Extended versus Local Fluctuations in Quantum Critical Ce(Ru1-xFex)2Ge2 (x=xc=0.76) (original) (raw)
Quantum critical point and intermediate valence fluctuations in CeRu2−xCoxGe2
Physical Review B, 2018
A detailed study of low-temperature properties across the series CeRu 2−x Co x Ge 2 (0 x 2) using magnetic susceptibility χ (T), isothermal magnetization M(H), heat capacity C(T), and electrical resistivity ρ(T) is presented. Using doping as a tuning parameter, a crossover from a Ruderman-Kittel-Kasuya-Yosida (RKKY) dominated region (0 x 1) to a Kondo dominated region (x 1.5) is evident. χ (T) and ρ(T) curves, analyzed in terms of theoretical models proposed by Sales and Freimuth for the Co (x 1.5) rich compounds, suggest an intermediate valence state of the Ce ion. The intricate balance between the competing RKKY and Kondo effect is attributed to the volume change upon Co substitution, owing to its smaller ionic size, which enhances the hybridization between 4f and conduction electrons. A quantum critical point (QCP) in the (T, x) phase diagram is reached for the critical concentration (x c ∼ 1.5) where the competing RKKY and Kondo energy scales tend to zero. Deviation in χ (T), C(T), and ρ(T) from Fermi-liquid behavior is observed in the vicinity of the QCP and the former is seen to recover with the application of magnetic field. Further support for the quantum criticality comes from the universal scaling behavior of M(H), χ (T), and ρ(T) data for x c ∼ 1.5. Also, the valence fluctuations in the vicinity of the compound showing non-Fermi-liquid behavior may suggest the possible role of valence fluctuations in the QCP, which makes the present series an interesting case.
Study of non-Fermi-liquid behaviour near the ferromagnetic quantum critical point in CePd0.15Rh0.85
Journal of Magnetism and Magnetic Materials, 2007
Recent bulk measurements on CePd 1Àx Rh x alloys indicate a ferromagnetic quantum critical point (FQCP) near the critical composition x c ¼ 0.85. We present here the first results of the spin dynamics near the FQCP in CePd 0.15 Rh 0.85 investigated using inelastic neutron scattering measurements over a wide temperature range between 5 and 260 K. Our study reveals a strong quasielastic scattering between 5 and 260 K, which is nearly temperature independent on the neutron energy loss side, but follows the population factor on the neutron energy gain side. Furthermore, we found a novel E/T scaling behaviour, with the scaling exponent a ¼ 0.6, of the dynamical susceptibility, w(E,T). At low temperatures (below 60 K) the quasielastic linewidth (G) exhibits a linear temperature dependence, which is in agreement with the theoretical prediction for non-Fermi-liquid behaviour near a QCP. We compare the observed scaling behaviour in CePd 0.15 Rh 0.85 near the FQCP with that of systems having an antiferromagnetic QCP or a spin-glass quantum-type critical point.
Evolution of quantum criticality in the system CeNi9Ge4
2011
The heavy fermion system CeNi9Ge4 exhibits a paramagnetic ground state with remarkable features such as: a record value of the electronic specific heat coefficient in systems with a paramagnetic ground state, γ = C/T 5.5 J/mol K 2 at 80 mK, a temperature-dependent Sommerfeld-Wilson ratio, R = χ/γ, below 1 K and an approximate single ion scaling of the 4f -magnetic specific heat and susceptibility. These features are related to a rather small Kondo energy scale of a few Kelvin in combination with a quasi-quartet crystal field ground state. Tuning the system towards long range magnetic order is accomplished by replacing a few at.% of Ni by Cu or Co. Specific heat, susceptibility and resistivity studies reveal TN ∼ 0.2 K for CeNi8CuGe4 and TN ∼ 1 K for CeNi8CoGe4. To gain insight whether the transition from the paramagnetic NFL state to the magnetically ordered ground state is connected with a heavy fermion quantum critical point we performed specific heat and ac susceptibility studies and utilized the µSR technique and quasi-elastic neutron scattering. 1 arXiv:1110.6090v1 [cond-mat.str-el]
Evolution of quantum criticality in the system
2012
