Quantum Critical Scaling and the Origin of Non-Fermi-Liquid Behavior in ${\mathrm{S}\mathrm{c}}_{1-x}{\mathrm{U}}_x{\mathrm{P}\mathrm{d}}_3$

We used inelastic neutron scattering to study magnetic excitations of ${\mathrm{S}\mathrm{c}}_{1-x}{\mathrm{U}}_x{\mathrm{P}\mathrm{d}}_3$ for U concentrations ($x=0.25$, 0.35) near the spin glass quantum critical point (QCP). The excitations are spatially incoherent, broad in energy ($E=\hslash \omega$), and follow $\omega /T$ scaling at all wave vectors investigated. Since similar $\omega /T$ scaling has been observed for ${\mathrm{U}\mathrm{C}\mathrm{u}}_{5-x}{\mathrm{P}\mathrm{d}}_x$ and ${\mathrm{C}\mathrm{e}\mathrm{C}\mathrm{u}}_{6-x}{\mathrm{A}\mathrm{u}}_x$ near the antiferromagnetic QCP, we argue that the observed non-Fermi-liquid behavior in these $f$-electron materials arises from the critical phenomena near a $T=0\mathrm{K}$ phase transition, irrespective of the nature of the transition.

Figure 1

(a) $E\mathrm{\text{−}}q$ image of ${\mathrm{S}\mathrm{c}}_{1-x}{\mathrm{U}}_x{\mathrm{P}\mathrm{d}}_3$ ($x=0.35$) at 5 K for $E_i=18\mathrm{m}\mathrm{e}\mathrm{V}$. The inset shows $E$-integrated [$E=3–6\mathrm{m}\mathrm{e}\mathrm{V}$ (top circles); 6–9 meV (middle circles); 9–12 meV (bottom filled circles)] $q$ cuts at 5 K. (b) The $q$-integrated ($0<q<2.5{\AA }^{-1}$) $S(\omega ,T)$ for $x=0.0$, 0.25, and 0.35. The dashed line shows the expected magnetic scattering for $x=0.25$ assuming simple U-concentration scaling. (c) The $q$-integrated ($0<q<1.5{\AA }^{-1}$) $S(\omega ,T)$ for $x=0.35$ at various temperatures. Dashed lines on the $E<0$ side reflect detailed balance expectations calculated from the magnetic scattering on the $E>0$ side. Grey, vertical dashed lines show the resolution half-width of 0.433 meV.

Figure 2

(a) $q$-integrated ($0<q<2.5{\AA }^{-1}$) $S(\omega ,T)$ for $x=0.35$ with $E_i=65\mathrm{m}\mathrm{e}\mathrm{V}$. Open triangles show the mapping background, and vertical dashed lines are the resolution half-width of 1.65 meV. (b) Net magnetic scattering at various temperatures. (c) Calculated CEF $S(\omega ,T)$ for two possible ground states: magnetic ${\Gamma }_5$ and nonmagnetic ${\Gamma }_3$.

Figure 3

(a) Energy scans at fixed $q=1.3{\AA }^{-1}$ for $x=0.35$ and 0.0 on SPINS. Dashed vertical lines show the resolution half-width of $0.12\mathrm{m}\mathrm{e}\mathrm{V}$. (b) $(q,E)$ map of magnetic fluctuations for $x=0.35$ at 1.4 K. The dashed grey line shows the AF ordering wave vector of $(0.5,0.5,0)$ for ${\mathrm{Y}}_{0.55}{\mathrm{U}}_{0.45}{\mathrm{P}\mathrm{d}}_3$ [18]. (c) $q$ dependence of magnetic excitations. Solid lines show calculated magnetic form factors for ${\mathrm{U}}^{3+}$ and ${\mathrm{U}}^{4+}$ ions.

Figure 4

Scaling plot for ${\mathrm{S}\mathrm{c}}_{0.65}{\mathrm{U}}_{0.35}{\mathrm{P}\mathrm{d}}_3$. The 300 K HET data exhibit a slight deviation due possibly to underestimation of phonon contributions.