Positive temperature-dependent thermal conductivity induced by wavelike phonons in complex Ag-based argyrodites

The phonon transport mechanisms and the anomalous temperature-dependent lattice thermal conductivities (${\ensuremath{\kappa}}_{\mathrm{L}}$) in Ag-based argyrodites have not been fully understood. Herein, we systematically study the phonon thermal transport of five Ag-based crystalline argyrodites ${\mathrm{Ag}}_{7}{\mathrm{PS}}_{6}, {\mathrm{Ag}}_{7}{\mathrm{AsS}}_{6}, {\mathrm{Ag}}_{8}{\mathrm{SnS}}_{6}, {\mathrm{Ag}}_{8}{\mathrm{GeS}}_{6}$, and ${\mathrm{Ag}}_{9}{\mathrm{GaS}}_{6}$ utilizing perturbation theory and the unified theory thermal transport model. Our results show that, as the complexity of the unit cell increases, the proportion of the population terms declines while the coherence contributions become more significant, leading to the relatively weak temperature-dependent ${\ensuremath{\kappa}}_{\mathrm{L}}$ of ${\mathrm{Ag}}_{7}{\mathrm{PS}}_{6}$ and ${\mathrm{Ag}}_{7}{\mathrm{AsS}}_{6}$, while the more complex crystalline argyrodites, ${\mathrm{Ag}}_{8}{\mathrm{SnS}}_{6}, {\mathrm{Ag}}_{8}{\mathrm{GeS}}_{6}$, and ${\mathrm{Ag}}_{9}{\mathrm{GaS}}_{6}$, exhibiting a glass-like behavior in their temperature dependence of ${\ensuremath{\kappa}}_{\mathrm{L}}$. We attribute the positive temperature-dependent and ultralow ${\ensuremath{\kappa}}_{\mathrm{L}}$ of ${\mathrm{Ag}}_{8}{\mathrm{SnS}}_{6}, {\mathrm{Ag}}_{8}{\mathrm{GeS}}_{6}$, and ${\mathrm{Ag}}_{9}{\mathrm{GaS}}_{6}$ to the dominance of wavelike phonons and the strong phonon broadening. Furthermore, using laser flash measurements and the homogeneous nonequilibrium molecular dynamics simulations based on accurate machine learning neuroevolution potentials, we provide further evidence for the glass-like temperature-dependent ${\ensuremath{\kappa}}_{\mathrm{L}}$ of ${\mathrm{Ag}}_{8}{\mathrm{SnS}}_{6}$ and ${\mathrm{Ag}}_{8}{\mathrm{GeS}}_{6}$.