Doniach Diagram Research Articles

Inhomogeneous Kondo destruction by RKKY correlations

The competition between the indirect exchange interaction (IEC) of magnetic impurities in metals and the Kondo effect gives rise to a rich quantum phase diagram, the Doniach Diagram (Doniach, 1977). A Kondo screened phase is separated from a spin ordered phase when the local exchange coupling J and the concentration of magnetic moments nM are varied. In disordered metals, both the Kondo temperature and the IEC are widely distributed due to the scattering of the conduction electrons from the impurity potential. Therefore, it is a question of fundamental importance, how this Doniach diagram is modified by the disorder, and if one can still identify separate phases. Recently, Nejati et al. (2017) investigated the effect of Ruderman–Kittel–Kasuya–Yosida (RKKY) correlations on the Kondo effect of two magnetic impurities, renormalizing the Kondo interaction based on the Bethe–Salpeter equation and performing the poor men’s renormalization group (RG) analysis with the RKKY-renormalized Kondo coupling. In the present study, we extend this theoretical framework, allowing for different Kondo temperatures of two RKKY-coupled magnetic impurities due to different local exchange couplings and density of states. As a result, we find that the smaller one of the two Kondo temperatures is suppressed more strongly by the RKKY interaction, thereby enhancing their initial inequality. In order to find out if this relevance of inequalities between Kondo temperatures modifies the distribution of the Kondo temperature in a system of a finite density of randomly distributed magnetic impurities, we present an extension of the RKKY coupled Kondo RG equations. We discuss the implication of these results for the interplay between Kondo coupling and RKKY interaction in disordered electron systems and the Doniach diagram in disordered electron systems.

Kondo temperature and Heavy Fermion behavior in Yb1−xYxCuAl series of alloys

Results on x-ray diffraction, electrical resistivity, specific heat and magnetization on the Yb1−xYxCuAl series of compounds are reported. The analysis of the x-ray data shows the increase of the unit cell volume with the Y dilution. The electrical resistivity shows an evolution from Kondo lattice regime for x≤0.6 to single impurity behavior for x = 0.8 and 0.94. The electronic coefficient γ shows values of Heavy Fermion systems along the series for 0 ≤x<1. On the other hand, dc magnetic susceptibility measurements show typical curves of intermediate valence systems with a maximum around 25K. Below this maximum, the values of low temperature susceptibility (χ(0)) decrease with the increase of Y content. From the dependence of χ(0) and γ upon Y substitution, an increase of 12% of the Kondo temperature (TK) for x = 0.8 alloy respect to the reference YbCuAl (x = 0) is estimated. This is further supported by the evolution of the temperature of the maximum in the magnetic contribution of the specific heat. The overall results can be explained by the increase of the hybridization as consequence of negative pressure effects obtained by the chemical substitution of Yb by Y, thus leading to the increase of TK, in agreement with the Doniach's diagram.

Study of the magnetic properties of the Cex La1−x Pt alloy system: Which interaction establishes ferromagnetism in Kondo systems?

In order to study Kondo ferromagnetism, particularly of the CePt compound, we investigate the magnetic properties of the CexLa1−xPt alloy system in the temperature range from 1.8K to 320K. The results of these investigations can be summarized as follows: dc-susceptibility can be described by the Curie–Weiss law at higher temperatures down to about 100K, but also at the low temperatures above the phase transition. At higher temperatures, the extracted Curie–Weiss constant, θp, is negative in contrast to the low temperatures, where θC is positive. The extracted effective magnetic moment from the higher temperatures is the same for all the alloys and is close to the theoretical value of the isolated Ce3+ ion, μ=2.54μB, indicating the hybridization is weak and, and consequently, Kondo interaction is weak. These observations confirm the main important conclusions inferred from an earlier transport properties investigation of this alloy system. The Curie temperature extracted by various approaches was compared to the extraction from the ac-susceptibility measurements. We show that its concentration dependence is not consistent with Doniach's diagram. Hence, RKKY interaction is not responsible for the ferromagnetism in this alloy system.

