Kondo Lattice State Research Articles

Ce2Pd21Si6 vs. Ce3Pd20Si6: Effect of Ce/Pd substitution on the physical properties

In this study, polycrystalline intermetallic compounds Ce3-xPd20+xSi6 (x = 0; 0.5; 1) as well as La-based analogues La3-xPd20+xSi6 (x = 0; 1) are synthesized. At the same time, R2Pd21Si6 (RCe, La) are new rare earth compounds presented here. An analysis of the crystal structure shows that the increase in x leads to partial (x = 0.5) or complete (x = 1) replacement of Ce/La ions by Pd in one of the two Wyckoff positions, namely, in position 4a. Ab initio DFT calculations demonstrate good agreement between the determined lattice parameters and those found experimentally for both Ce3-xPd20+xSi6 (x = 0; 0.5; 1) and La3-xPd20+xSi6 (x = 0; 1). A comparative analysis of resistivity and specific heat of Ce3-xPd20+xSi6 with x = 0; 0.5; 1 makes it possible to associate the Ce ions in the 8c position with Kondo behaviour in all three compositions, which manifests itself in an increase in resistivity with cooling, as well as in a broad peak of the magnetic contribution of specific heat. The Kondo temperature TK ≈ 25 K obtained from the analysis of the temperature dependences of the heat capacity turns out to be the same for all Ce compounds. The appearance of cerium ions in the position 4a in compositions with х = 0 and х = 0.5 leads to an additional contribution to the specific heat, the value of which increases with decreasing temperature, as well as, to the formation of a coherent Kondo-lattice state with a maximum of the resistivity at Tcoh ≈ 15 K, followed by the subsequent onset of negative magnetoresistance regime below Tinv≈ 7 K. Apparently, this behaviour is associated with the appearance of spin and orbital correlations proceeding the quadrupole and antiferromagnetic transitions occurring at lower temperatures. Magnetization measurements show more localized character of magnetic moments of Ce ions at T = 2 K in Ce3Pd20Si6 as compared to the Ce2Pd21Si6.

Symmetric Kondo Lattice States in Doped Strained Twisted Bilayer Graphene.

We use the topological heavy fermion (THF) model and its Kondo lattice (KL) formulation to study the possibility of a symmetric Kondo (SK) state in twisted bilayer graphene. Via a large-N approximation, we find a SK state in the KL model at fillings ν=0,±1,±2 where a KL model can be constructed. In the SK state, all symmetries are preserved and the local moments are Kondo screened by the conduction electrons. At the mean-field level of the THF model at ν=0,±1,±2,±3 we also find a similar symmetric state that is adiabatically connected to the symmetric Kondo state. We study the stability of the symmetric state by comparing its energy with the ordered (symmetry-breaking) states found in [H. Hu etal., Phys. Rev. Lett. 131, 026502 (2023).PRLTAO0031-900710.1103/PhysRevLett.131.026502, Z.-D. Song and B. A. Bernevig, Phys. Rev. Lett. 129, 047601 (2022).PRLTAO0031-900710.1103/PhysRevLett.129.047601] and find the ordered states to have lower energy at ν=0,±1,±2. However, moving away from integer fillings by doping the light bands, our mean-field calculations find the energy difference between the ordered state and the symmetric state to be reduced, which suggests the loss of ordering and a tendency toward Kondo screening. In order to include many-body effects beyond the mean-field approximation, we also performed dynamical mean-field theory calculations on the THF model in the nonordered phase. The spin susceptibility follows a Curie behavior at ν=0,±1,±2 down to ∼2 K where the onset of screening of the local moment becomes visible. This hints to very low Kondo temperatures at these fillings, in agreement with the outcome of our mean-field calculations. At noninteger filling ν=±0.5,±0.8,±1.2 dynamical mean-field theory shows deviations from a 1/T susceptibility at much higher temperatures, suggesting a more effective screening of local moments with doping. Finally, we study the effect of a C_{3z}-rotational-symmetry-breaking strain via mean-field approaches and find that a symmetric phase (that only breaks C_{3z} symmetry) can be stabilized at sufficiently large strain at ν=0,±1,±2. Our results suggest that a symmetric Kondo phase is strongly suppressed at integer fillings, but could be stabilized either at noninteger fillings or by applying strain.

