  We use neutron diffraction and muon spin relaxation to study the effect of
in-plane uniaxial pressure on the antiferromagnetic (AF) orthorhombic phase in
BaFe$_2$As$_2$ and its Co- and Ni-substituted members near optimal
superconductivity. In the low temperature AF ordered state, uniaxial pressure
necessary to detwin the orthorhombic crystals also increases the magnetic
ordered moment, reaching an 11$\%$ increase under 40 MPa for
BaFe$_{1.9}$Co$_{0.1}$As$_2$, and a 15$\%$ increase for
BaFe$_{1.915}$Ni$_{0.085}$As$_2$. We also observe an increase of the AF
ordering temperature ($T_N$) of about 0.25 K/MPa in all compounds, consistent
with density functional theory calculations that reveal better Fermi surface
nesting for itinerant electrons under uniaxial pressure. The doping dependence
of the magnetic ordered moment is captured by combining dynamical mean field
theory with density functional theory, suggesting that the pressure-induced
moment increase near optimal superconductivity is closely related to quantum
fluctuations and the nearby electronic nematic phase.
