The hidden order phase in URu$_2$Si$_2$ is highly sensitive to electronic doping. A special interest in silicon-to-phosphorus substitution is due to the fact that it may allow one, 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 $xgtrsim0.27$. Time-of-flight neutron diffraction of a single crystal ($x=0.28$) reveals $c$-axis collinear $mathbf{q}_mathrm{m}=(frac12,frac12,frac12)$ magnetic structure with localized magnetic moments ($approx2.1,mu_mathrm{B}$). This points to an unexpected analogy between the (Si,P) and (Ru,Rh) substitution series. Through further comparisons with other tuning studies of URu$_2$Si$_2$, 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.
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