A review of the Kondo insulator materials class of strongly correlated electron systems: Selected systems and anomalous behavior

Studies of strongly correlated electron systems have been at the forefront of research in condensed matter physics ever since the discovery of the co-existence of strong Pauli-paramagnetism and superconductivity in the archetypal heavy-fermion compound CeCu2Si2 in 1979. The construct of correlated electron physics typifies the behavior of thermal and electronic properties of a material when the Coulomb interaction between conduction electrons exceeds the electron kinetic energy at a given thermal energy and redefines in remarkable ways our understanding of the behavior of a metal near its ground state. While correlated electron behavior has by now been demonstrated in a variety of different types of materials, Kondo systems in particular are arguably the most intensively studied among these. The Kondo interaction is used to describe the effect that a spin-magnetic ion has on its environment when immersed in the conduction electron sea of a metal. The localized spin of the Kondo ion polarizes nearby conduction electrons to form a so-called Kondo cloud, which acts to screen and magnetically (partially) neutralize the localized spin. In Kondo systems, the low-temperature behavior is prone to the formation of heavy fermions, which is the term given to quasiparticle excitations that define the emergence of effective electron masses that can be up to three orders of magnitude greater than that of a free electron. The Kondo effect presents itself in three guises: first, the single-ion Kondo state which is found in a metal having only a small amount of magnetic ions dissolved into it; second, the incoherent Kondo state in materials where there is a Kondo ion in every crystallographic unit cell of the material, but the Kondo ions remain incoherent or uncoupled from each other; and third, the coherent Kondo lattice state which manifests itself toward low temperatures where the interaction between Kondo ions becomes comparable to the thermal energy of conduction electrons that mediate magnetic exchange between Kondo ions. In a small number of cases, the outcome of a material condensing into the Kondo state turns out to be the peculiar formation of a very narrow energy band gap at the metallic Fermi energy. Such a band gap has significant consequences in practically all of the physical properties of a material that stem from the behavior of conduction electrons in proximity of the Fermi energy. This is most readily seen in electrical resistivity, heat capacity, and magnetic susceptibility. The band gapping gives cause to the term Kondo insulator (also referred to as Kondo semimetal or heavy-fermion semiconductor) that is used to describe this exceptional variety of Kondo systems. The term Kondo insulator is in general use although most Kondo insulators have a small but finite electrical conduction in the low-temperature limit where Kondo screening may be accomplished to its full extent. While the Kondo lattice ground state is exemplified by a very high density of electronic states at the Fermi energy, Kondo insulators, on the other hand, have, by virtue of narrow band gapping, a low density of electronic states. It remains a counter-intuitive observation, therefore, that despite their low density of states, Kondo insulators have curiously strong spin polarization energy scales and accompanying high values of their Kondo temperature, being the defining quantity which acts as an organizing principle in their temperature-dependent physical properties. In this article, we review the fundamentals of the Kondo insulating state, and we discuss the theoretical principles of what is presently understood about the formation of a Kondo insulator. The experimental results of a selected number of examples that have gained prominence in this class of materials are compared to each other in order to seek out similarities that may help deepen our understanding of the Kondo insulating state.

Ce site dilution effects in the antiferromagnetic heavy fermion CeIn3

La-doped intermetallic single crystals of ${{\mathrm{Ce}}_{1}}_{\ensuremath{-}x}{\mathrm{La}}_{x}{\mathrm{In}}_{3}$ were synthesized via an In self-flux method throughout the entire range $(x=0--1)$. The prototypical heavy-fermion compound ${\mathrm{CeIn}}_{3}$ shows an antiferromagnetic phase transition at 10.1 K and becomes superconducting near a critical pressure where ${T}_{N}$ is completely suppressed. As the La concentration increases, Ce moments are diluted, and the lattice constant increases linearly, satisfying Vegard's law. The electrical resistivity of the high-quality single crystals of ${{\mathrm{Ce}}_{1}}_{\ensuremath{-}x}{\mathrm{La}}_{x}{\mathrm{In}}_{3}$ shows a gradual suppression of ${T}_{N}$ to 0 K at approximately ${x}_{c}=0.65$. The sign of the slope of the low-temperature resistivity vs temperature changes from positive to negative in the vicinity of the critical concentration ${x}_{c}$, indicating a change in the Kondo ground states from the Kondo lattice to the Kondo impurity state. In the Kondo lattice state $(x<{x}_{c})$, the coherence temperature $(=50\phantom{\rule{0.16em}{0ex}}\mathrm{K})$ assigned as the peak in the resistivity is almost independent of the La concentration. In the Kondo impurity state $(x>{x}_{c})$, on the other hand, a kinklike feature in the resistivity appears at $\ensuremath{\sim}50\phantom{\rule{0.16em}{0ex}}\mathrm{K}$ and persists up to $x=0.97$, indicating a change of the Kondo scattering owing to the crystalline electric field effects. These results suggest that the critical concentration is closely connected to the emergence of the Kondo coherence state.

