Magnetic response trends in cuprates and the t − t ′ Hubbard model

We perform a systematic study of static and dynamical magnetic properties of the $t\text{\ensuremath{-}}{t}^{\ensuremath{'}}$ Hubbard model in a parameter regime relevant for high-temperature superconducting cuprates. We adopt as solution method the dynamical mean-field theory approximation and its real-space cluster extension. Our results show that large ${t}^{\ensuremath{'}}/t$ suppresses incommensurate features and eventually leads to ferromagnetic instabilities for sufficiently large hole doping $x$. We identify isosbestic points which separate parts of the Brillouin zone with different scaling behaviors. Calculations are compared to available nuclear magnetic resonance, nuclear quadrupole resonance, inelastic neutron scattering, and resonant inelastic x-ray scattering experiments. We show that while many trends are correctly described, e.g., the evolution with $x$, some aspects of the spin-lattice relaxation rates can apparently only be explained invoking accidental cancellations. In order to capture the material dependence of magnetic properties in full, it may be necessary to add further degrees of freedom.