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

Abstract

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 $x\gtrsim 0.27$. Time-of-flight neutron diffraction of a single crystal ($x=0.28$) reveals $c$-axis collinear ${\mathbf{q}}_{\mathrm{m}}=(\frac{1}{2},\frac{1}{2},\frac{1}{2})$ magnetic structure with localized magnetic moments ($\approx 2.1\hat{I}{¼}_{\mathrm{B}}$). 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.