Enhancement of hidden order and antiferromagnetism in Fe and Os substituted URu$_{\mathrm{2}}$Si$_{\mathrm{2}}$ under pressure.

We present electrical resistivity measurements made under pressure for the Fe and Os substituted URu$_{\mathrm{2}}$Si$_{\mathrm{2}}$. The parent compound URu$_{\mathrm{2}}$Si$_{\mathrm{2}}$ exhibits a hidden order (HO) phase below $T_{\mathrm{0}} \quad =$ 17.5 K at ambient pressure. A phase transition from HO to a large moment antiferromagnetic (LMAFM) phase is induced by applying pressure $P$ or by substituting Fe or Os for Ru ions. While the substitution of smaller Fe ions reduces the unit cell volume thus creating a positive chemical pressure $P_{\mathrm{ch}}$, the substitution of larger Os ions results in a negative $P_{\mathrm{ch}}$. As Fe concentration ($x)$ is increased, the critical pressure $P_{\mathrm{c}}$ forcing the HO to LMAFM phase transition is reduced from 1.4 GPa at $x \quad =$ 0 to 0 GPa at $x \quad =$ 0.15. By converting $x$ to $P_{\mathrm{ch}}(x)$, we found that $P_{\mathrm{ch}}(x) \quad + \quad P_{\mathrm{c}} \quad \approx $ 1.5 GPa at the phase transition. These results suggest that $P_{\mathrm{ch\thinspace }}$behaves like external $P $in inducing the HO $\to $ LMAFM phase transition. However, we also found that as the Os concentration ($y)$ is increased, a smaller $P_{\mathrm{c}}$ is required to induce the HO $\to $ LMAFM phase transition: $P_{\mathrm{c}} \quad \sim $ 1.4 GPa at $y \quad =$ 0 reduces to $P_{\mathrm{c}} \quad \sim $ 0 GPa at $y \quad =$ 0.065. This is contrary to what one would expect from a negative $P_{\mathrm{ch}}$ effect. Hence, the Os substitution study suggests that $P_{\mathrm{ch}}$ is not solely responsible for inducing the LMAFM phase.