The heavy fermion system CeNi9Ge4 exhibits a paramagnetic ground state with remarkable features such as: a record value of the electronic specific heat coefficient in systems with a paramagnetic ground state, γ = C/T 5.5 J/mol K 2 at 80 mK, a temperature-dependent Sommerfeld-Wilson ratio, R = χ/γ, below 1 K and an approximate single ion scaling of the 4f-magnetic specific heat and susceptibility. These features are related to a rather small Kondo energy scale of a few Kelvin in combination with a quasi-quartet crystal field ground state. Tuning the system towards long range magnetic order is accomplished by replacing a few at.% of Ni by Cu or Co. Specific heat, susceptibility and resistivity studies reveal TN ∼ 0.2 K for CeNi8CuGe4 and TN ∼ 1 K for CeNi8CoGe4. To gain insight whether the transition from the paramagnetic NFL state to the magnetically ordered ground state is connected with a heavy fermion quantum critical point we performed specific heat and ac susceptibility studies and utilized the µSR technique and quasi-elastic neutron scattering. 1
Spin fluctuations and non-Fermi-liquid behavior of CeNi 2 Ge 2
Physical Review B, 2003
Neutron scattering shows that non-Fermi-liquid behavior of the heavy-fermion compound CeNi2Ge2 is brought about by the development of low-energy spin fluctuations with an energy scale of 0.6 meV. They appear around the antiferromagnetic wave vectors (1 2 1 2 0) and (00 3 4) at low temperatures, and coexist with high-energy spin fluctuations with an energy scale of 4 meV and a modulation vector (0.23, 0.23, 1 2). This unusual energy dependent structure of Imχ(Q, E) in Q space suggests that quasiparticle bands are important.
Local fluctuations in quantum critical metals
Physical Review B, 2003
We show that spatially local, yet low-energy, fluctuations can play an essential role in the physics of strongly correlated electron systems tuned to a quantum critical point. A detailed microscopic analysis of the Kondo lattice model is carried out within an extended dynamical mean-field approach. The correlation functions for the lattice model are calculated through a self-consistent Bose-Fermi Kondo problem, in which a local moment is coupled both to a fermionic bath and to a bosonic bath (a fluctuating magnetic field). A renormalization-group treatment of this impurity problemperturbative in ǫ = 1 -γ, where γ is an exponent characterizing the spectrum of the bosonic bath-shows that competition between the two couplings can drive the local-moment fluctuations critical. As a result, two distinct types of quantum critical point emerge in the Kondo lattice, one being of the usual spin-density-wave type, the other "locally critical." Near the locally critical point, the dynamical spin susceptibility exhibits ω/T scaling with a fractional exponent. While the spin-density-wave critical point is Gaussian, the locally critical point is an interacting fixed point at which long-wavelength and spatially local critical modes coexist. A Ginzburg-Landau description for the locally critical point is discussed. It is argued that these results are robust, that local criticality provides a natural description of the quantum critical behavior seen in a number of heavy-fermion metals, and that this picture may also be relevant to other strongly correlated metals.
Quantum criticality in heavy-fermion metals
Nature Physics, 2008
Quantum criticality describes the collective fluctuations of matter undergoing a second-order phase transition at zero temperature. Heavy-fermion metals have in recent years emerged as prototypical systems to study quantum critical points. There have been considerable efforts, both experimental and theoretical, that use these magnetic systems to address problems that are central to the broad understanding of strongly correlated quantum matter. Here, we summarize some of the basic issues, including the extent to which the quantum criticality in heavy-fermion metals goes beyond the standard theory of order-parameter fluctuations, the nature of the Kondo effect in the quantum-critical regime, the non-Fermi-liquid phenomena that accompany quantum criticality and the interplay between quantum criticality and unconventional superconductivity.
