We study magnetic and charge susceptibilities in the half-filled two-dimensional triangular Hubbard model within the dual fermion approximation in the metallic, Mott insulating, and crossover regions of parameter space. In the \textcolor{ black}{ insulating state}, we find strong spin fluctuations at the K point at low energy corresponding to the \textcolor{ black}{ 120$^{ \circ}$} antiferromagnetic order. These spin fluctuations persist into the metallic phase and move to higher energy. We also present data for simulated neutron spectroscopy and \textcolor{ black}{ spin-lattice} relaxation times, and perform direct comparisons to inelastic neutron spectroscopy experiments on the triangular material Ba$_8$CoNb$_6$O$_{ 24}$ and to the relaxation times on $\kappa$-(ET)$_2$Cu$_2$(CN)$_3$. Finally, we present charge susceptibilities in different areas of parameter space, which should correspond to momentum-resolved electron-loss spectroscopy measurements on triangular compounds.
Categories: cond-mat.str-el