8k B T c ͒ below the superconducting transition temperature T c Ϸ 96 K. The resonance is energy-resolution limited and exhibits an intrinsic momentum width of about 0.2 Å −1 , consistent with prior work on several other cuprates. The rather large value of r is identical to the characteristic energy of the electron-boson spectral density obtained from recent optical conductivity work, consistent with the notion that the charge carriers are strongly coupled to magnetic fluctuations.

A neutron scattering investigation of the magnetoelectric coupling in PbFe 1/2 Nb 1/2 O 3 has been undertaken. Ferroelectric order occurs below 400 K, as evidenced by the softening with temperature and subsequent recovery of the zone center transverse optic phonon mode energy (h 0 ). Over the same temperature range, magnetic correlations become resolution limited on a terahertz energy scale. In contrast to the behavior of nonmagnetic disordered ferroelectrics [namely Pb(Mg,Zn) 1/3 Nb 2/3 O 3 ], we report the observation of a strong deviation from linearity in the temperature dependence of (h 0 ) 2 . This deviation is compensated by a corresponding change in the energy scale of the magnetic excitations, as probed through the first moment of the inelastic response. The coupling between the short-range ferroelectric and antiferromagnetic correlations is consistent with calculations showing that the ferroelectricity is driven by the displacement of the body-centered iron site, illustrating the multiferroic nature of magnetic-lead-based relaxors in the dynamical regime.

Neutron scattering for Nd 2−x Ce x CuO 4+␦ ͑x Ϸ 0.155, T c =25 K͒ reveals two distinct magnetic energy scales in the superconducting state: 1 Ϸ 6.4 meV and 2 Ϸ 4.5 meV. These magnetic energies agree quantitatively with the B 1g / B 2g and A 1g features observed in electronic Raman scattering, where the former is believed to indicate the maximum superconducting gap and the origin of the latter has remained unexplained. The data are inconsistent with previous claims of the existence of a magnetic resonance mode near 10 meV, but consistent with a resonance at 2 and with the recently established universal ratio of resonance energy to superconducting gap in unconventional superconductors ͓G. Yu et al., Nat. Phys. 5, 873 ͑2009͔͒.