Colinear antiferromagnetic order in URu$_2$Si$_{2-x}$P$_x$ revealed by neutron diffraction

The hidden order phase in \urusi~is highly sensitive to electronic doping. A special interest in silicon-to-phosphorus substitution is due to the fact that it may allow in part to isolate the effects of tuning the chemical potential from the complexity of the correlated $f$ and $d$ electronic states. We investigate the new antiferromagnetic phase that is induced in URu$_2$Si$_{2-x}$P$_x$ at $x\gtrsim0.27$. Time-of-flight neutron diffraction of a single crystal ($x=0.28$) reveals $c$-axis colinear $\mathbf{q}_\mathrm{m}=(\frac12,\frac12,\frac12)$ magnetic structure with localized magnetic moments ($\approx2.1\,\mu_\mathrm{B}$). This reveals an unexpected analogy between the (Si,P) and (Ru,Rh) substitution series. Through further comparisons with other tuning studies of \urusi, we are able to delineate the mechanisms by which silicon-to-phosphorus substitution affects the system. In particular, both the localization of itinerant 5$f$ electrons as well as the choice of $\mathbf{q}_m$ appears to be consequences of the increase in chemical potential. Further, enhanced exchange interactions are induced by chemical pressure and lead to magnetic order, in which an increase in inter-layer spacing may play a special role.