Anion Engineering Enables Concurrent Optimization of Phonon and Carrier Transport in AMg$_2$X$_2$ Zintl Thermoelectrics

The simultaneous suppression of lattice heat transport and enhancement of carrier transport is central to the development of high-performance thermoelectric materials. Here, we investigate the microscopic mechanisms governing phonon and carrier transport in CaAl$_2$Si$_2$-type AMg$_2$X$_2$ (A = Ca, Sr, Ba; X = P, As, Sb, Bi) Zintl compounds using first-principles calculations, machine-learning interatomic potentials, and Boltzmann transport theory. As X changes from P to Bi, the widening phonon band gap restricts three-phonon scattering channels and increases the relative importance of four-phonon processes. In CaMg$_2$Bi$_2$ and BaMg$_2$Bi$_2$, four-phonon scattering dominates the relaxation of low-frequency heat-carrying modes at 900 K. The Bi-based series also exhibits an anomalous increase in lattice thermal conductivity from Ca to Ba despite the increasing cation mass. Mode-resolved analysis links the lower thermal conductivity of CaMg$_2$Bi$_2$ to reduced low-frequency group velocities and stronger anharmonic scattering, with Ca-related mid-frequency vibrations providing additional four-phonon scattering channels. Including both particle-like and coherent contributions, its lattice thermal conductivity reaches 0.23 W$\cdot$m$^{-1}$K$^{-1}$ at 900 K. Meanwhile, the increasing covalent character of the vertical Mg-X bonds is accompanied by enhanced band-edge dispersion and reduced carrier effective masses. These electronic changes, together with conduction-band convergence, favor n-type transport and yield a predicted peak $ZT$ of 3.68 at 900 K in CaMg$_2$Bi$_2$. These results elucidate the interplay of phonon spectral structure and higher-order anharmonicity in thermal transport, alongside the distinct electronic response to anion substitution.