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

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.

💡 Research Summary

In this work the authors investigate the magnetic excitation spectrum of the heavy‑fermion compound CeCu5.8Ag0.2 using high‑resolution inelastic neutron scattering on the time‑of‑flight spectrometer LET at ISIS and the multiplexing spectrometer CAMEA at PSI. The study focuses on two characteristic wave vectors, Q1 ≈ (±0.65, 0, ±0.3) and Q2 = (1, 0, 0), which were previously identified as the loci of quantum critical fluctuations in the parent compound CeCu6 and its Au‑ or Ag‑substituted variants. By applying magnetic fields along the crystallographic c‑axis and b‑axis, the authors map out the field‑direction dependence of the fluctuations over a temperature range of 0.05 K to 4 K and fields up to 8 T.

Key experimental observations are as follows. At zero field and 250 mK, the Q1 response is quasielastic, well described by a modified Lorentzian with an almost vanishing offset (E0 ≈ 50 µeV) and a half‑width at half‑maximum (FWHM) of ≈ 0.07 meV. The Q2 response, by contrast, shows a small gap of ≈ 0.19 meV and a conventional Lorentzian line shape. When the field is applied along the c‑axis, both Q1 and Q2 intensities drop rapidly; the fluctuations are essentially extinguished by µ0H ≈ 5 T. In stark contrast, a field up to µ0H = 8 T applied along the b‑axis leaves the spectra unchanged, demonstrating a pronounced anisotropy in the magnetic response.

Spatial correlation lengths extracted from two‑dimensional Lorentzian fits reveal ξ‖ ≈ 30 Å and ξ⊥ ≈ 46 Å for Q1, indicating relatively isotropic, long‑range correlations, whereas for Q2 the correlations are shorter and anisotropic (ξa ≈ 23 Å, ξc ≈ 12 Å). Temperature dependence further distinguishes the two modes: Q1 intensity grows and the linewidth narrows as temperature is lowered, a hallmark of quantum critical slowing down, while Q2 intensity also increases but the spectral weight shifts to lower energies without a comparable narrowing.

To identify the universality class of the quantum critical point, the authors perform an E/T scaling analysis of χ″(Q,E). The data collapse is best described by the Hertz‑Millis‑Moriya (HMM) model for a three‑dimensional spin‑density‑wave (SDW) quantum critical point, with scaling exponents α = β = 1.5 and a functional form f(x) = ax/(1+(bx)^2). This model yields R² ≈ 0.97 for both field orientations, whereas a local‑Kondo‑breakdown scenario (α ≈ 0.8, β = 1) provides a significantly poorer fit (R² ≈ 0.86). Consequently, the critical fluctuations are identified as three‑dimensional SDW excitations rather than local Kondo‑breakdown modes.

The anisotropic field response is interpreted in the context of the known magnetic anisotropy of the CeCu6‑xAgx series, where the c‑axis is the magnetic easy axis and the b‑axis the hard axis. The authors argue that the quantum critical fluctuations at x = 0.2 inherit the spin orientation of the long‑range ordered state that appears at higher Ag concentrations, and that the exchange couplings are weaker along the c‑axis. This picture is consistent with the observed suppression of fluctuations by c‑axis fields and their robustness against b‑axis fields.

In summary, the paper provides compelling evidence that CeCu5.8Ag0.2 hosts a three‑dimensional SDW quantum critical point governed by HMM criticality. The magnetic field anisotropy offers a direct probe of the underlying spin texture and highlights the importance of directional exchange interactions. The work sets the stage for future investigations of the Fermi‑surface topology, crystal‑electric‑field effects, and possible spin‑orbit coupling contributions that could further elucidate the microscopic Hamiltonian of the CeCu6 family.