Magnetic excitations and their anisotropy inYBa2Cu3O6+x: Slave-boson mean-field analysis of the bilayert-Jmodel

摘要: We perform a comprehensive analysis of the dynamical magnetic susceptibility $\ensuremath{\chi}(\mathbf{q},\ensuremath{\omega})$ in slave-boson mean-field scheme bilayer $t$-$J$ model. use model parameters appropriate for ${\mathrm{YBa}}_{2}{\mathrm{Cu}}_{3}{\mathrm{O}}_{6+x}$ (YBCO), typical high-${T}_{c}$ cuprate compound well studied by neutron scattering experiments. In $d$-wave pairing state, strongest spectral weight appears at $\mathbf{q}=\mathbf{Q}\ensuremath{\equiv}(\ensuremath{\pi},\ensuremath{\pi})$ and $\ensuremath{\omega}={\ensuremath{\omega}}_{\mathbf{Q}}^{\mathrm{res}}$, spreads into diamond-shaped shell around $\mathbf{Q}$ $\mathbf{q}$ space $\ensuremath{\omega}l{\ensuremath{\omega}}_{\mathbf{Q}}^{\mathrm{res}}$. This is due to collective mode, namely particle-hole bound which has downward $\ensuremath{\omega}$ versus dispersion $\mathbf{Q}$. Within high intensity shell, incommensurate (IC) signals $\mathbf{q}=(\ensuremath{\pi},\ensuremath{\pi}\ifmmode\pm\else\textpm\fi{}2\ensuremath{\pi}\ensuremath{\eta})$ $(\ensuremath{\pi}\ifmmode\pm\else\textpm\fi{}2\ensuremath{\pi}\ensuremath{\eta},\ensuremath{\pi})$ tend be stronger than diagonal (DIC) $\mathbf{q}=(\ensuremath{\pi}\ifmmode\pm\else\textpm\fi{}2\ensuremath{\pi}{\ensuremath{\eta}}^{\ensuremath{'}},\ensuremath{\pi}\ifmmode\pm\else\textpm\fi{}2\ensuremath{\pi}{\ensuremath{\eta}}^{\ensuremath{'}})$, especially large hole density $\ensuremath{\delta}$. For $\ensuremath{\omega}\ensuremath{\ll}{\ensuremath{\omega}}_{\mathbf{Q}}^{\mathrm{res}}$ IC completely disappear remains only DIC positions. $\ensuremath{\omega}g{\ensuremath{\omega}}_{\mathbf{Q}}^{\mathrm{res}}$ strong $\mathrm{Im}\phantom{\rule{0.2em}{0ex}}\ensuremath{\chi}(\mathbf{q},\ensuremath{\omega})$ tracing an upward are found interpreted as overdamped excitation near ${\ensuremath{\omega}}_{\mathbf{Q}}^{\mathrm{res}}$. normal $\mathrm{Im}\ensuremath{\chi}(\mathbf{q},\ensuremath{\omega})$ broad peak $\mathbf{q}=\mathbf{Q}$. That is, appear state. also study effects small orthorhombic anisotropy, intrinsic untwinned YBCO crystals. Because electron-electron correlations favoring shaped Fermi surface deformations, we expect enhanced anisotropy spectra. effect particularly pronounced low $\ensuremath{\delta}$ relatively temperature. The present theory provides rather detailed microscopic explanation most salient properties excitations observed YBCO.