Heavy Fermi-liquid State Research Articles

Triangular Kondo lattice in YbV6Sn6 and its quantum critical behavior in a magnetic field

We report on the magnetization, specific heat, and electrical resistivity for a newly discovered heavy-fermion (HF) compound, ${\mathrm{YbV}}_{6}{\mathrm{Sn}}_{6}$, which is crystallized in a hexagonal ${\mathrm{HfFe}}_{6}{\mathrm{Ge}}_{6}$-type structure, highlighted by the stacking of the triangular ytterbium sublattice and kagome vanadium sublattice. Above 2 K, ${\mathrm{YbV}}_{6}{\mathrm{Sn}}_{6}$ shows typical HF properties due to the Kondo effect on the Kramers doublet of ${\mathrm{Yb}}^{3+}$ ions in the crystalline electric field. A remarkable magnetic ordering occurs at ${T}_{\mathrm{N}}=0.40$ K in zero field, while a weak external field suppresses the ordering and induces non-Fermi-liquid behavior. In strong magnetic field, the compound shows a heavy Fermi-liquid state. ${\mathrm{YbV}}_{6}{\mathrm{Sn}}_{6}$ is represented as one of the few examples of Yb-based HF compounds hosting a triangular Kondo lattice on which a magnetic field induces quantum criticality near zero temperature.

Lifshitz transition in triangular lattice Kondo-Heisenberg model**Project supported by the National Natural Science Foundation of China (Grant Nos. 11674139, 11704166, and 11834005), the Fundamental Research Funds for the Central Universities, China, and PCSIRT, China (Grant No. IRT-16R35).

Motivated by recent experimental progress on triangular lattice heavy-fermion compounds, we investigate possible Lifshitz transitions and the scanning tunnel microscope (STM) spectra of the Kondo–Heisenberg model on the triangular lattice. In the heavy Fermi liquid state, the introduced Heisenberg antiferromagnetic interaction (JH) results in the twice Lifshitz transition at the case of the nearest-neighbour electron hopping but with next-nearest-neighbour hole hopping and the case of the nearest-neighbour hole hopping but with next-nearest-neighbour electron hopping, respectively. Driven by JH, the Lifshitz transitions on triangular lattice are all continuous in contrast to the case on square lattice. Furthermore, the STM spectra shows rich line-shape which is influenced by the Kondo coupling JK, the Heisenberg antiferromagnetic interaction JH, and the ratio of the tunneling amplitude of f-electron tf versus conduction electron tc. Our work provides a possible scenario to understand the Fermi surface topology and the quantum critical point in heavy-fermion compounds.

Effect of Anisotropic Hybridization in YbAlB_{4} Probed by Linear Dichroism in Core-Level Hard X-Ray Photoemission Spectroscopy.

We have probed the crystalline electric-field ground states of pure |J=7/2,J_{z}=±5/2⟩ as well as the anisotropic c-f hybridization in both valence fluctuating systems α- and β-YbAlB_{4} by linear polarization dependence of angle-resolved core level photoemission spectroscopy. Interestingly, the small but distinct difference between α- and β-YbAlB_{4} was found in the polar angle dependence of linear dichroism, indicating the difference in the anisotropy of c-f hybridization, which may be a key to understanding a heavy Fermi liquid state in α-YbAlB_{4} and a quantum critical state in β-YbAlB_{4}.

Unconventional and conventional quantum criticalities in CeRh0.58Ir0.42In5

An appropriate description of the state of matter that appears as a second order phase transition is tuned toward zero temperature, viz. quantum-critical point (QCP), poses fundamental and still not fully answered questions. Experiments are needed both to test basic conclusions and to guide further refinement of theoretical models. Here, charge and entropy transport properties as well as AC specific heat of the heavy-fermion compound CeRh0.58Ir0.42In5, measured as a function of pressure, reveal two qualitatively different QCPs in a single material driven by a single non-symmetry-breaking tuning parameter. A discontinuous sign-change jump in thermopower suggests an unconventional QCP at pc1 accompanied by an abrupt Fermi-surface reconstruction that is followed by a conventional spin-density-wave critical point at pc2 across which the Fermi surface evolves smoothly to a heavy Fermi-liquid state. These experiments are consistent with some theoretical predictions, including the sequence of critical points and the temperature dependence of the thermopower in their vicinity.

