Magnetic Field Dependence of the Spin Fluctuations in CeCu$_{5.8}$Ag$_{0.2}$

TL;DR

The study investigates quantum critical fluctuations in CeCu5.8Ag0.2 using inelastic neutron scattering, resolving fluctuations at two reciprocal-space positions $Q_1$ and $Q_2$. It reveals a pronounced anisotropy in field suppression: $H$ along the $c$-axis rapidly quenches fluctuations, while $H$ along $b$ up to 8 T has little effect, indicating spin-anisotropic responses tied to the ground-state magnetism. Scaling analysis shows the $Q_1$ fluctuations follow the Hertz–Millis–Moriya SDW quantum critical form with α=β=1.5, whereas a local quantum critical model fits less well, supporting a three-dimensional SDW QPT driven by long-range spin fluctuations. The results imply anisotropic exchange couplings and encourage further reciprocal-space and Fermi-surface studies to fully map the quantum critical landscape in CeCu6-xAgx and related Ce-based systems.

Abstract

Quantum phase transitions are among the most intriguing phenomena that can occur when the electronic ground state of correlated metals are tuned by external parameters such as pressure, magnetic field or chemical substitution. Such transitions between distinct states of matter are driven by quantum fluctuations, and can give rise to macroscopically coherent phases that are at the forefront of condensed matter research. However, the nature of the critical fluctuations, and thus the fundamental physics controlling many quantum phase transitions, remain poorly understood in numerous strongly correlated metals. Here we study the model material CeCu$_{5.8}$Ag$_{0.2}$ to gain insight into the implications of critical fluctuations originating from different regions in reciprocal space. By employing an external magnetic field along the crystallographic $a$- and $c$-axis as auxiliary tuning parameter we observe a pronounced anisotropy in the suppression of the quantum critical fluctuations, reflecting the spin anisotropy of the long-range ordered ground state at larger silver concentration. Coupled with the temperature dependence of the quantum critical fluctuations, these results suggest that the quantum phase transition in CeCu$_{5.8}$Ag$_{0.2}$ is driven by three-dimensional spin-density wave fluctuations.

Figures (9)

• Figure 1: Background-subtracted imaginary part of the dynamic susceptibility $\chi^{\prime \prime}(\textbf{Q},E)$ at (a)$\bf{Q_1}$ = ($\pm$0.65, 0, $\pm$0.3) in reciprocal lattice units (rlu) and (b) at $\bf{Q_2}$ = (1, 0, 0) as function of energy transfer $E$. The results were obtained at LET. Each data point was measured at $T$ = 250 mK and integrated over 0.04 rlu$^2$ in the $(H, 0, L)$-plane, 0.4 rlu along the $(0, K, 0)$-axis and over a 0.075 meV energy window. Spectra collected at $\mu_0H$ = 5 T were used as a background (see SM Note 1 for details). (c-f) Integrated intensity $\chi_{\textbf{Q}}^{int}$ and full-width at half-maximum (FWHM) extracted from modified quasielastic-Lorentzian fits at $\bf{Q_1}$ and Lorentzian fits at $\bf{Q_2}$ (see text for details).
• Figure 1: Zero-field raw data of the (a) ($H$, $K$, 0) and (b) ($H$, 0, $L$)-plane measured at LET. The data were integrated over an energy transfer window $E$ = 0.15-0.35 meV and out-of-plane momentum transfer $Q_{\perp}$ = $\pm$ 0.2 in reciprocal lattice units (rlu) using an in-plane pixel size $0.02 \times 0.02$ rlu. (c) Fluctuations at $\bf{Q_1}$ = ($\pm$0.65, 0, $\pm$0.3) and (d)$\bf{Q_2}$ = (1, 0, 0) in rlu. Plotted is the imaginary part of the susceptibility $\chi^{\prime \prime}(\textbf{Q},E)$ as function of energy transfer $E$ for $\mu_0$H = 0 and 5 T obtained by box integration around the relevant $Q$-points. The dashed line represents the average value of the $\mu_{0}H$ = 5 T data set.
• Figure 2: (a) Background-subtracted constant energy slice ($E$ integrated from 0.15 to 0.3 meV) in the ($H$, 0, $L$)-plane measured at $T$ = 50 mK with CAMEA. (b)-(d) Parametrization of the experimental data using a combination of two-dimensional Lorentzians for the fluctuations at $\bf{Q_1}$ = ($\pm$0.65, 0, $\pm$0.3) and $\bf{Q_2}$ = (1, 0, 0) (see text for details).
• Figure 2: Schematic description of the reciprocal space geometry used to parametrize the data at ($Q_H$, 0, $Q_L$) with respect to $\bf{Q_1}$ = ($Q_{H_1}$, 0, $Q_{L_1}$). $\xi_{\parallel}$ and $\xi_{\perp}$ are the correlations lengths parallel and perpendicular to $\bf{Q_1}$ defined by the angle $\theta_0$ with respect to the ($H$, 0, 0)-axis. $\theta$ is the angle representing a counterclockwise rotation from the axis defined by ($Q_H$-$Q_{H_1}$, 0, $Q_L$-$Q_{L_1}$).
• Figure 3: Energy dependence of the fluctuation amplitude $A_{\textbf{Q}}$($E$) at $\bf{Q_1}$ = ($\pm$0.65, 0, $\pm$0.3) [panels (a), (c) and (e)] and $\bf{Q_2}$ = (1, 0, 0) [panels (b), (d) and (f)] using the parametrization in Eq. \ref{['equ:2D_Lorentzian']}. In panels (a) and (b) the magnetic field dependence of $A_{\textbf{Q}}$ is shown for a field applied along the crystallographic $b$-axis at $T$ = 50 mK. (a) and (b) report the temperature dependence for a field of $\mu_0H$ = 8 T applied along the $b$-axis. Panels (e) and (f) summarize the field and temperature dependence for a magnetic field along the the $c$-axis.