The structure of the high-energy spin excitations in YBa$_2$Cu$_3$O$_{6+x}$*

The most obvious feature in the magnetic excitations of high-$T_{c}$ superconductors is the so-called `resonance-mode'. This mode is strongly coupled to the superconductivity, however, it has not been found in the La$_{2-x}$(Ba,Sr)$_{x}$CuO$_{4}$ family and is not universally present in Bi$_{2}$Sr$_{2}$CaCu$_{2}$O$_{8+\delta }$. Here we use inelastic neutron scattering to characterize other excitations at higher energies which may be relevant to the superconductive pairing in YBa$_{2}$Cu$_{3}$O$_{6.6}$. We observe a square-shaped continuum of excitations in reciprocal space [1]. These excitations have energies greater than the superconducting pairing energy, are present at $T_{c}$, and have spectral weight far exceeding that of the `resonance'. The discovery of similar excitations in La$_{2-x}$Ba$_{x}$CuO$_{4}$\ [2] suggests that they are a general property of the copper oxides, and a candidate for mediating the electron pairing. Our data show that the high-energy magnetic excitations in the high-temperature superconductor YBa$_{2}$Cu$_{3}$O$_{6.6}$ consists of a continuum of scattering bounded by a square and peaked at wavevector positions \textbf{Q}$_{\varepsilon }$ =(1/2$\pm \varepsilon $,1/2$\pm \varepsilon )$ and (1/2$\pm \varepsilon $,1/2$\mp \varepsilon )$. A similar structure is observed in the high-energy magnetic excitations of the magnetically ordered but weakly superconducting compound La$_{1.85}$Ba$_{0.125}$CuO$_{4}$\ [2]. This suggests there is universality, both in the low-energy and the high-energy spin dynamics between two very different classes of high-$T_{c}$ superconductor. \\ \ [1] S.M. Hayden, H.A. Mook, P.C. Dai, T.G. Perring, and F. Dogan, Nature \textbf{429}, 531-534 (2004) \\ \ [2] J.M. Tranquada, H. Woo, T.G. Perring, H. Goka, G.D. Gu , G. Xu, M. Fujita, K.Yamada K, Nature \textbf{429,} 534-538 (2004).