Non-Fermi-liquid behavior in $\mathrm{Ce}{({\mathrm{Ru}}_{1\ensuremath{-}x}{\mathrm{Fe}}_{x})}_{2}{\mathrm{Ge}}_{2}$: Cause and effect

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Non-Fermi-liquid behavior in $Ce {({Ru}_{1 - x} {Fe}_{x})}_{2} {Ge}_{2}$ : Cause and effect

W. Montfrooij, M. C. Aronson, B. D. Rainford, J. A. Mydosh, R. Hendrikx, T. Gortenmulder, A. P. Murani, P. Haen, I. Swainson, and A. de Visser

Phys. Rev. B 73, 140401(R) – Published 4 April 2006

Abstract

We present inelastic neutron scattering measurements on the intermetallic compounds $Ce {({Ru}_{1 - x} {Fe}_{x})}_{2} {Ge}_{2}$ ( $x = 0.65$ , 0.76, and 0.87). These compounds represent samples in a magnetically ordered phase, at a quantum critical point, and in the heavy-fermion phase, respectively. We show that at high temperatures the three compositions have the identical response of a local moment system. However, at low temperatures the spin fluctuations in the critical composition are given by non-Fermi-liquid dynamics, while the spin fluctuations in the heavy-fermion system show a simple exponential decay in time. In both compositions, the lifetime of the fluctuations is determined solely by the distance to the quantum critical point. We discuss the implications of these observations regarding the possible origins of non-Fermi-liquid behavior in this system.

Received 30 December 2005

DOI:https://doi.org/10.1103/PhysRevB.73.140401

Authors & Affiliations

W. Montfrooij¹, M. C. Aronson², B. D. Rainford³, J. A. Mydosh^4,5, R. Hendrikx⁴, T. Gortenmulder^4,6, A. P. Murani⁷, P. Haen⁸, I. Swainson⁹, and A. de Visser⁶

¹Department of Physics and Missouri Research Reactor, University of Missouri, Columbia, Missouri 65211, USA
²University of Michigan, Ann Arbor, Michigan 48109, USA
³University of Southampton, Southampton SO17 1BJ, United Kingdom
⁴Leiden University, 2300 RA Leiden, the Netherlands
⁵University of Cologne, 50937 Koeln, Germany
⁶Van der Waals-Zeeman Institute, University of Amsterdam, 1018 XE Amsterdam, the Netherlands
⁷Institute Laue-Langevin, BP 156, 38042 Genoble cedex 9, France
⁸CRTBT, CNRS, BP 166, 38042 Grenoble cedex 9, France
⁹Steacie Institute for Molecular Sciences, NRC, Chalk River, Canada KOJ 1J0

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Vol. 73, Iss. 14 — 1 April 2006

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Figure 1
Energy integrated magnetic intensity per formula unit (fu) for $Ce {({Ru}_{1 - x} {Fe}_{x})}_{2} {Ge}_{2}$ over three energy ranges: $0.1 < E < 0.3$ (lower points), $0.1 < E < 0.9$ (middle), and $0.1 < E < 1.7$ (upper). The lack of a distinct $q$ dependence combined with the virtual identical results for all three samples show that at high temperatures $Ce {({Ru}_{1 - x} {Fe}_{x})}_{2} {Ge}_{2}$ is a paramagnetic local moment system with the moments residing on the cerium $f$ electrons. The sample compositions are indicated on the phase diagram (Refs. 12, 16) in the inset. FM stands for ferromagnetic, AF for antiferromagnetic, and nFl for non-Fermi-liquid behavior.Reuse & Permissions
Figure 2
The symmetrized imaginary part of the dynamic susceptibility $χ^{″} (q, E, T) ∕ (E ∕ T)$ for $q = 0.4$ and $1.4 Å^{- 1}$ for $Ce {({Ru}_{1 - x} {Fe}_{x})}_{2} {Ge}_{2}$ ( $x = 0.76$ open lozenges; $x = 0.87$ filled circles). The various curves are offset for clarity, with zero intensity given by the horizontal lines. Data for $T = 100$ , 15, and $7 K$ can be found in Ref. 15. The response for both concentrations is identical at $T = 200 K$ , but on cooling down the onset of critical fluctuations is clearly seen for the critical concentration, while a major part of the temperature dependence of $χ^{″} (q, E, T)$ for the HF concentration is accounted for by the temperature dependence of the symmetrization factor $E ∕ T$ .Reuse & Permissions
Figure 3
Lorentzian line fits to the symmetrized dynamic susceptibility for $q = 0.5$ and $1.4 Å^{- 1}$ for the critical composition (a), and for the HF composition (b). In contrast to the critical composition (only shown for $T = 7 K$ ), no deviations from Lorentzian line shapes are observed for the HF compound (b). The curves in part (b) are offset, with the zeroes of the intensity scale given by the horizontal lines. (a) and (b) do not share the same intensity scale.Reuse & Permissions
Figure 4
The temperature (a) and wave-number (c) dependence of the Lorentzian linewidth for the HF sample. The linewidth follows a linear temperature dependence below $50 K$ , similar to the temperature dependence of the linewidth for the critical composition (Ref. 12 [solid line in (a), times 6]. The static susceptibility $χ_{q} (T)$ displays a $T^{- 0.5}$ temperature dependence (b), with the effects of Kondo screening visible at the lowest temperatures. For comparison, we show the residual linewidth obtained from a fit to $Γ (T) = Θ_{q} + a T$ in part (d) (solid circles). The results for the critical composition are shown as open circles, multiplied by $b_{x} = 6$ , and augmented by $Θ_{x} = 20 K$ . Note that both samples show a similar $q$ dependence, suggesting that $Θ_{q}$ can be interpreted as the distance to the QCP in $q$ space.Reuse & Permissions

Physical Review B

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Non-Fermi-liquid behavior in $Ce {({Ru}_{1 - x} {Fe}_{x})}_{2} {Ge}_{2}$ : Cause and effect

W. Montfrooij, M. C. Aronson, B. D. Rainford, J. A. Mydosh, R. Hendrikx, T. Gortenmulder, A. P. Murani, P. Haen, I. Swainson, and A. de Visser

Phys. Rev. B 73, 140401(R) – Published 4 April 2006

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Physical Review B

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Non-Fermi-liquid behavior in Ce(Ru1−xFex)2Ge2: Cause and effect

W. Montfrooij, M. C. Aronson, B. D. Rainford, J. A. Mydosh, R. Hendrikx, T. Gortenmulder, A. P. Murani, P. Haen, I. Swainson, and A. de Visser

Phys. Rev. B 73, 140401(R) – Published 4 April 2006

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Non-Fermi-liquid behavior in $Ce {({Ru}_{1 - x} {Fe}_{x})}_{2} {Ge}_{2}$ : Cause and effect