Non-Fermi Liquid Behaviour in the Heavy-Fermion Kondo Lattice Ce2Rh3Al9
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In the heavy fermion class of strongly correlated electron systems, the Landau Fermi liquid description of metals has become a rather fragile basis on which to formulate an understanding of their ground state. The proximity to cooperative phenomena such as magnetic order and superconductivity and the amenability of Ce- and Yb-based compounds to be tuned into quantum criticality have been found to have extraordinary effects on the T→0 thermal scaling of electronic and magnetic properties. A collection of non-Fermi liquid scaling relations have thus far been proposed in the search for universality. Here we report on the physical properties of the heavy fermion Kondo lattice Ce2Rh3Al9. The low-temperature specific heat and electrical resistivity are best described by power laws in their temperature dependence, and we model these according to the expectation for a system close to a magnetic phase transition. We demonstrate how applied magnetic fields drive the transition from the Kondo coherent state, through a cross-over phase, and into Fermi-liquid behaviour at high fields and low temperatures.
KeywordsHeavy fermions Kondo lattice Non-Fermi liquid
Highly correlated electron systems, and in particular the heavy-fermion class of materials, have proven over the last 3 decades to be exceptionally rich in physics. New phenomena emerging from magnetic instabilities in metals have been an enduring and fertile research field in condensed matter physics. Two topics have remained at the forefront of investigations into highly correlated electrons systems: the coexistence of superconductivity and magnetic order, and unconventional effects at the proximity of cooperative electron behaviour [1, 2]. When a phase transition is either suppressed to zero using a suitable tuning parameter such as magnetic field or pressure , or alternatively when a magnetic phase transition happens to be situated arbitrarily close to zero [4, 5] under ambient conditions, quantum criticality arises. This condition governs the scaling of thermal electronic properties, for which a quantitative description of scaling relations and the notion of universality in the presence of quantum criticality remains elusive. The standard model of metals invokes the well-established Fermi-liquid paradigm. Here, the point of departure is that electronic properties of a metal in its ground state can be described by assuming that excitations within the sea of fermions may be renormalized out of the energy spectrum. In an interacting system, and with the extreme example of highly correlated electron systems when electron-electron interactions are turned on adiabatically from the ground state, single-particle excitations of the Fermi liquid evolve into quasiparticle excitations of the composite electron fluid . Thus it is that even in heavy-fermion systems where Coulomb energy may exceed the electron kinetic energy many times over, ground states that are not close to cooperative behaviour may still be adequately described by Fermi-liquid theory.
On the other hand, non-Fermi liquid behaviour describes an anomalous state in a metal when electronic properties are found not to scale according to the simple, non-interacting condition, and this is the subject of this paper. A small but growing number of correlated systems are now realized to behave in a manner that is not reconcilable with Fermi-liquid behaviour, yet without a magnetic phase transition that may otherwise have the physics in such systems governed by the existence of a quantum critical point. We focus in this work on selected compounds in the R2T3X9 series, where R is a rare-earth element, T stands for a d-block element, and X is a p-electron element such as Al or Ga.
The existence and exploratory physical properties of compounds in the series Ce2T3X9 (T=Rh, Ru, Ir; X=Al, Ga) were first announced by Buschinger et al. . Ce2Rh3Al9 is classified as a non-magnetically ordered (reportedly  down to 1.4 K) moderate heavy-fermion system. The nature of the ground state in this compound remains controversial. The magnetic susceptibility at intermediate temperatures produces intermediate valent type scaling, which is thought  to be understandable in terms of an energy scale T χ ≃150 K much higher than the Kondo-lattice characteristic energy T K∼20 K found in the electrical resistivity . One plausible description of the physics in Ce2Rh3Al9 is therefore that there are two energy scales at work, separated by an order of magnitude in temperature. An inelastic neutron study  attributed a localized picture to the magnetic density in Ce2Rh3Al9. A more recent x-ray photoluminescent spectroscopy plus density of state calculation study  however supported a Ce mixed-valent state in Ce2Rh3Al9. Our study of Ce2Rh3Al9 with results reported here is intended to explore the low-temperature region in search of the origin of non-Fermi liquid scaling in the electrical resistivity and specific heat.
2 Experimental Detail
Physical properties were studied using a PPMS-9T system from Quantum Design, San Diego, equipped with low temperature facilities including a 3He recirculating insert and a 3He−4He dilution refrigerator. Magnetic properties were studied in a squid-type MPMS magnetometer also from Quantum Design, in conjunction with a 3He insert from iQuantum Corporation in Tsukuba, Japan.
One approach to understand the low-temperature χ(T) data of Ce2Rh3Al9, is shown by the line superimposed onto the 7 T data in Fig. 3. This line illustrates a χ(T)=χ 0+A χ T n (n=1.6) temperature dependence, which is most pronounced for the 7 T data but evidently so also for the 4 T and 2 T data sets, albeit with the plateau in χ(T) shifted to lower temperatures as the field value is decreased. This particular temperature dependence of χ(T) was predicted by Moriya and Takimoto  for weakly interacting spin fluctuations in the proximity of a quantum phase transition. In Ce2Rh3Al9 it was established  that spin fluctuations due to Rh 4d electrons are well separated from the 4f-electron dynamics which are responsible for the non-Fermi liquid behaviour that we are concerned with here.
An important point of departure in the study of quantum criticality and the non-Fermi liquid effects that arise in metals as a result, is the distinction between quantum criticality in itinerant electron materials, and that found in local-moment systems. 4f-electron compounds based on Ce or Yb dominate the latter class of systems. A burning issue in creating an understanding of the so-called unconventional or local-moment quantum criticality in heavy fermion systems, is whether the heavy electrons form a spin-density wave composed of heavy, itinerant quasiparticles, or whether the Kondo screening prevalent in heavy fermion systems cause the heavy quasiparticles to decompose during the onset of quantum criticality . Aside from comprehensive evidence for the destruction of the Kondo effect occurring in YbRh2Si2, the cubic system Ce3Pd20Si6 has recently been found  to be a supreme example of the phenomenon of Kondo breakdown, and moreover in the anomalous situation of cubic crystal symmetry of the magnetic ions. In this work we have forwarded evidence that the heavy-fermion Kondo lattice Ce2Rh3Al9 displays non-Fermi liquid behaviour at ambient conditions at low temperature. Our studies of specific heat and electrical resistivity at the lowest temperatures demonstrate that magnetic order seems to be avoided in this compound, an observation that may have its roots in the extremely small magnetic moment that resides on the Ce+3 ions as a result of severe Kondo screening. The electrical resistivity however demonstrates how the electron scattering rate becomes decidedly non-Fermi liquid like in applied magnetic fields of 0.5–1.5 T, and for higher fields Fermi-liquid scaling is recovered. Our results presented here open up the question of whether Kondo breakdown associated with quantum criticality is in fact contingent on magnetic ordering among the Kondo spins, or whether the Kondo effect itself in heavy fermions may be intrinsically instable in the presence of quantum criticality.
A.M.S. gratefully thanks the URC of UJ, and the SA-NRF (78832) for financial assistance. M.F. acknowledges support from the UJ Faculty of Science and URC for Postdoctoral Fellowship. Douglas Britz is thanked for experimental assistance.
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