A new look at the ground state properties of Ce2Ir3Al9: Coexistence of two competing energy scales

We present an extended research on characterization of the ground state in a polycrystalline compound Ce2Ir3Al9 using powder x-ray diffraction, magnetic susceptibility χ(T), isothermal magnetization M(B), specific heat Cp(T), electrical resistivity ρ(T), magnetoresistivity ρ(B), thermoelectric power S(T) and thermal conductivity κ(T) measurements, together with a theoretical description of the obtained data to develop a more profound understanding of the physics in this compound. Ce2Ir3Al9 crystallizes in the orthorhombic Y2Co3Ga9-type of structure (space group Cmcm, No. 63, oC56, Z = 4). The χ(T) and Cp(T)/T data reveal the signatures of intermediate valence behaviour on Ce ions with the approximate value of the Kondo temperature TK = 96 K and the Sommerfeld coefficient γ = 31 mJ/mol ⋅ K2. In contrast to the magnetometric and thermodynamic measurements, the transport data (ρ(T) and S(T)) indicate the development of the Kondo lattice state. Accordingly, we expect that for Ce2Ir3Al9 the most likely scenario, which develops in a wide T range is the coexistence and competition of two energy scales of interactions between conduction electrons and 4f spins on Ce ions, located in one unique crystallographic site in the unit cell, in consequence carrying out our system from Ce4+Temp.→ Ce3+. At higher temperatures, where the Kondo interaction becomes dominant the influence of the crystal electric field effect seems to play an influential role in the ground state of this compound too.

Pressure influence on the valence and magnetic state of Yb ions in noncentrosymmetric heavy-fermionYbNiC2

We present studies of neutron diffraction, electrical resistivity, magnetic susceptibility, magnetization, and specific heat of noncentrosymmetric $\mathrm{Yb}\mathrm{Ni}{\mathrm{C}}_{2}$. At normal pressure, $\mathrm{Yb}\mathrm{Ni}{\mathrm{C}}_{2}$ is a moderate heavy-fermion compound with Kondo lattice. At 16 K we observe an anomaly in the temperature dependence of specific heat which is ascribed to an abrupt valence change of Yb ions. At pressures above 7 GPa, the valence change and the Kondo lattice state are suppressed, and near a temperature of 10 K we detect the appearance of magnetic order. Above 5 GPa, the temperature dependence of the resistivity behaves similarly to other compounds of the $\mathrm{Ce}\mathrm{Ni}{\mathrm{C}}_{2}$-type family, indicating the formation of charge density waves. This is attributed to the nesting properties of the Fermi surface (FS) found within the density functional $\mathrm{theory}+\mathrm{dynamical}$ mean field theory treatment. Our ab initio calculations also show that the valence of Yb in $\mathrm{Yb}\mathrm{Ni}{\mathrm{C}}_{2}$ at normal conditions is 2.85, which increases with temperature and pressure. The FS of $\mathrm{Yb}\mathrm{Ni}{\mathrm{C}}_{2}$ is anisotropic in shape in comparison with the 3D surface of $\mathrm{Yb}\mathrm{Co}{\mathrm{C}}_{2}$.

Kondo-Induced Giant Isotropic Negative Thermal Expansion.

