Neutron scattering measurements of the lowest-energy TO phonons in the relaxor Pb(Mg 1/3 Nb 2/3 )O3 (PMN) are reported for 10 ≤ T ≤ 750 K. The soft mode, which is overdamped by the polar nanoregions below the Burns temperature T d = 620 K, surprisingly recovers below 220 K. The square of the soft mode energy (hω0) 2 increases linearly with decreasing temperature, and is consistent with the behavior of a ferroelectric soft mode. At 10 K hω0 reaches 11 meV, the same value observed in ferroelectric Pb(Zn 1/3 Nb 2/3 )O3 at low-T . An unusual broadening of the TA phonon starts at T d and disappears at 220 K, coincident with the recovery of the TO mode. These dynamics suggest that a well-developed ferroelectric state is established below 220 K.

We report neutron inelastic scattering measurements of the lowest-energy transverse optic (TO) phonon branch in the relaxor Pb(Mg1/3Nb2/3)O3 from 400 to 1100 K. Far above the Burns temperature T(d) approximately 620 K we observe well-defined propagating TO modes at all wave vectors q, and a zone center TO mode that softens in a manner consistent with that of a ferroelectric soft mode. Below T(d) the zone center TO mode is overdamped. This damping extends up to, but not above, the waterfall wave vector q(wf), which is a measure of the average size of the polar nanoregions.

We report a resonant inelastic x-ray scattering study of the dispersion relations of charge transfer excitations in insulating La2CuO4. These data reveal two peaks, both of which show two-dimensional characteristics. The lowest energy excitation has a gap energy of ∼ 2.2 eV at the zone center, and a dispersion of ∼ 1 eV. The spectral weight of this mode becomes dramatically smaller around (π, π). The second peak shows a smaller dispersion (∼ 0.5 eV) with a zone-center energy of ∼ 3.9 eV. We argue that these are both highly dispersive exciton modes damped by the presence of the electron-hole continuum.PACS numbers: 74.25.Jb, 74.72.Dn, 78.70.Ck, Understanding strongly correlated electron systems, such as the cuprate superconductors, remains at the heart of much of current condensed matter research. As a first step toward elucidating electron correlation effects in these systems, it is important to study the behavior of elementary excitations using various spectroscopic tools. For example, angle resolved photoemission spectroscopy (ARPES) has become an indispensable probe for studying the excitation spectrum of a single quasiparticle [1,2], while inelastic neutron scattering has been invaluable in the investigation of low-energy collective modes (1 ∼ 100 meV), such as phonons and magnons [3]. However, to date only limited information has been available on collective excitations at an energy scale on the order of ∼ 1 eV. This is unfortunate, since in this energy range, the electron dynamics are governed directly by the various hopping integrals and by the Coulomb interaction. Thus, an investigation of the dispersion relations of such collective charge excitations would yield invaluable information for any microscopic theory of charge dynamics in the copper oxides.In this Letter, we present a detailed study of the momentum-dependence of the charge excitations in La 2 CuO 4 , utilizing resonant inelastic x-ray scattering (RIXS). In the simplest picture of this insulating cuprate, the ground state consists of one hole per copper ion (Cu 2+ ), and the low-lying electronic excitations include excitons formed via a charge-transfer (CT) process, in which charge is moved from the oxygen onto the copper [4,5,6]. Specifically, an electron-hole pair, created by exciting an electron from the valence band -the ZhangRice (ZR) band [7] -to the conduction band across the CT gap, can form a bound exciton state as a result of the Coulomb interaction. This CT exciton is expected to have a large dispersion, since it has zero spin and can move without disturbing the antiferromagnetic order of the copper oxide plane. Consistent with this, our highresolution measurements have enabled us to identify an exciton-like feature at 2.2 eV with a dispersion of 1 eV. In addition, a second peak at slightly higher energy is also observed. This has a zone-center energy of 3.9 eV and a dispersion of 0.5 eV. Finally, we also discuss a dramatic reduction in spectral weight of the CT exciton observed near the (π π) position.The RIXS technique in the hard...

We present a comprehensive study of the temperature and doping dependence of the 500 meV peak observed at q = ͑ ,0͒ in resonant inelastic x-ray scattering ͑RIXS͒ experiments on La 2 CuO 4 . The intensity of this peak persists above the Néel temperature ͑T N = 320 K͒, but decreases gradually with increasing temperature, reaching zero at around T = 500 K. The peak energy decreases with temperature in close quantitative accord with the behavior of the two-magnon B 1g Raman peak in La 2 CuO 4 and, with suitable rescaling, agrees with the Raman peak shifts in EuBa 2 Cu 3 O 6 and K 2 NiF 4 . The overall dispersion of this excitation in the Brillouin zone is found to be in agreement with theoretical calculations for a two-magnon excitation. Upon doping, the peak intensity decreases analogous to the Raman mode intensity and appears to track the doping dependence of the spincorrelation length. Taken together, these observations strongly suggest that the 500 meV mode is magnetic in character and is likely a two-magnon excitation.