Hidden Order Signatures in the Antiferromagnetic Phase of U(Ru$_{1-x}$Fe$_x$)$_2$Si$_2$

We present a comprehensive set of elastic and inelastic neutron scattering measurements on a range of Fe-doped samples of U(Ru$_{1-x}$Fe$_x$)$_2$Si$_2$ with 0.01~$\le~x~\le$~0.15. All of the samples measured exhibit long-range antiferromagnetic order, with the size of the magnetic moment quickly increasing to 0.51~$\mu_B$ at 2.5\% doping and continuing to increase monotonically with doping, reaching 0.69~$\mu_B$ at 15\% doping. Time-of-flight and inelastic triple-axis measurements show the existence of excitations at (1~0~0) and (1.4~0~0) in all samples, which are also observed in the parent compound. While the excitations in the 1\% doping are quantitatively identical to the parent material, the gap and width of the excitations change rapidly at 2.5\% Fe doping and above. The 1\% doped sample shows evidence for a separation in temperature between the hidden order and antiferromagnetic transitions, suggesting that the antiferromagnetic state emerges at very low Fe dopings. The combined neutron scattering data suggests not only discontinuous changes in the magnetic moment and excitations between the hidden order and antiferromagnetic phases, but that these changes continue to evolve up to at least $x$~=~0.15.