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

Uniaxial pressure effect on the magnetic ordered moment and transition temperatures in BaFe$_{2-x}T_x$As$_2$ ($T=$Co, Ni)