Anomalous Pressure Dependence of the Charge Density Wave and Fermi Surface Reconstruction in <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mrow> <mml:msub> <mml:mrow> <mml:mi>BaFe</mml:mi> </mml:mrow> <mml:mrow> <mml

We investigate the pressure evolution of charge density wave (CDW) order in the intermetallic compound BaFe_{2}Al_{9}, which undergoes a pronounced first-order CDW transition ∼112 K at ambient pressure. High-pressure electrical resistivity and magnetization measurements reveal a systematic enhancement of the CDW transition temperature (T_{CDW}) at a rate of ∼60 K/GPa, reaching 300 K under ∼3.2 GPa. The transition sharpness diminishes with pressure, indicating a crossover from first- to second-order behavior. Fermi liquid (FL) fits to the low-temperature resistivity reveal an increase in residual resistivity and a nonmonotonic evolution of the FL coefficient, indicating a pressure-induced Fermi surface (FS) reconstruction. Synchrotron x-ray diffraction reveals anisotropic lattice compression, a change in the compression trend of lattice parameters, and an abrupt change in microstrain at ∼3.6 GPa. Density functional theory calculations reveal pressure-induced flattening of quasi-two-dimensional FS sheets associated with the CDW nesting vector, consistent with enhanced nesting. These findings highlight the critical role of lattice strain and electronic structure evolution in stabilizing a high-temperature CDW phase, making BaFe_{2}Al_{9} a rare example of a three-dimensional material where pressure promotes rather than suppresses the CDW order.