Kondo Effect in CeXc (Xc = S, Se, Te) Studied by Electrical Resistivity Measurements under High Pressure

We have measured the electrical resistivity of cerium monochalcogenices, CeS, CeSe, and CeTe, under high pressures up to 8 GPa. Pressure dependences of the antiferromagnetic ordering temperature $T_{N}$, crystal field splitting, and the $\ln T$ anomaly of the Kondo effect have been studied to cover the whole region from the magnetic ordering regime at low pressure to the Fermi liquid regime at high pressure. $T_{N}$ initially increases with increasing pressure, and starts to decrease at high pressure as expected from the Doniach's diagram. Simultaneously, the $\ln T$ behavior in the resistivity is enhanced, indicating the enhancement of the Kondo effect by pressure. It is also characteristic in CeX$_{c}$ that the crystal field splitting rapidly decreases at a common rate of $-12.2$ K/GPa. This leads to the increase in the degeneracy of the $f$ state and further enhancement of the Kondo effect. It is shown that the pressure dependent degeneracy of the $f$ state is a key factor to understand the pressure dependence of $T_{N}$, Kondo effect, magnetoresistance, and the peak structure in the temperature dependence of resistivity.

Coexistence of magnetic order and Kondo effect in the Kondo-Heisenberg model

The Kondo lattice model is investigated through a fermionic mean-field approximation. The obtained phase diagram, including the pure ferromagnetic (FM), antiferromagnetic (AF), Kondo (K), and mixed phases, is in good agreement with previous studies. Calculations on the simple cubic and square lattices confirm a robust coexistence of ferromagnetism and Kondo effect (FM + K), sustained by a partial Kondo screening, which leads to the concept of a spin selective Kondo insulator. We have also obtained a coexistence of antiferromagnetism and Kondo effect (AF + K), which requires the intervenience of a next-nearest-neighbor hopping ${t}^{\ensuremath{'}}$ and a Heisenberg exchange ${J}_{ij}$. The effect of temperature and pressure is described by the behavior of the order parameters. The corresponding N\'eel temperature ${T}_{N}$ and Kondo temperature ${T}_{K}$ are plotted in the form of a Doniach diagram. The presence of the intermediate mixed phases is fundamental to determine the order of the magnetic phase transitions as one approaches the quantum critical point.

Magnetic quantum phase diagram of magnetic impurities in two-dimensional disordered electron systems

The quantum phase diagram of disordered electron systems as function of the concentration of magnetic impurities nm and the local exchange coupling J is studied in the dilute limit. We take into account the Anderson localisation of the electrons by a nonperturbative numerical treatment of the disorder potential. The competition between RKKY interaction JRKKY and the Kondo effect, as governed by the temperature scale TK, is known to gives rise to a rich magnetic quantum phase diagram, the Doniach diagram. Our numerical calculations show that in a disordered system both the Kondo temperature TK and JRKKY are widely distributed. Accordingly, also their ratio, JRKKY /TK is widely distributed as shown in Fig. 1 (a). However, we find a sharp cutoff of that distribution, which allows us to define a critical density of magnetic impurities nc below which Kondo screening wins at all sites of the system above a critical coupling Jc, forming the Kondo phase[see Fig. 1 (b)]. As disorder is increased, Jc increases and a spin coupled phase is found to grow at the expense of the Kondo phase. From these distribution functions we derive the magnetic susceptibility which show anomalous power law behavior. In the Kondo phase that power is determined by the wide distribution of the Kondo temperature, while in the spin coupled phase it is governed by the distribution of JRKKY. At low densities and small J < Jc we identify a paramagnetic phase. We also report results on a honeycomb lattice, graphene, where we find that the spin coupled phase is more stable against Kondo screening, but is more easily destroyed by disorder into a PM phase.

Lifshitz phase transitions in the ferromagnetic regime of the Kondo lattice model

We establish the low-temperature phase diagrams of the spin-1/2 and spin-1 Kondo lattice models as a function of the conduction-band filling n and the exchange coupling strength J in the regime of ferromagnetic effective exchange interactions (n ~< 0.5). We show that both models have several distinct ferromagnetic phases separated by continuous Lifshitz transitions of the Fermi-pocket vanishing or emergence type: one of the phases has a true gap in the minority band (half metal), the others only a pseudogap. They can be experimentally distinguished by their magnetization curves; only the gapped phase exhibits magnetization rigidity. We find that, quite generically, ferromagnetism and Kondo screening coexist rather than compete, both in spin-1/2 and spin-1 models. We compute the Curie temperatures and establish a "ferromagnetic Doniach diagram" for both models.