Magnetic fluctuations and possible formation of a spin-singlet cluster under pressure in the heavy-fermion spinelLiV2O4probed byLi7andV51NMR

$^{7}\mathrm{Li}$ and $^{51}\mathrm{V}$ NMR measurements up to 9.8 GPa have been made to elucidate local magnetic properties of a heavy-fermion spinel oxide ${\mathrm{LiV}}_{2}{\mathrm{O}}_{4}$ which undergoes a metal-insulator transition above $\ensuremath{\sim}7$ GPa. The temperature $T$ and pressure $P$ dependences of the $^{7}\mathrm{Li}$ and $^{51}\mathrm{V}$ Knight shifts and the nuclear spin-lattice relaxation rates $1/{T}_{1}$ show that in the metallic phase, there is a crossover from a high-$T$ region with weak ferromagnetic fluctuations to a low-$T$ one with antiferromagnetic (AFM) fluctuations. The AFM fluctuations are enhanced below 20 K and 1.5 GPa, where a heavy Fermi-liquid state with the modified Korringa relation is formed. The evolution of the magnetic fluctuations is discussed from the aspect of the competition among several magnetic interactions. Above ${P}_{\mathrm{MI}}\ensuremath{\sim}6.7$ GPa, we find the coexistence of metallic and insulating phases due to the first-order metal-insulator transition. The $^{7}\mathrm{Li}$ and $^{51}\mathrm{V}$ NMR spectra coming from the insulating phase have $T$-independent small Knight shifts and ${}^{7}(1/{T}_{1})$ with the thermally activated $T$ dependence, indicating the formation of a spin-singlet cluster. We propose a model of a spin-singlet tetramer as discussed in geometrically frustrated materials.

Transport, Thermal, and Magnetic Properties of YbNi3X9(X= Al, Ga): A Newly Synthesized Yb-Based Kondo Lattice System

We have succeeded in synthesizing a new Yb-based Kondo lattice system, YbNi 3 X 9 ( X = Al, Ga). Our study reveals that YbNi 3 Al 9 shows typical features of a heavy-fermion antiferromagnet with a Neel temperature of T N = 3.4 K. All of the properties reflect a competition between the Kondo effect and the crystalline electric field (CEF) effect. The moderate heavy-fermion state leads to an enhanced Sommerfeld coefficient of 100 mJ/(mol·K 2 ), even if ordered antiferromagnetically. On the other hand, the isostructural gallide YbNi 3 Ga 9 is an intermediate-valence system with a Kondo temperature of T K = 570 K. A large hybridization scale can overcome the CEF splitting energy, and a moderately heavy Fermi-liquid ground state with high local moment degeneracy should form at low temperatures. Note that the quality of single-crystalline YbNi 3 X 9 is extremely high compared with those of other Yb-based Kondo lattice compounds. We conclude that YbNi 3 X 9 is a suitable system for investigating the electronic s...

Anisotropic heavy-Fermi-liquid formation in valence-fluctuatingα-YbAlB4

$\alpha$-YbAlB$_4$ is the locally isostructural polymorph of $\beta$-YbAlB$_4$, the first example of an Yb-based heavy fermion superconductor which exhibits pronounced non-Fermi-liquid behavior above $T_{\rm c}$. Interestingly, both $\alpha$-YbAlB$_4$ and $\beta$-YbAlB$_4$ have strongly intermediate valence. Our single crystal study of the specific heat, magnetization and resistivity has confirmed the Fermi liquid ground state of $\alpha$-YbAlB$_4$ ~in contrast with the quantum criticality observed in $\beta$-YbAlB$_4$. Both systems exhibit Kondo lattice behavior with the characteristic temperature scale $T^* \sim$ 8 K in addition to a valence fluctuation scale $\sim 200$ K. Below $T^*$, $\alpha$-YbAlB$_4$ a heavy Fermi liquid state with an electronic specific heat coefficient $\gamma\sim$ 130 mJ/mol K$^2$ and a large Wilson ratio more than 7, which indicates ferromagnetic correlation between Yb moments. A large anisotropy in the resistivity suggests that the hybridization between 4$f$ and conduction electrons is much stronger in the $ab$-plane than along the c-axis. The strongly anisotropic hybridization as well as the large Wilson ratio is the key to understand the unusual Kondo lattice behavior and heavy fermion formation in mixed valent compounds.

