Session S1: Magnetic Excitations in High Tc Superconductors

Spin Dynamics in the electron-doped high-$T_c$ superconductors Pr$_{0.88}$LaCe$_{0.12}$CuO$_{4-\delta}$

We briefly review results of recent neutron scattering experiments designed to probe the evolution of antiferromagnetic (AF) order and spin dynamics in the electron- doped Pr$_{0.88}$LaCe$_{0.12}$CuO$_{4-\delta}$ (PLCCO) as the system is tuned from its as-grown non-superconducting AF state into an optimally doped superconductor ($T_c$ = 27.5 K) without static AF order [1-3]. For under doped materials, a quasi-two- dimensional spin-density wave was found to coexist with three- dimensional AF order and superconductivity. In addition, the low-energy spin excitations follow Bose statistics. In the case of optimally doped material, we have discovered a magnetic resonance intimately related to superconductivity analogous to the resonance in hole-doped materials. On the other hand, the low energy spin excitations have very weak temperature dependence and do not follow Bose statistics, in sharp contrast to the as-grown nonsuperconducting materials. 1 Stephen D. Wilson, Pengcheng Dai, Shiliang Li, Songxue Chi, H. J. Kang, and J. W. Lynn, Nature (London) {\bf 442}, 59 (2006). 2 Stephen D. Wilson, Shiliang Li, Hyungje Woo, Pengcheng Dai, H. A. Mook, C. D. Frost, S. Komiya, and Y. Ando, Phys. Rev. Lett. {\bf 96}, 157001 (2006). 3. Stephen D. Wilson, Shiliang Li, Pengcheng Dai, Wei Bao, J. H. Chung, H. J. Kang, S.-H. Lee, S. Komiya, and Y. Ando, Phys. Rev. B {\bf 74}, 144514 (2006).   

Spin dynamics of YBa$_{2}$Cu$_{3}$O$_{6+x}$

We have used inelastic neutron scattering to determine the spin dynamics in untwinned single crystals of YBa$_{2}$Cu$_{3}$O$_{6+x}$ over a wide range of doping levels [1], with particular attention on its in-plane anisotropy [2]. Among other observations, we have found that the spin dynamics in the superconducting and pseudogap states are qualitatively different. The results allow incisive tests of current theories; including in particular theories based on static and fluctuating spin-charge stripes. We will also present initial results of an effort to provide a quantitative description of both the spin dynamics and the charge dynamics (determined by infrared and angle-resolved photoemission spectroscopies [3]) in the same YBa$_{2}$Cu$_{3}$O$_{6+x}$ single crystals. [1] S. Pailhes et al., Phys. Rev. Lett. 93, 167001 (2004)~; Phys. Rev. Lett. 96, 257001 (2006). \newline [2] V. Hinkov et al., Nature 430, 650 (2004); cond-mat/0601048. \newline [3] S.V. Borisenko et al., Phys. Rev. Lett. 96, 117004 (2006); V.B. Zabolotnyy et al., cond-mat/0608295.   

New Insight into an Under-doped Regime of High Tc Superconductivity - NMR Studies of Multi-layered Cuprates