Low-temperature properties of CeAu2Ge2single crystals grown from Au-Ge and Sn flux

The specific heat of CeAu2Ge2 single crystals grown from Au-Ge (AGF) or Sn flux (SF) was measured at temperatures T between 1.8 and 200 K. Two magnetic transitions are observed in the zero-field specific heat at 12.1 and 14.5 K in the AGF sample, while only a single sharp transition at 9.2 K is seen in the SF sample, confirming our recent susceptibility results [Fritsch et al., Phys. Rev. B 84, 104446 (2011)]. We observe several field-induced transitions in the magnetoresistance of the AGF sample measured at 1.6 and 2.3 K in accordance with the B-T phase diagram constructed from isothermal magnetization curves M(B). In addition, we have measured M(B) under hydrostatic pressure P up to 10.5 kbar. The Neel temperature TN increases linearly with P at a small rate of 0.049 K/kbar, which suggests that, if TN(P ) is attributed to a pure volume effect, this compound is close to the maximum transition temperature of the Doniach diagram. The transition fields BM between the field-induced phases increase linearly with P as well. The comparable Gruneisen parameters of TN and BM indicate that the energy scale depending on the sample’s volume is given by the antiferromagnetic correlations and not by the Kondo effect. We discuss possible reasons for the different magnetic behavior of AGF and SF samples.

Thermal and magnetic properties of the low-temperature antiferromagnetCe4Pt12Sn25

We report specific heat $(C)$ and magnetization $(M)$ of single crystalline ${\text{Ce}}_{4}{\text{Pt}}_{12}{\text{Sn}}_{25}$ at temperature down to $\ensuremath{\sim}50\text{ }\text{mK}$ and in fields up to 3 T. $C/T$ exhibits a sharp anomaly at 180 mK, with a large $\ensuremath{\Delta}C/T\ensuremath{\sim}30\text{ }\text{J}/\text{mol}\text{ }\text{Ce}\text{ }{\text{K}}^{2}$, which, together with the corresponding cusplike magnetization anomaly, indicates an antiferromagnetic (AFM) ground state with a N\'eel temperature ${T}_{\text{N}}=180\text{ }\text{m}\text{ }\text{K}$. Numerical calculations based on a Heisenberg model reproduce both zero-field $C$ and $M$ data, thus placing ${\text{Ce}}_{4}{\text{Pt}}_{12}{\text{Sn}}_{25}$ in the weak exchange coupling $J&lt;{J}_{\text{c}}$ limit of the Doniach diagram, with a very small Kondo scale ${T}_{\text{K}}⪡{T}_{\text{N}}$. Magnetic field suppresses the AFM state at ${H}^{\ensuremath{\ast}}\ensuremath{\approx}0.7\text{ }\text{T}$, much more effectively than expected from the Heisenberg model, indicating additional effects possibly due to frustration or residual Kondo screening.

Kondo behaviour of the solid solution (Ce 1− xLa x)PtGa

The solid solution (Ce 1− x La x )PtGa has been studied through X-ray diffraction, magnetization ( σ( B)), magnetic susceptibility ( χ( T)), electrical resistivity ( ρ( T)), magnetoresistivity (MR) and heat capacity ( C P( T)) measurements. The Néel temperature ( T N=3.3 K) for CePtGa is lowered upon La substitution as observed from χ( T) and ρ( T) measurements. The Kondo temperature T K as calculated from MR measurements is comparable to T N and also decreases with La substitution. The volume dependence of T K is in accordance with the compressible Kondo lattice model and a Doniach diagram of the results is presented. C P( T) measurements are presented for CePtGa, Ce 0.2La 0.8PtGa and LaPtGa and the results are discussed in terms of the electronic and magnetic properties. Other features of interest are anomalies in ρ( T) and C P( T) due to crystalline electric field effects and metamagnetism as observed in σ( B) studies for samples with 0 ≤ x ≤ 0.3.

Pressure effects on the antiferromagnetic order of the hydride CeRuSiH

The non-magnetic heavy fermion CeRuSi upon hydrogen absorption develops an antiferromagnetic behaviour, mainly due to the pronounced expansion of the unit cell. The effects of pressure on the χ(T) and M(H) curves of the hydride CeRuSiH up to 10.3 kbar are presented. Both, the Néel temperatures and the critical fields of the metamagnetic transitions, increase with pressure, whereas the net magnetization decreases. This evolution could be understood within the framework of the Doniach diagram.

Underscreened Kondo lattice model versus underscreened Anderson lattice model: Application to uranium compounds