Kondo lattices with inequivalent local moments: Competitive versus cooperative Kondo screening

While standard heavy fermion metals feature a single spin-1/2 local moment per unit cell, more complicated systems with multiple distinct local moments have been synthesized as well, with Ce_3Pd_20(Si,Ge)_6 being one example. Here, we discuss the physics of a Kondo lattice model with two local-moment sublattices, coupled with different Kondo couplings to conduction electrons. The phase diagram will be strongly modified from that of the standard Kondo lattice if the characteristic screening temperatures of the distinct moments are well separated. Therefore, we investigate the interplay between the two Kondo effects using a local self-energy approximation via slave bosons. We find that the two Kondo effects can either compete or co-operate depending on the conduction-band filling. In the regime of competition, small differences in the two Kondo couplings can lead to huge differences in the respective Kondo scales, due to non-trivial many-body effects. We also study the low-temperature properties of the collective heavy Fermi-liquid state and propose a connection to depleted Kondo lattice systems.

Spatial fluctuations in two-orbital Hubbard model

We study spin and orbital correlations in the two-orbital Hubbard model with the different bandwidths at quarter filling by means of the cellular dynamical mean field theory combined with the noncrossing approximation. We demonstrate that the ferromagnetic-antiferro-orbital insulating state is stabilized in the system with the same bandwidth and the antiferromagnetic-ferro-orbital insulating state appears when the difference of the bandwidth is quite large. In the intermediate region, we find that the competition between the two states occurs and this competition gives rise to the heavy Fermi-liquid metallic state.

Room for one more

In YbRh2Si2, the transitions to a heavy Fermi-liquid state and to a magnetic phase occur at a single quantum critical point. But under chemical pressure, these transitions separate, and a new phase of matter appears in between.

Evolution of a Large Fermi Surface in the Kondo Lattice

The single-particle spectrum of the Kondo lattice model is derived with the use of the continuous-time quantum Monte Carlo method, combined with the dynamical mean-field theory. Crossover behavior is traced quantitatively either to a heavy Fermi-liquid state or to a magnetically ordered state from the local-moment state at high temperatures. The momentum distribution in the low-temperature limit acquires a discontinuity at the location that involves the local-spin degrees of freedom. Even without the charge degrees of freedom for local electrons, the excitation spectra exhibit hybridized bands similar to those in the Anderson lattice. Temperature dependence in the zero-energy component of the self-energy is crucial in forming the Fermi-liquid state with the large Fermi surface.

Investigation of Yb2Pt6Al15 single crystals: heavy fermion system with a large local moment degeneracy

We grew single crystals of Yb2Pt6Al15 and investigated the magnetic properties of this compound by means of susceptibility χ(T), specific heat C(T), resistivity ρ (T) and thermoelectric power S(T) measurements. While all properties follow in general the behavior typical for Kondo-lattice systems, χ(T) and C(T)/T present broad maxima in the T range 17–35 K, which matches nicely the prediction of the Coqblin–Schrieffer model for J= 7/2. A large degeneracy of the local moment is also supported by a reduced Kadowaki–Woods ratio. Thus, the analysis of all investigated properties evidences Yb2Pt6Al15 to be a paramagnetic Kondo-lattice system with the whole J= 7/2 multiplet involved in the formation of the Kondo state, a Kondo temperature of the order of 60 K, and a heavy Fermi-liquid ground state with a Sommerfeld coefficient γ 0 = 0.33 J (mol-Yb)−1 K−2 corresponding to a mass enhancement of the order of 30.

