Unusual Single-Ion Non-Fermi Liquid Behavior in Ce_(1-x)La_xNi_9Ge_4

We report on specific heat, magnetic susceptibility and resistivity measurements on the compound Ce_(1-x)La_xNi_9Ge_4 for various concentrations ranging from the stoichiometric system with x=0 to the dilute limit x=0.95. Our data reveal single-ion scaling with the Ce-concentration and the largest ever recorded value of the electronic specific heat c/T approximately 5.5 J K^(-2)mol^(-1) at T=0.08K for the stoichiometric compound x=0 without any trace of magnetic order. While in the doped samples c/T increases logarithmically below 3K down to 50mK, their magnetic susceptibility behaves Fermi liquid like below 1K. These properties make the compound Ce_(1-x)La_xNi_9Ge_4 a unique system on the borderline between Fermi liquid and non-Fermi liquid physics.Comment: 4 pages, 5 figures; v2 contains additional resisitivity measurements; final version to appear in Phys. Rev. Let

Every plane graph of maximum degree 8 has an edge-face 9-colouring

An edge-face colouring of a plane graph with edge set $E$ and face set $F$ is a colouring of the elements of $E \cup F$ such that adjacent or incident elements receive different colours. Borodin proved that every plane graph of maximum degree $\Delta\ge10$ can be edge-face coloured with $\Delta+1$ colours. Borodin's bound was recently extended to the case where $\Delta=9$. In this paper, we extend it to the case $\Delta=8$.Comment: 29 pages, 1 figure; v2 corrects a contraction error in v1; to appear in SIDM

Low temperature magnetic phase diagram of the cubic non-Fermi liquid system CeIn_(3-x)Sn_x

In this paper we report a comprehensive study of the magnetic susceptibility (\chi), resistivity (\rho), and specific heat (C_P), down to 0.5 K of the cubic CeIn_(3-x)Sn_x alloy. The ground state of this system evolves from antiferromagnetic (AF) in CeIn_3(T_N=10.2 K) to intermediate-valent in CeSn_3, and represents the first example of a Ce-lattice cubic non-Fermi liquid (NFL) system where T_N(x) can be traced down to T=0 over more than a decade of temperature. Our results indicate that the disappearance of the AF state occurs near x_c ~ 0.7, although already at x ~ 0.4 significant modifications of the magnetic ground state are observed. Between these concentrations, clear NFL signatures are observed, such as \rho(T)\approx \rho_0 + A T^n (with n<1.5) and C_P(T)\propto -T ln(T) dependencies. Within the ordered phase a first order phase transition occurs for 0.25 < x < 0.5. With larger Sn doping, different weak \rho(T) dependencies are observed at low temperatures between x=1 and x=3 while C_P/T shows only a weak temperature dependence.Comment: 7 pages, 7 figures. Accepted in Eur. J. Phys.

Quantum Criticality in doped CePd_1-xRh_x Ferromagnet

CePd_1-xRh_x alloys exhibit a continuous evolution from ferromagnetism (T_C= 6.5 K) at x = 0 to a mixed valence (MV) state at x = 1. We have performed a detailed investigation on the suppression of the ferromagnetic (F) phase in this alloy using dc-(\chi_dc) and ac-susceptibility (\chi_ac), specific heat (C_m), resistivity (\rho) and thermal expansion (\beta) techniques. Our results show a continuous decrease of T_C (x) with negative curvature down to T_C = 3K at x*= 0.65, where a positive curvature takes over. Beyond x*, a cusp in cac is traced down to T_C* = 25 mK at x = 0.87, locating the critical concentration between x = 0.87 and 0.90. The quantum criticality of this region is recognized by the -log(T/T_0) dependence of C_m/T, which transforms into a T^-q (~0.5) one at x = 0.87. At high temperature, this system shows the onset of valence instability revealed by a deviation from Vegard's law (at x_V~0.75) and increasing hybridization effects on high temperature \chi_dc and \rho. Coincidentally, a Fermi liquid contribution to the specific heat arises from the MV component, which becomes dominant at the CeRh limit. In contrast to antiferromagnetic systems, no C_m/T flattening is observed for x > x_cr rather the mentioned power law divergence, which coincides with a change of sign of \beta. The coexistence of F and MV components and the sudden changes in the T dependencies are discussed in the context of randomly distributed magnetic and Kondo couplings.Comment: 11 pages, 11 figure

Thermodynamic analysis of the Quantum Critical behavior of Ce-lattice compounds

A systematic analysis of low temperature magnetic phase diagrams of Ce compounds is performed in order to recognize the thermodynamic conditions to be fulfilled by those systems to reach a quantum critical regime and, alternatively, to identify other kinds of low temperature behaviors. Based on specific heat ($C_m$) and entropy ($S_m$) results, three different types of phase diagrams are recognized: i) with the entropy involved into the ordered phase ($S_{MO}$) decreasing proportionally to the ordering temperature ($T_{MO}$), ii) those showing a transference of degrees of freedom from the ordered phase to a non-magnetic component, with their $C_m(T_{MO})$ jump ($\Delta C_m$) vanishing at finite temperature, and iii) those ending in a critical point at finite temperature because their $\Delta C_m$ do not decrease with $T_{MO}$ producing an entropy accumulation at low temperature. Only those systems belonging to the first case, i.e. with $S_{MO}\to 0$ as $T_{MO}\to 0$, can be regarded as candidates for quantum critical behavior. Their magnetic phase boundaries deviate from the classical negative curvature below $T\approx 2.5$\,K, denouncing frequent misleading extrapolations down to T=0. Different characteristic concentrations are recognized and analyzed for Ce-ligand alloyed systems. Particularly, a pre-critical region is identified, where the nature of the magnetic transition undergoes significant modifications, with its $\partial C_m/\partial T$ discontinuity strongly affected by magnetic field and showing an increasing remnant entropy at $T\to 0$. Physical constraints arising from the third law at $T\to 0$ are discussed and recognized from experimental results

Interpretation of experimental results on Kondo systems with crystal field

We present a simple approach to calculate the thermodynamic properties of single Kondo impurities including orbital degeneracy and crystal field effects (CFE) by extending a previous proposal by K. D. Schotte and U. Schotte [Physics Lett. A 55, 38 (1975)]. Comparison with exact solutions for the specific heat of a quartet ground state split into two doublets shows deviations below $10\%$ in absence of CFE and a quantitative agreement for moderate or large CFE. As an application, we fit the measured specific heat of the compounds CeCu$_2$Ge$_2$, CePd$_{3}$Si$_{0.3}$, CePdAl, CePt, Yb$_2$Pd$_2$Sn and YbCo$_2$Zn$_{20}$. The agreement between theory and experiment is very good or excellent depending on the compound, except at very low temperatures due to the presence of magnetic correlations (not accounted in the model)