Negative thermal expansion is an unusual phenomenon appearing in only a handful of materials, but pursuit and mastery of the phenomenon holds great promise for applications across disciplines and industries. Here we report use of x-ray spectroscopy and diffraction to investigate the 4f-electronic properties in Y-doped SmS and employ the Kondo volume collapse model to interpret the results. Our measurements reveal an unparalleled decrease of the bulk Sm valence by over 20% at low temperatures in the mixed-valent golden phase, which we show is caused by a strong coupling between an emergent Kondo lattice state and a large isotropic volume change. The amplitude and temperature range of the negative thermal expansion appear strongly dependent on the Y concentration and the associated chemical disorder, providing control over the observed effect. This finding opens avenues for the design of Kondo lattice materials with tunable, giant, and isotropic negative thermal expansion.

Competing magnetic correlations across the ferromagnetic quantum critical point in the Kondo system CeTi1−xVxGe3 : V51 NMR as a local probe

$^{51}$V nuclear magnetic resonance (NMR) and magnetization studies on CeTi$_{1-x}$V$_x$Ge$_3$ have been performed to explore the evolution from the ferromagnetic ($x = 0.113$) to the antiferromagnetic Kondo lattice state ($x = 1$), with focus on the emergence of a possible ferromagnetic quantum critical point (FMQCP) at $x_c \approx 0.4$. From the temperature dependence of the nuclear spin-lattice relaxation rate, $1/T_1T$, and the Knight shift, \textit{K}, for $x=0.113$ and $x=1$ a considerable competition between ferro- and antiferromagnetic correlations is found. Around the critical concentration ($x = 0.35, 0.405$) quantum-critical spin fluctuations entail weak antiferromagnetic spin fluctuations admixed with ferromagnetic spin fluctuations. The FMQCP in CeTi$_{1-x}$V$_x$Ge$_3$ therefore is not purely ferromagnetic in nature.

Record high magnetic ordering temperature in a lanthanide at extreme pressure

Today’s best permanent magnet materials, SmCo5 and Nd2Fe14B, could likely be made significantly more powerful were it not necessary to dilute the strong magnetism of the rare earth ions (Sm, Nd) with the 3d transition elements (Fe, Co). Since the rare-earth metals order magnetically at relatively low temperatures To ≤ 292 K, transition elements must be added to bring To to temperatures well above ambient. Under pressure To(P) for the neighboring lanthanides Gd, Tb, and Dy follows a notably nonmonotonic, but nearly identical, dependence to ∼60 GPa. At higher pressures, however, Tb and Dy exhibit highly anomalous behavior, To for Dy soaring to temperatures well above ambient. We suggest that this anomalously high magnetic ordering temperature is an heretofore unrecognized feature of the Kondo lattice state.

The Kondo lattice state in the presence of Van Hove singularities: Next-to-leading order scaling

A renormalization group treatment of the Kondo model with logarithmic Van Hove singularity in the electron density of states is performed within next-leading order scaling, different magnetic phases being considered. The effective coupling constant remains small, renormalized magnetic moment and spin-fluctuation frequency decreasing by several orders of magnitude. Thus wide non-Fermi-liquid behavior regions are found from the scaling trajectories in a broad interval of the bare coupling parameter. Applications to itinerant magnetism theory are discussed.

Pressure-tuned quantum criticality in the antiferromagnetic Kondo semimetal CeNi2−δAs2

The easily tuned balance among competing interactions in Kondo-lattice metals allows access to a zero-temperature, continuous transition between magnetically ordered and disordered phases, a quantum-critical point (QCP). Indeed, these highly correlated electron materials are prototypes for discovering and exploring quantum-critical states. Theoretical models proposed to account for the strange thermodynamic and electrical transport properties that emerge around the QCP of a Kondo lattice assume the presence of an indefinitely large number of itinerant charge carriers. Here, we report a systematic transport and thermodynamic investigation of the Kondo-lattice system CeNi2-δAs2 (δ ≈ 0.28) as its antiferromagnetic order is tuned by pressure and magnetic field to zero-temperature boundaries. These experiments show that the very small but finite carrier density of ~0.032 E-/formular unit in CeNi2-δAs2 leads to unexpected transport signatures of quantum criticality and the delayed development of a fully coherent Kondo-lattice state with decreasing temperature. The small carrier density and associated semimetallicity of this Kondo-lattice material favor an unconventional, local-moment type of quantum criticality and raises the specter of the Nozières exhaustion idea that an insufficient number of conduction-electron spins to separately screen local moments requires collective Kondo screening.