Low-energy spin fluctuations in filled skutteruditesYbFe4Sb12 andLaFe4Sb12 investigatedthrough 121Sb nuclearquadrupole and 139La nuclear magnetic resonance measurements

We have elucidated low-energy spin fluctuations in the new filled skutteruditesYbFe4Sb12 andLaFe4Sb12 synthesized at highpressures, through 121Sb nuclear quadrupole resonance (NQR) and139La nuclear magnetic resonance (NMR) measurements. The longitudinal spin–lattice relaxation rate1/T1 of121Sb inYbFe4Sb12 provides evidence thatupon cooling below ∼20 K, the compound transforms from the localized 4f electron state ofYb3+ ions to a nonmagnetic heavy Fermi liquid state, originating from the mixing of 4felectrons with conduction electrons. Whereas, the Curie–Weiss type behaviour of the139La Knightshift and 121Sb- 1/T1 in LaFe4Sb12 indicate that the compound remains in the localized electron statedown to 1.4 K, it in fact originates from 3d electrons of Fe in[Fe4Sb12 ] anions. In both compounds, the transversal nuclear spin–spin relaxation rate1/T2 exhibits a clear peak at and K, respectively. The origin of the1/T2 peak is discussed in terms of the freezing of the thermal vibration of Sb cages or rare-earthions filled in each Sb cage. By comparing the experimental results of the presentstudy with those previously reported for the compounds synthesized at ambientpressure, it is pointed out that both the strongly correlated electron properties andthe thermal vibrations are greatly modified with the increase of rare-earth atomdeficiency.

Effect of Rare-Earth Filling Rate for the Physical Properties of Skutterudites Investigated through NMR/NQR Measurements

We have microscopically elucidated low-energy fluctuations in the completely filled skutterudites YbFe 4 Sb 12 and LaFe 4 Sb 12 through 121 Sb nuclear quadrupole resonance and 139 La nuclear magnetic resonance measurements. It provides evidence that upon cooling, YbFe 4 Sb 12 transforms into a nonmagnetic heavy Fermi liquid state and LaFe 4 Sb 12 remains the paramagnetic one, in contrast to the ferromagnetically ordered state and the heavy Fermi liquid-like one previously reported for the corresponding skutterudites with rare-earth deficiencies of about 10%. The local maxima in the longitudinal spin–lattice relaxation rate 1/ T 1 and transversal spin–spin relaxation rate 1/ T 2 for both LaFe 4 Sb 12 and YbFe 4 Sb 12 are ascribed to the freezing of thermal motions of rare-earth ion in each Sb-cage. It is suggested that the thermal motion of La ion ( f 0 ) is of incoherent motion, whereas that of Yb ion ( f 13 ) is of coherent one originating from possible interactions between f electrons in neighboring cag...

Unusual Evolution of the Conduction-Electron State inCexLa1−xB6from Non-Fermi Liquid to Fermi Liquid

We report unusual evolution of the conduction-electron state in the localized f electron system CexLa1-xB6 from normal electron state to heavy Fermi liquid (FL) state through local FL and non-FL states with increasing Ce concentration and/or with increasing magnetic field. The effective mass of quasiparticle or the coefficient A of T2 term of resistivity is found to increase divergently near the boundary between FL state and non-FL state. The features of the non-FL state are also different from those of the typical non-FL systems previously observed or theoretically predicted.

Tricritical Phenomena at theγ→αTransition inCe0.9−xLaxTh0.1Alloys

The $\gamma \to \alpha$ isostructural transition in the Ce$_{0.9-x}$La$_x$Th$_{0.1}$ system is measured as a function of La alloying using specific heat, magnetic susceptibility, resistivity, thermal expansivity/striction measurements. A line of discontinuous transitions, as indicated by the change in volume, decreases exponentially from 118 K to close to zero with increasing La doping and the transition changes from being first-order to continuous at a critical concentration $0.10 \leq x_c \leq 0.14$. At the tricritical point, the coefficient of the linear $T$ term in the specific heat $\gamma$ and the magnetic susceptibility start to increase rapidly near $x$ = 0.14 and gradually approaches large values at $x$=0.35 signifying that a heavy Fermi-liquid state evolves at large doping. Near $x_c$, the Wilson ratio, $R_W$, has a value of 3.0, signifying the presence of magnetic fluctuations. Also, the low-temperature resistivity shows that the character of the low-temperature Fermi-liquid is changing.