High-temperature superconductivity (HTSC) has not been fully understood yet despite 20 year's intensive research. In particular, a possible interplay between antiferromagnetism (AFM) and HTSC remains as a most interesting problem. It is believed that they all fit into a universal phase diagram which suggests a competition between AFM and HTSC. Recently, however, through the systematic Cu-NMR studies on the Hg-, Tl- and Cu-based five-layered HTSC, we propose a novel phase diagram [1-3], which differs from the generic phase diagram of the HTSC reported so far, for instance, such as LSCO. The multi-layered HTSC compounds include two types of CuO$_{2}$ planes, an outer CuO$_{2}$ plane (OP) in a pyramidal coordination and an inner CuO$_{2}$ plane (IP) in a square one with no apical oxygen. Remarkable feature of the multi-layered HTSC is the presence of ideally flat CuO$_{2}$ planes that are homogeneously doped, which is ensured by the narrowest NMR spectral width among the various HTSC compounds with very high quality to date. It should be noted that the nearly non-doped AFM in the IP and the IP* takes place, whereas inhomogeneous magnetic phases such as spin-glass phase or stripe phase are not observed at both the IP's and the OP's. Instead, the existence of the doped AFM metallic (AFMM) phase at the IP and the IP* is remarkable at the boundary between AFM insulating (AFMI) phase and SC. This differs from the case of LSCO where the disorder-driven magnetic phases exist between the AFMI phase in N$_{h}<$ 0.02 and the SC phase in N$_{h}>$ 0.05. In an underlying phase diagram, the AFMM is extended to a higher hole density due to the flatness of CuO$_{2}$ plane with no apical oxygen and the homogeneous distribution of carrier density. By contrast, the prototype phase diagrams reported thus far are under the inevitable disorder effect associated with the chemical substitution introduced into the CuO$_{2}$ out-of-planes as corroborated by the observation of a disorder-driven transition from AFMM phase to AFMI phase found in theCu-based multi-layered system [3]. Through the discovery of the uniform mixing of AFM and HTSC in a single CuO$_{2 }$layer (OP) at Hg-1245(UD) with M$_{AFM}$=0.1$\mu _{B}$ and T$_{c}$=72 K., we will shed new light on the generic phase diagram of HTSC in the under-doped regimes. Namely, both phases may be mediated by the same magnetic interaction. It is this global phase diagram presented here to make one convince the presence of \textit{the AFM+SC uniformly coexisting phase}. From the results presented in this talk, we may raise a question; \textit{Do we need a bosonic glue to pair electrons in the uniformly coexisting state of AFM and SC ?} References: [1]. H. Mukuda et al.Phys. Rev. Lett. \textbf{96}, 087001 (2006); [2] N. Shimizu et al., submitted to PRL (2006). [3] H. Mukuda et al.,J. Phys. Soc. Jpn. \textbf{75}, No.12 (2006).   

Two Energy Scales in the Spin Excitations of La$_{2-x}$Sr$_{x}$Cu0$_{4}$

There has recently been considerable progress in electronic quasiparticle spectroscopy of high-\textit{Tc} superconductors. Angle resolved photoemission and tunnelling indicate that the quasiparticles are strongly coupled to excitations with energies in the range 40-70 meV. The recent debate has focused around phonons being the coupled excitations. The focus on phonons is largely because high-resolution phonon spectra are available and they contain considerable structure. Collective spin excitations are promising candidates for the strongly coupled excitations. However high resolution neutron data in the relevant 40-70 meV energy range have not been available for compounds where the quasiparticle anomalies are observed. In order to fill this gap in our knowledge, we have prepared 50g of single crystals of La$_{1.84}$Sr$_{0.16}$CuO$_{4}$ and carried out a new study of the magnetic excitations over a wide energy range, with considerably better energy resolution than our previous studies, and with good momentum resolution. Experiments were carried out using the MAPS spectrometer at the ISIS spallation neutron source. Our results demonstrate that the magnetic excitations have a two component structure with a low-frequency component strongest around 18 meV and a broader component strongest near 40-70 meV. The second component carries most of the spectral weight and its energy matches structure seen in photoemission and tunnelling spectra in the range 50-90 meV. Thus collective spin excitations may explain features of quasiparticle spectroscopies and are therefore likely to be strongly coupled excitations. The high-frequency excitations are most naturally interpreted as being due to residual antiferromagnetic interactions. \newline \newline [1] e.g. A. Lanzara, Nature 412, p510 (2001) \newline [2] e.g. J Lee et al., Nature 442, p546 (2006)   

Magnetic Excitations and the Exchange Energy Available for Superconductivity

We have made detailed comparisons of theoretical calculations and experimental neutron scattering results in absolute units in order to determine the temperature change of the nearest neighbor spin correlations in optimally doped YBCO as one goes from the normal to the superconducting state [1]. This allows us to estimate the magnetic exchange energy change that becomes available for superconducting condensation. Our results show that the available magnetic energy change is about 10-15 times larger than the energy necessary for superconducting condensation [1]. We discuss the issue of the spin sum rule and implications for a spin fluctuation driven pairing interaction as well as implications for low energy excitations in angular photoemission spectroscopy [2]. \newline \newline [1] H. Woo et al, Nature Physics 2, 600 (2006). \newline [2] T. Dahm et al, Phys. Rev. B 72, 214512 (2005).