Chemical pressure tuning of ${\mathrm{URu}}_2{\mathrm{Si}}_2$ via isoelectronic substitution of Ru with Fe

We have used specific heat and neutron diffraction measurements on single crystals of ${\mathrm{URu}}_{2-x}{\mathrm{Fe}}_x{\mathrm{Si}}_2$ for Fe concentrations $x\le 0.7$ to establish that chemical substitution of Ru with Fe acts as “chemical pressure” $P_{ch}$ as previously proposed by Kanchanavatee et al. [Phys. Rev. B 84, 245122 (2011)] based on bulk measurements on polycrystalline samples. Notably, neutron diffraction reveals a sharp increase of the uranium magnetic moment at $x=0.1$, reminiscent of the behavior at the “hidden order” to large-moment-antiferromagnetic phase transition observed at a pressure $P_x\approx 0.5-0.7$ GPa in ${\mathrm{URu}}_2{\mathrm{Si}}_2$. Using the unit-cell volume determined from our measurements and an isothermal compressibility ${\kappa }_T=5.2\times {10}^{-3} {\mathrm{GPa}}^{-1}$ for ${\mathrm{URu}}_2{\mathrm{Si}}_2$, we determine the chemical pressure $P_{ch}$ in ${\mathrm{URu}}_{2-x}{\mathrm{Fe}}_x{\mathrm{Si}}_2$ as a function of $x$. The resulting temperature $\left(T\right)$–chemical pressure $\left(P_{ch}\right)$ phase diagram for ${\mathrm{URu}}_{2-x}{\mathrm{Fe}}_x{\mathrm{Si}}_2$ is in agreement with the established temperature $\left(T\right)$–external pressure $\left(P\right)$ phase diagram of ${\mathrm{URu}}_2{\mathrm{Si}}_2$.

Figure 1

Electronic specific heat $C_e$ divided by temperature $T$ vs $T$ for single crystals of ${\mathrm{URu}}_{2-x}{\mathrm{Fe}}_x{\mathrm{Si}}_2$. The phonon contribution to the specific heat was subtracted according to the procedure described in the text.

Figure 2

Temperature dependence $T$ of the magnetic moment per uranium ion in ${\mathrm{URu}}_{2-x}{\mathrm{Fe}}_x{\mathrm{Si}}_2$ for various Fe concentrations $x$ determined via magnetic neutron diffraction (see text for details). The solid (brown) line is a guide to the eye that smoothly connects the transition temperatures $T_0$ from the paramagnetic state into the hidden order/large-moment antiferromagnetic phase as determined from order parameter fits for all measured $x$ (see text for details).

Figure 3

Summary of the main results of our study on single crystals of ${\mathrm{URu}}_{2-x}{\mathrm{Fe}}_x{\mathrm{Si}}_2$. (a) Temperature $T$ vs Fe concentration $x$ phase diagram constructed from specific heat and neutron-diffraction measurements. The Fe concentration $x$ was converted to “chemical pressure” $P_{ch}$ on the top horizontal axis (see text). We have also plotted the phase boundaries in ${\mathrm{URu}}_2{\mathrm{Si}}_2$ obtained by various pressure studies for comparison [28, 29, 40, 41, 42, 43, 44]. The acronyms PM, HO, and LMAFM denote the paramagnetic, hidden order, and large-moment antiferromagnetic phases, respectively. (b) The magnetic moment $m$ per uranium site vs $x$ at $T=5$ K determined from our neutron-diffraction measurements (see text). The inset shows the full range of measured $x$ up to 0.7. (c) Energy gap $\Delta$ that opens on the FS due to the onset of the HO phase as determined via fits to the low-temperature electronic specific heat $C_e\left(T\right)$ data (see text). We also show the size of the incommensurate spin gap $E_S$ at the wave vector ${\mathit{Q}}_1=(0.4,0,0)$, determined via inelastic neutron scattering, vs $P_{ch}$ for comparison [22]. (d) Unit-cell volume $V$ vs $x$. For the axis on the right-hand side (and the top horizontal axis), the unit-cell volume was converted to chemical pressure (see text). The lines are guides to the eye.