The cuprate high temperature superconductors exhibit a pronounced trend in which the superconducting transition temperature, $T_{rm c}$, increases with the number of CuO$_2$ planes, $n$, in the crystal structure. We compare the magnetic excitation sp
ectrum of Bi$_{2+x}$Sr$_{2-x}$CuO$_{6+delta}$ (Bi-2201) and Bi$_2$Sr$_2$Ca$_2$Cu$_3$O$_{10 + delta}$ (Bi-2223), with $n=1$ and $n=3$ respectively, using Cu $L_3$-edge resonant inelastic x-ray scattering (RIXS). Near the anti-nodal zone boundary we find the paramagnon energy in Bi-2223 is substantially higher than that in Bi-2201, indicating that multilayer cuprates host stronger effective magnetic exchange interactions, providing a possible explanation for the $T_{rm c}$ vs. $n$ scaling. In contrast, the nodal direction exhibits very strongly damped, almost non-dispersive excitations. We argue that this implies that the magnetism in the doped cuprates is partially itinerant in nature.
The charge and spin correlations in La$_{1.875}$Ba$_{0.125}$CuO$_4$ (LBCO 1/8) are studied using Cu $L_3$ edge resonant inelastic x-ray scattering (RIXS). The static charge order (CO) is observed at a wavevector of $(0.24,0)$ and its charge nature co
nfirmed by measuring the dependence of this peak on the incident x-ray polarization. The paramagnon excitation in LBCO 1/8 is then measured as it disperses through the CO wavevector. Within the experimental uncertainty no changes are observed in the paramagnon due to the static CO, and the paramagnon seems to be similar to that measured in other cuprates, which have no static CO. Given that the stripe correlation modulates both the charge and spin degrees of freedom, it is likely that subtle changes do occur in the paramagnon due to CO. Consequently, we propose that future RIXS measurements, realized with higher energy resolution and sensitivity, should be performed to test for these effects.
We investigate the high-energy magnetic excitation spectrum of the high-$T_c$ cuprate superconductor Bi$_2$Sr$_2$CaCu$_2$O$_{8+delta}$ (Bi-2212) using Cu $L_3$ edge resonant inelastic x-ray scattering (RIXS). Broad, dispersive magnetic excitations ar
e observed, with a zone boundary energy of $sim$300 meV and a weak dependence on doping. These excitations are strikingly similar to the bosons proposed to explain the high-energy `kink observed in photoemission. A calculation of the spin-response based on the ARPES-derived electronic structure and YRZ-quasi-particles reproduces the key features of the observed magnetic dispersions with no adjustable parameters. These results show that it is possible to reconcile the magnetic and electronic properties of the cuprates within a unified framework.
The dynamics of S=1/2 quantum spins on a 2D square lattice lie at the heart of the mystery of the cuprates cite{Hayden2004,Vignolle2007,Li2010,LeTacon2011,Coldea2001,Headings2010,Braicovich2010}. In bulk cuprates such as LCO{}, the presence of a weak
interlayer coupling stabilizes 3D N{e}el order up to high temperatures. In a truly 2D system however, thermal spin fluctuations melt long range order at any finite temperature cite{Mermin1966}. Further, quantum spin fluctuations transfer magnetic spectral weight out of a well-defined magnon excitation into a magnetic continuum, the nature of which remains controversial cite{Sandvik2001,Ho2001,Christensen2007,Headings2010}. Here, we measure the spin response of emph{isolated one-unit-cell thick layers} of LCO{}. We show that coherent magnons persist even in a single layer of LCO{} despite the loss of magnetic order, with no evidence for resonating valence bond (RVB)-like spin correlations cite{Anderson1987,Hsu1990,Christensen2007}. Thus these excitations are well described by linear spin wave theory (LSWT). We also observe a high-energy magnetic continuum in the isotropic magnetic response. This high-energy continuum is not well described by 2 magnon LSWT, or indeed any existing theories.
Graphene phonons are measured as a function of electron doping via the addition of potassium adatoms. In the low doping regime, the in-plane carbon G-peak hardens and narrows with increasing doping, analogous to the trend seen in graphene doped via t
he field-effect. At high dopings, beyond those accessible by the field-effect, the G-peak strongly softens and broadens. This is interpreted as a dynamic, non-adiabatic renormalization of the phonon self-energy. At dopings between the light and heavily doped regimes, we find a robust inhomogeneous phase where the potassium coverage is segregated into regions of high and low density. The phonon energies, linewidths and tunability are remarkably similar for 1-4 layer graphene, but significantly different to doped bulk graphite.
We present the results of a neutron scattering study of the high energy phonons in the superconducting graphite intercalation compound CaC$_6$. The study was designed to address hitherto unexplored aspects of the lattice dynamics in CaC$_6$, and in p
articular any renormalization of the out-of-plane and in-plane graphitic phonon modes. We present a detailed comparison between the data and the results of density functional theory (DFT). A description is given of the analysis methods developed to account for the highly-textured nature of the samples. The DFT calculations are shown to provide a good description of the general features of the experimental data. This is significant in light of a number of striking disagreements in the literature between other experiments and DFT on CaC$_6$. The results presented here demonstrate that the disagreements are not due to any large inaccuracies in the calculated phonon frequencies.
