Magnetic short-range correlations and quantum critical scattering in the non-Fermi liquid regime of ${\text{URu}}_{2-x}{\text{Re}}_x{\text{Si}}_2\left(x=0.2–0.6\right)$

The spin dynamics of uranium ions in the non-Fermi liquid compounds ${\text{URu}}_{2-x}{\text{Re}}_x{\text{Si}}_2$, for $x=0.2$ to 0.6, have been investigated using inelastic neutron scattering. The wave vector $\left(q\right)$ dependence of the magnetic scattering provides evidence of short-range antiferromagnetic correlations at low temperatures for $x=0.2,0.25$, but the scattering is nearly $q$ independent at $x=0.35,0.6$. The magnetic response, $\overline{S}\left(\omega \right)$, obtained from the $q$-independent part of neutron scattering, varies as ${\omega }^{-\alpha }$ with a composition-dependent exponent $\alpha =0.2–0.5$. The dynamic magnetic susceptibility ${\chi }^{″}\left(q,\omega \right)$ of the $q$-independent part exhibits $\omega /T$ scaling for the energy transfer $\hslash \omega$ between 3.5 and 17 meV in the temperature $\left(T\right)$ range of 5–300 K at all the compositions. This scaling, which indicates local quantum criticality, breaks down in the $q$ range, $0.6–1.1{\text{Å}}^{-1}$ at $x=0.2$ and 0.25, that is dominated by short-range antiferromagnetic correlations. The appearance of power laws in the magnetic response measured by inelastic neutron scattering over a wide Re doping region indicates a disorder driven non-Fermi liquid mechanism for the low-temperature physical properties in these compounds.

Figure 1

(Color online) (a) Magnetic phase diagram of ${\text{URu}}_{2-x}{\text{Re}}_x{\text{Si}}_2$, consisting of superconducting (SC), antiferromagnetic (AF), and ferromagnetic phases. The shaded region indicates the quantum critical composition range with NFL behavior in electrical resistivity and specific heat. (b)-(e) Inelastic neutron scattering intensity map as a function of energy transfer and wave vector $q$, i.e., $S\left(q,\omega \right)$ (mb/meV/Sr/f.u.) in ${\text{URu}}_{2-x}{\text{Re}}_x{\text{Si}}_2$ for $x=0.2$, 0.25, 0.35, and 0.6 at 5 K. The phonon contribution, which is of the order of 10%–20% of the total intensity in the $q$ range of $0.5–1.7{\text{Å}}^{-1}$, has been subtracted.

Figure 2

(Color online) (a)-(d) Wave-vector-dependent structure factor $\overline{S}\left(q\right)$ in ${\text{URu}}_{2-x}{\text{Re}}_x{\text{Si}}_2$ at four Re doping compositions $x=0.2$, 0.25, 0.35, and 0.6 at 5 K. The peak at about $0.8–0.9{\text{Å}}^{-1}$ indicates short-range antiferromagnetic correlations. For a comparison, $\overline{S}\left(q\right)$ in ${\text{ThRu}}_{1.8}{\text{Re}}_{0.2}{\text{Si}}_2$ at 5 K is included in (a). (e) Parameter $\widehat{S}\left(\omega \right)$ for the $q$ range of $0.6–1.7{\text{Å}}^{-1}$ in ${\text{URu}}_{1.8}{\text{Re}}_{0.2}{\text{Si}}_2$ and ${\text{ThRu}}_{1.8}{\text{Re}}_{0.2}{\text{Si}}_2$, measured at 5 K, showing that the magnetic response from uranium $5f$ electrons is mainly in the inelastic scattering and the quasielastic scattering is negligible.

Figure 3

(Color online) (a) Temperature and $q$ dependence of ${\chi }^{\prime }$ showing short-range magnetic order in ${\text{URu}}_{1.8}{\text{Re}}_{0.2}{\text{Si}}_2$. The solid lines are best fits by the liquid type structure factor, i.e., Eq. (1), described in the text. (b) The expectation values $a_i$ for the first and the second near-neighbor U-U interatomic distances at $x=0.2$ as a function of temperature. (c) Temperature dependence of the ${\chi }_{\text{loc}}^{\prime }$ extracted from Eq. (1) at $x=0.2$. Inset shows ${\chi }_{\text{loc}}^{\prime }$ vs T in a log-log plot.

Figure 4

(Color online) (a) Structure factor $\overline{S}\left(\omega \right)$ versus energy plots as a function of $x$ in ${\text{URu}}_{2-x}{\text{Re}}_x{\text{Si}}_2$. The solid lines are best fits described in the text. (b) Composition dependence of exponents $\alpha$ from neutron scattering and $n$ from dc susceptibility (Ref. 12).

Figure 5

(Color online) Semi-log plot of ${\chi }^{″}{T}^{\alpha }$ versus $\omega /T$, showing the $\omega /T$ scaling at (a) $x=0.2$, (b) $x=0.35$, and (c) at $x=0.6$. The solid line is a fit by Eq. (3).

Figure 6

(Color online) (a) Structure factor $\overline{S}\left(\omega \right)$ versus energy plot in ${\text{URu}}_{1.8}{\text{Re}}_{0.2}{\text{Si}}_2$ for the coherent part of the scattering, i.e., $q$ covering the short-range order peak. The solid line is the best fit by Eq. (2). (b) Semi-log plot of ${\chi }^{″}{T}^{\alpha }$ versus $\omega /T$ for the $q$ range covering the short-range order peak in $x=0.2$ alloy, showing that $\omega /T$ scaling breaks down when the coherent part of the scattering is considered. The solid line is a simulation by the equation given in the figure with exponent $\alpha =0.4$.