Evolution of the Magnetic Structure in ${\mathrm{CeCu}}_{5.5}{\mathrm{Au}}_{0.5}$ under Pressure towards Quantum Criticality

In the prototypical heavy-fermion system ${\mathrm{CeCu}}_{6-x}{\mathrm{Au}}_x$, a magnetic quantum critical point can be tuned by Au concentration $x$, hydrostatic pressure $p$, or magnetic field $B$. A striking equivalence of the tuning behavior with $x$ or $p$ had been found with respect to thermodynamic and transport properties. By means of elastic neutron scattering on single crystalline ${\mathrm{CeCu}}_{5.5}{\mathrm{Au}}_{0.5}$, we demonstrate this $x-p$ equivalence on a microscopic level by showing that the magnetic ordering wave vector ${\mathbf{q}}_m$ can be tuned accordingly. At ambient pressure,${\mathrm{CeCu}}_{5.5}{\mathrm{Au}}_{0.5}$ orders at ${\mathbf{q}}_m\approx (0.5900)$. Upon applying $p=4.1\mathrm{kbar}$, ${\mathbf{q}}_m\approx (0.6100.21)$ is found corresponding to ${\mathrm{CeCu}}_{5.6}{\mathrm{Au}}_{0.4}$ at ambient pressure. The transition seems to occur in a first-order fashion and to be governed by slight changes in the nesting properties of the Fermi surface.

Figure 1

Data shown in black: The Néel temperature $T_{\mathrm{N}}$ of ${\mathrm{CeCu}}_{6-x}{\mathrm{Au}}_x$ at ambient pressure $p=0$ vs Au concentration $x$ as determined from specific heat and magnetic susceptibility [25, 29]. The line is a linear fit taking into account additional data (not shown) up to $x=1$. Data shown in blue: $T_{\mathrm{N}}$ of ${\mathrm{CeCu}}_{5.7}{\mathrm{Au}}_{0.3}$ ($x=0.3$) at different $p$ as determined from specific heat [9]. Data shown in red: $T_{\mathrm{N}}$ of ${\mathrm{CeCu}}_{5.5}{\mathrm{Au}}_{0.5}$ ($x=0.5$) at different $p$ as determined from neutron scattering data and explained in the following (cf. Fig. 3). In order to compare the effects of Au doping and hydrostatic pressure, $T_{\mathrm{N}}$ was mapped onto $x$ by virtue of the linear fit.

Figure 2

(a–d) Pressure $p$ dependence [zero (a) to 8 kbar (d)] of neutron intensity ($\mathrm{\text{counts}}/500$ mon., see color code) at base temperature ($T=73–107\mathrm{mK}$) revealing magnetic Bragg peaks of ${\mathrm{CeCu}}_{5.5}{\mathrm{Au}}_{0.5}$ in the reciprocal ($h$ 0 $l$) plane. $\mathbf{Q}={\mathbf{q}}_m+\mathbf{G}$ is shown with $\mathbf{G}=(200)$. The color scale is adapted to reveal weak remnant peaks around $l\approx 0$ in (b, c, d); thus, strong peaks look less well-defined than they are. (e–h) Intensity along (0 0 $l$) summed along ($h$ 0 0) for $1.34\le h\le 1.47$ at $T$ below (black) and above (red) $T_{\mathrm{N}}(p)$. Solid lines are fits to data above $T_{\mathrm{N}}(p)$. Insets show the range $-0.05\le l\le 0.05$ on an expanded scale.

Figure 3

$T$ dependence of the magnetic Bragg peak intensity normalized to the nuclear (2 0 0) Bragg peak. Data shown in black were measured at the peak position extracted from a 2D Gaussian fit to data shown in Figs. 2a, 2b, 2c, 2d. Red symbols reveal the amplitude extracted from 2D fitting several scans over the Bragg peak along ($h$ 0 0) and (0 0 $l$) at each $T$ and are in agreement with black symbols. Lines depict fits of Eq. (1) to the data. For clarity, data and fits for different pressures are shifted vertically by 0.005 with respect to each other.

Figure 4

Components $q_l$ (a) and $q_h$ (b) of the magnetic ordering wave vector ${\mathbf{q}}_m=(q_{h}0q_l)$ vs $T_{\mathrm{N}}$ of several systems ${\mathrm{CeCu}}_{6-x}{\mathrm{Au}}_x$. The $p$ dependence at $x=0.5$ (red) is shown in comparison to the $x$-dependence at $p=0$ (black, previous work [23, 25]). Data are mapped onto $T_{\mathrm{N}}(x)$ by virtue of the linear fit shown in Fig. 1. Dashed lines are guides to the eye.