Magnetic phase diagram and magnetic dynamics of YBa$_{2}$Cu$_{3}$O$_{6+x}$: Implications for the mechanism of high-T$_{c}$ superconductivity

We will present a comprehensive study of the magnetic phase diagram of the high-temperature superconductor YBa$_{2}$Cu$_{3}$O$_{6+x}$. Using elastic neutron scattering, we show that the phase diagram includes incommensurate spin density wave and electronic liquid-crystal states, in addition to the well-known antiferromagnetic, d-wave superconducting, and paramagnetic phases [1]. Using a combination of inelastic neutron scattering and resonant inelastic x-ray scattering, we have also arrived at a comprehensive picture of the magnetic excitation spectrum in all of these phases [2]. The dispersion relations and spectral weights of all compounds, including the slightly overdoped superconductor YBa$_{2}$Cu$_{3}$O$_{7}$, are closely similar to those of magnons in undoped, antiferromagnetically ordered YBa$_{2}$Cu$_{3}$O$_{6}$. The results are in excellent agreement with the spin excitations obtained by exact diagonalization of the t-J Hamiltonian on finite-sized clusters. A numerical solution of the Eliashberg equations based on the experimental spin excitation spectrum of YBa$_{2}$Cu$_{3}$O$_{7}$ reproduces its superconducting transition temperature T$_{c}$ within a factor of two, strongly supporting magnetic Cooper pairing models for the cuprates. Neutron scattering data of the buckling phonon in YBa$_{2}$Cu$_{3}$O$_{7}$ suggest that coupling to this phonon does not substantially enhance d-wave pairing [3]. \\[4pt] [1] D. Haug, V. Hinkov, Y. Sidis, P. Bourges, N. B. Christensen, A. Ivanov, T. Keller, C. T. Lin, B. Keimer, New J. Phys. \textbf{12}, 105006 (2010). \\[0pt] [2] M. Le Tacon, G. Ghiringhelli, J. Chaloupka, M. Moretti Sala, V. Hinkov, M. W. Haverkort, M. Minola, M. Bakr, K. J. Zhou, S. Blanco-Canosa, C. Monney, Y. T. Song, G. L. Sun, C. T. Lin, G. M. De Luca, M. Salluzzo, G. Khaliullin, T. Schmitt, L. Braicovich, B. Keimer, to be published. \\[0pt] [3] M. Raichle \textit{et al}., to be published.