Evolution of Phonon Transport Across Structural Phase Transitions in MgAgSb

MgAgSb, a promising thermoelectric material, undergoes reversible phase transitions that drastically alter its thermal transport behavior. Using first-principles calculations, we systematically investigate the lattice thermal conductivity ($\kappa_L$) of its three phases: $\alpha$, $\beta$, and $\gamma$, revealing a progressive increase following $\alpha < \beta < \gamma$. This trend originates from distinct scattering mechanisms. Four-phonon scattering substantially suppresses the particle-like conductivity ($\kappa_p$) in the $\beta$ and $\gamma$ phases, while electron-phonon scattering provides a minor additional reduction. In contrast, the wave-like conductivity ($\kappa_c$) from coherent phonon tunneling is highest in the complex $\alpha$ phase, contributing up to 44\% of $\kappa_L$. Notably, the temperature dependence of $\kappa_L$ differs fundamentally between phases: in $\beta$, the weak $\kappa_p$ variation arises from a decreasing Gr\"{u}neisen parameter with temperature; in $\alpha$, the strong rise in $\kappa_c$ with temperature counteracts the decay of $\kappa_p$. Our findings establish a comprehensive picture of thermal transport in MgAgSb, highlighting the phase-dependent interplay between particle-like and wave-like phonon contributions.