Robust topological surface state in Kondo insulator SmB6 thin films

Topological insulators are a class of materials with insulating bulk but protected conducting surfaces due to the combination of spin-orbit interactions and time-reversal symmetry. The surface states are topologically non-trivial and robust against non-magnetic backscattering, leading to interesting physics and potential quantum computing applications1, 2. Recently there has been a fast growing interest in samarium hexboride (SmB6), a Kondo insulator predicted to be the first example of a correlated topological insulator3, 4. Here we fabricated smooth thin films of nanocrystalline SmB6 films. Their transport behavior indeed shows that SmB6 is a bulk insulator with topological surface states. Upon decreasing the temperature, the resistivity \r{ho} of Sm0.14B0.86 (SmB6) films display significant increase below 50 K due to hybridization gap formation, and it shows a saturation behavior below 10 K. The saturated resistance of our textured films is similar to that of the single crystals, suggesting that this conduction is from the surface and robust against grain boundary scatterings. Point contact spectroscopy (PCS) of the film using a superconducting tip displays both a Kondo Fano resonance and Andreev reflection, suggesting the existence of both an insulating Kondo lattice and metallic surface states.

Longitudinal magnetoresistance of Ce(Cu1−x Ni x )2Si2

The longitudinal magnetoresistance (LMR) of polycrystalline Ce(Cu1−xNix)2Si2 samples is investigated between T = 2 and 15 K up to H = 80 kOe. The application of magnetic field induces anomalous temperature dependence of the resistivity with the power index n 0.03) is observed at 2 K. The negative LMR at 80 kOe is maximized (∼ −4 % at T = 2 K) around x ∼ 0.10 and subsequently disappears at higher Ni concentrations. Disappearance of the positive LMR in lower x region and the negative LMR at higher Ni concentrations implies a collapse of a coherent Kondo lattice state, and a rapid enhancement of Kondo temperature, respectively. Anomalous quantum fluctuations are probably developed around x ∼ 0.10.

Evidence of a hidden-order pseudogap state in URu2Si2using ultrafast optical spectroscopy

Ultrafast optical spectroscopy was utilized to investigate carrier dynamics in the heavy-fermion compound URu${}_{2}$Si${}_{2}$ from 5 to 300 K. The amplitude and decay time of the photoinduced reflectivity increase in the vicinity of the coherence temperature ${T}^{*}\ensuremath{\sim}57$ K, consistent with the presence of a hybridization gap. At 25 K, a crossover regime manifests as a new feature in the carrier dynamics saturating below the hidden-order transition temperature of 17.5 K. This is indicative of a psuedogap region (17.5 K $<$ $T$ $<$ 25 K) separating the normal Kondo-lattice state from the hidden-order phase. Rothwarf-Taylor modeling of the data yields values of $\ensuremath{\sim}$10 meV (5 meV) for the hybridization gap (hidden-order gap).

ChemInform Abstract: Superstructure and Magnetic Properties of R15X9C Compounds (R = Rare Earth; X: Si and Ge).

AbstractLn15Si9C (Ln: Sm.

Superstructure and magnetic properties of R 15X 9C compounds (R = rare earth; X = Si and Ge)

We report the synthesis of the new compounds R 15Si 9C with R = Sm, Gd–Er, Y and R 15Ge 9C with R = Ce, Pr and Nd. These compounds crystallize in the hexagonal La 15Ge 9Fe structure type (hP50, P6 3mc, Z = 2) which is an ordered superstructure of La 5Ge 3 (Mn 5Si 3-type, hP16, P6 3/mcm, Z = 2). The superstructure is absent in a single-phase R 5Ge 3C 0.33 alloy with R = Sm and Gd. The addition of interstitial carbon modifies the magnetic properties significantly as regards the magnetic transition temperature and the nature of the magnetic ordering. Carbon doping induces mostly a ferromagnetic or ferrimagnetic configuration. The preponderance of ferromagnetic interactions in the superstructure compounds, with respect to the parent phases, can tentatively be attributed to a change in the sign of the RKKY interactions. The dense Kondo lattice state of Ce in ferrimagnetic Ce 5Ge 3 is preserved in Ce 15Ge 9C. Large coercive fields (∼4–5 kOe) at low temperatures are observed in most compounds, which exceed ∼50 kOe in the two Sm based compound.