Low-energy spin fluctuations in heavy-Fermion filled-skutterudite compounds [formula omitted] and [formula omitted] investigated by 31P-NMR and 121Sb-NQR

To microscopically elucidate the magnetic quantum criticality of Yb-based filled skutterudites YbFe 4 Sb 12 and YbFe 4 P 12 , each of which has an intermediate valence and transforms into the heavy Fermi-liquid (HFL) state at low temperatures, we have carried out 121Sb-NQR below ∼ 30 K and 31P-NMR below ∼ 200 K . The nuclear spin–lattice relaxation rates divided by temperature 1 / T 1 T in both compounds are dominated by the generalized susceptibility χ ( q ) with a finite wave vector q far from q = 0 . 1 / T 1 T of 121Sb in YbFe 4 Sb 12 in zero field exhibits a near T -independent behavior with the small broad maximum around 4 K, indicating that the HFL state with rather small antiferromagnetic (AFM) spin fluctuations with T N ∼ 4 K takes place below at least ∼ 20 K . 1 / T 1 T of 31P in YbFe 4 P 12 at high field H = 7 T also exhibits the near T -independent behavior, indicating that the HFL state takes place below at least ∼ 200 K . The most important feature is that 1 / T 1 T of 31P at low- H strongly depends on both temperature and field and follows the power-law relation 1 / T 1 T = AT - α over one decade with α ≃ 0.7 at 0.2 T. This result leads to the conclusion that YbFe 4 Sb 12 at low- H region is located very close to the non-Fermi-liquid state than YbFe 4 Sb 12 is.

Quantum critical behavior at the Kondo insulator–non-Fermi liquid boundary for CeRhSb 1−xSn x

We have observed a critical behavior at x ⩾ 0.13 for CeRhSb 1− x Sn x , where a transition from Kondo insulator to critical regime for a non-Fermi liquid takes place. The non-Fermi liquid (NFL) state emerges from a moderately heavy Fermi liquid state ( γ ≈ 63 mJ / K 2 mol ) upon cooling. Both the specific heat C/ T and the magnetic susceptibility χ diverge on the metallic side with temperature T → 0 . The divergent character of the susceptibility and the specific heat is attributed to the quantum critical behavior χ = a T - m and C / T = b T - s in the whole metallic (non-Fermi liquid) region; the corresponding critical exponents for x = 0.13 are m = 0.17 and s ≈ 0.3 . The resistivity then diverges logarithmically. On the insulating side, x ⩽ 0.12 , it has been observed that the resistivity scales linearly with χ - 1 in the temperature regime below the coherence peak. On the basis of the experimental results we propose a schematic T– x phase diagram with the quantum critical point (QCP) separating Kondo insulating (KI) and the NFL phases.

Quantum phase transitions out of the heavy Fermi liquid

We review recent work on the instability of the heavy Fermi liquid state (FL) of the Kondo lattice towards a magnetic metal in which the local moments are not part of the Fermi sea. Using insights drawn from the theory of deconfined quantum criticality of insulating antiferromagnets, we discuss the possibility of a direct second-order transition between the heavy Fermi liquid and such a magnetic metal. We suggest the presence of at least two distinct diverging time scales—the shorter one describes fluctuations associated with the reconstruction of the Fermi surface, while a longer one describes fluctuations of the magnetic order parameter. The intermediate time scale physics on the magnetic side is suggested to be that of a novel fractionalized Fermi liquid (FL*) state with deconfined neutral S = 1 2 excitations. This could ultimately devolve into the magnetic phase with conventional order at one of the larger time scales. Experimental implications for this scenario are noted.

Field-dependent response of the heavy Fermi-liquid ground state in YbNi 2B 2C

We measured the specific heat of YbNi 2B 2C in applied fields up to 18 T. As the magnetic field is increased, the peak in the specific heat associated with the Kondo anomaly moved to higher temperatures. This behavior is consistent with theoretical predictions, and a semi-quantitative description of this continuous evolution of the specific heat is presented. Previously, the magnetoresistance of this system was measured, and a comparison is made between field-dependent response of the thermodynamic and transport properties of YbNi 2B 2C.