Robust antiferromagnetic spin waves across the metal-insulator transition in hole-doped BaMn$_{2}$As$_{2}$

BaMn$_{2}$As$_{2}$ is an antiferromagnetic insulator where a metal-insulator transition occurs with hole doping via the substitution of Ba with K. The metal-insulator transition causes only a small suppression of the N\'eel temperature ($T_\mathrm{N}$) and the ordered moment, suggesting that doped holes interact weakly with the Mn spin system. Powder inelastic neutron scattering measurements were performed on three different powder samples of Ba$_{1-x}$K$_{x}$Mn$_{2}$As$_{2}$ with $x=$0, 0.125 and 0.25 to study the effect of hole doping and metallization on the spin dynamics of these compounds. We compare the neutron intensities to a linear spin wave theory approximation to the $J_{1}-J_{2}-J_{c}$ Heisenberg model. Hole doping is found to introduce only minor modifications to the exchange energies and spin gap. The changes observed in the exchange constants are consistent with the small drop of $T_\mathrm{N}$ with doping.