The Kondo-lattice state and non-Fermi-liquid behavior in the presence of Van Hovesingularities

A scaling consideration of the Kondo lattices is performed with account of logarithmicVan Hove singularities (VHS) in the electron density of states. The scaling trajectories arepresented for different magnetic phases. It is demonstrated that VHS lead to a considerableincrease of the non-Fermi-liquid behavior region owing to softening of magnon branchesduring the renormalization process. Although the effective coupling constant remainsmoderate, the renormalized magnetic moment and spin-fluctuation frequency can decreaseby several orders of magnitude. A possible application to f-systems and weak itinerantmagnets is discussed.

Visualizing the formation of the Kondo lattice and the hidden order in URu 2 Si 2

Heavy electronic states originating from the f atomic orbitals underlie a rich variety of quantum phases of matter. We use atomic scale imaging and spectroscopy with the scanning tunneling microscope to examine the novel electronic states that emerge from the uranium f states in URu(2)Si(2). We find that, as the temperature is lowered, partial screening of the f electrons' spins gives rise to a spatially modulated Kondo-Fano resonance that is maximal between the surface U atoms. At T = 17.5 K, URu(2)Si(2) is known to undergo a second-order phase transition from the Kondo lattice state into a phase with a hidden order parameter. From tunneling spectroscopy, we identify a spatially modulated, bias-asymmetric energy gap with a mean-field temperature dependence that develops in the hidden order state. Spectroscopic imaging further reveals a spatial correlation between the hidden order gap and the Kondo resonance, suggesting that the two phenomena involve the same electronic states.

Half-metallic ferromagnetic ground state in CePdSb

The CeMX compounds, where M is a transition metal, and X is an sp element, have a number of different types of ground state including magnetic, metallic, and insulating, and they exhibit anomalous physical properties, such as the Kondo effect, heavy-fermion behavior, valence fluctuations, etc. Recently, a Kondo-lattice state has been proposed for ferromagnetic CePdSb, which seems to be unusual. Many Kondo systems have an antiferromagnetic ground state due to the antiferromagnetic nature of the coupling of Ce 4f and the conduction electrons, however, the coexistence of ferromagnetism and Kondo behavior is an unexpected feature. In addition, our band structure calculations for CePdSb show a state very close to a half-metallic ferromagnets (HMF). On the base of Kondo-like HMF ground state properties of CePdSb we discuss its magnetic properties and electrical resistivity data.

From Kondo semiconductor to a singular non-Fermi liquid via a quantum critical point: The case ofCeRhSb1−xSnx

We discuss and interpret the properties of the $\mathrm{Ce}\mathrm{Rh}{\mathrm{Sb}}_{1\ensuremath{-}x}{\mathrm{Sn}}_{x}$ systems in the concentration interval $0\ensuremath{\leqslant}xl0.2$. For $x\ensuremath{\cong}0.13$ a quantum critical point has been observed by us recently and separates the Kondo-insulator (KI) from the metallic non-Fermi-liquid (NFL) state. We present the temperature dependence of the resistivity, the ac and dc magnetic susceptibilities, the specific heat, and the magnetization data through the critical concentration regime $x\ensuremath{\sim}0.12--0.13$, as well as provide their discussion in terms of the transition from the nonmagnetic (Kondo-lattice) insulator to a weakly magnetic and singular non-Fermi liquid. The difference between the Kondo-lattice and the Mott-Hubbard semiconductors at temperature $Tg0$ is emphasized. Also, the difference between those two types of insulating states is discussed. On the basis of the experimental results we propose a schematic phase diagram on the plane $T\text{\ensuremath{-}}x$ and demonstrate the rationale for the existence of the quantum critical point separating KI and NFL phases. Namely, we propose that the metallization of the insulating Kondo lattice in terms of the collective spin-singlet Kondo-lattice state destruction and a concomitant delocalization of the $4f$ electrons, within an effective $f$-band model of correlated electrons undergoing the phase transition to the insulating state.