Philosophical Magazine, 2018
In this paper the low-temperature properties of two isostructural canonical heavy-fermion compounds are contrasted with regards to the interplay between antiferromagnetic (AF) quantum criticality and superconductivity. For CeCu 2 Si 2 , fully-gapped d-wave superconductivity forms in the vicinity of an itinerant three-dimensional heavy-fermion spin-density-wave (SDW) quantum critical point (QCP). Inelastic neutron scattering results highlight that both quantum critical SDW fluctuations as well as Mott-type fluctuations of local magnetic moments contribute to the formation of Cooper pairs in CeCu 2 Si 2. In YbRh 2 Si 2 , superconductivity appears to be suppressed at T ≳ 10 mK by AF order (T N = 70 mK). Ultra-low temperature measurements reveal a hybrid order between nuclear and 4f-electronic spins, which is dominated by the Yb-derived nuclear spins, to develop at T A slightly above 2 mK. The hybrid order turns out to strongly compete with the primary 4felectronic order and to push the material towards its QCP. Apparently, this paves the way for heavy-fermion superconductivity to form at T c = 2 mK. Like the pressure-induced QCP in CeRhIn 5 , the magnetic field-induced one in YbRh 2 Si 2 is of the local Kondo-destroying variety which corresponds to a Mott-type transition at zero temperature. Therefore, these materials form the link between the large family of about fifty low-T unconventional heavyfermion superconductors and other families of unconventional superconductors with higher T c s, notably the doped Mott insulators of the cuprates, organic charge-transfer salts and some of the Fe-based superconductors. Our study suggests that heavy-fermion superconductivity near an AF QCP is a robust phenomenon. Heavy-fermion metals, superconductivity, quantum critical phenomena 1. Quantum criticality in antiferromagnetic heavy-fermion metals Unconventional superconductivity, i.e., superconductivity which is not driven by lattice vibrations, frequently develops in strongly correlated metals on the brink of antiferromagnetic (AF) order [1, 2]. The continuous suppression of AF order by non-thermal control parameters, such as external/chemical pressure and magnetic field gives rise to a quantum critical point (QCP) which determines the physical properties in a wide range of parameters. Strong deviations from the predictions of Landau's Fermi-liquid theory [3], socalled non-Fermi-liquid (NFL) phenomena, are commonly observed in the normal metallic state out of which superconductivity develops. The interplay between quantum criticality and superconductivity in strongly correlated electron systems is a timely, controversial and much debated topic which has been studied over the last two decades, most intensively with AF heavy-fermion metals [4, 5]. These are intermetallic compounds of certain lanthanides, such as Ce and Yb, or actinides, such as U and Pu. The lanthanide-based heavyfermion metals are model systems for the Kondo lattice, where at the QCP the on-site Kondo screening, characterized by k B T K , with T K being the Kondo temperature of the crystalfield (CF)-derived lowest-lying Kramers doublet of the localized 4f-shell, exactly cancels the intersite magnetic Ruderman Kittel Kasuya Yoshida (RKKY) interaction, characterized by k B T RKKY. So far, two different types of AF QCPs have been established for heavy-fermion metals. Some of them exhibit a "conventional" QCP, which means that in this scenario the AF order is of itinerant nature [6-8]. This kind of spin-density wave (SDW) order, with three-dimensional (3D) quantum critical fluctuations of the AF order parameter, is common to transition-metal compounds where d-electrons contribute to the conduction band. A 2. CeCu 2 Si 2 : Fully gapped d-wave superconductivity in the vicinity of a threedimensional spin-density-wave quantum critical point Heavy-fermion superconductivity was first discovered in the Kondo lattice system CeCu 2 Si 2 with almost trivalent Ce (T K ≃ 20 K) [21]. It has been considered an unconventional superconductor from early on: (i) The non-f-electron reference compound LaCu 2 Si 2 does not superconduct (at T ≥ 20 mK) [21], which implies that superconductivity in the Ce homologue should be ascribed to the periodic lattice of 100 % magnetic Ce 3+ ions. (ii) The reduced jump in the Sommerfeld coefficient of the electronic specific heat [γ(T) = C(T)/T] at the superconducting transition temperature, ΔC/γ 0 T c [γ 0 ≃1 J/(K 2 mol)], is of order unity, which implies that the Cooper pairs are formed by heavy-mass quasiparticles, i.e., slowly propagating Kondo singlets. As their Fermi velocity v F * is only of the order of the velocity of sound, the electron-phonon interaction is not retarded, i.e., the direct Coulomb repulsion among the charge carriers cannot be avoided. (iii) Therefore, an alternative pairing mechanism must be at work which, in analogy to superfluidity in 3 He [22], was early on assumed to be magnetic in origin [23-25]. (iv) Already a tiny amount of nonmagnetic impurities was found to fully suppress superconductivity in CeCu 2 Si 2 [26], similar to the