Abstract We present here two theoretical models, the underscreened Kondo lattice (UKL) model and the underscreened Anderson lattice (UAL) model, which are appropriate models for a description of the coexistence of Kondo effect and ferromagnetic order experimentally observed in various uranium compounds. First we discuss a Kondo-ferromagnetic diagram (KFD), obtained in the framework of the UKL model with S = 1 [N.B. Perkins, M.D. Nunez-Regueiro, J.R. Iglesias, B. Coqblin, Phys. Rev. B 76 (2007) 125101]. The KFD differs significantly from the analogous Doniach diagram for the regular Kondo lattice with S = 1 2 . While both the Kondo and Curie temperatures in KFD increase with an increase of the intrasite Kondo coupling, J K , the Neel temperature in the Doniach diagram decreases with increase of J K . Ferromagnetism is not suppressed by the Kondo interaction, but instead the coexistence between the two phenomena takes place. Then, we compare the obtained phase diagram with available experimental data. Indeed, the predicted behavior has been observed in some uranium compounds. However, there are certain difficulties in describing the pressure dependence of the Curie temperature of UTe, which firstly passes through a maximum and then decreases at higher pressures. This pressure dependence of the Curie temperature clearly indicates that the character of 5f electrons changes with pressure, becoming more and more itinerant. Then, the UKL model cannot capture the change of localization of the 5f electrons. In this case, the underscreened Anderson lattice (UAL) model, taking explicitly into account the possibility of the formation of a f-band, becomes more appropriate. It allows to treat the case of a non-integer number of f electrons and a finite f bandwidth. We present here the two-orbital UAL model and discuss some preliminary results.

Structure, magnetic and electrical properties of CeIrSb and its hydride CeIrSbH 0.8

The ternary antimonide CeIrSb absorbs hydrogen under moderate temperature and pressure conditions (4 MPa and 573 K), leading to the hydride CeIrSbH 0.8. The crystal structures of both compounds have been investigated by X-ray diffraction on powders and single crystals: TiNiSi type, space group Pnma, a=735.07(7), b=456.93(4), c=792.8(1) pm, R1/w R2=0.0206/0.0395, 601 F 2 values for CeIrSb and a=728.16(14), b=460.35(6), c=825.87(2) pm, R1/w R2=0.0322/0.0735, 528 F 2 values for CeIrSbH 0.8 with 20 variables per refinement. Hydrogenation induces both an increase of the cell volume V (+4%) and a strongly anisotropic expansion of the unit cell with a maximum of 4.3% in the c direction, leading to a significant increase of the Ce–Ir and Ce–Ce distances in this direction. The H-insertion into CeIrSb leads to a magnetic transition from intermediate valence to antiferromagnetic behavior ( T N=7.0 K) evidenced by magnetization, electrical resistivity and specific heat measurements. This transition can be explained on the basis of the Doniach diagram considering the J cf interaction between the 4 f(Ce) and conduction electrons.

Scaling the Kondo lattice

The origin of magnetic order in metals has two extremes: an instability in a liquid of local magnetic moments interacting through conduction electrons, and a spin-density wave instability in a Fermi liquid of itinerant electrons. This dichotomy between 'local-moment' magnetism and 'itinerant-electron' magnetism is reminiscent of the valence bond/molecular orbital dichotomy present in studies of chemical bonding. The class of heavy-electron intermetallic compounds of cerium, ytterbium and various 5f elements bridges the extremes, with itinerant-electron magnetic characteristics at low temperatures that grow out of a high-temperature local-moment state. Describing this transition quantitatively has proved difficult, and one of the main unsolved problems is finding what determines the temperature scale for the evolution of this behaviour. Here we present a simple, semi-quantitative solution to this problem that provides a basic framework for interpreting the physics of heavy-electron materials and offers the prospect of a quantitative determination of the physical origin of their magnetic ordering and superconductivity. It also reveals the difference between the temperature scales that distinguish the conduction electrons' response to a single magnetic impurity and their response to a lattice of local moments, and provides an updated version of the well-known Doniach diagram.

Doniach diagram for ordered, disordered and underscreened Kondo lattices

The Doniach's diagram has been originally proposed to describe the competition between the local Kondo effect and the inter-site RKKY interactions in cerium compounds. Here we discuss the extension of this diagram to different variations of Kondo lattice model. We consider (a) ordered cerium compounds where the competition between magnetic order and Kondo effect plays an important role, as in CeRh 2Si 2, (b) disordered cerium systems with competing spin glass phase, magnetic ordered phases and a Kondo phase, as in the heavy fermion cerium alloy CeCu x Ni 1 - x and (c) uranium compounds where a coexistence between Kondo effect and ferromagnetic order has been observed, as in UTe. We show that all these cases can be described by a generalized Doniach phase diagram.

Hydrogenation inducing antiferromagnetism in the heavy-fermion ternary silicide CeRuSi

The hydride $\mathrm{Ce}\mathrm{Ru}\mathrm{Si}{\mathrm{H}}_{1.0}$ with space group $P4∕nmm$ was synthesized by exposure at $523\phantom{\rule{0.3em}{0ex}}\mathrm{K}$ of the heavy-fermion ternary silicide CeRuSi under $4\phantom{\rule{0.3em}{0ex}}\mathrm{MPa}$ of hydrogen gas. The investigation of the hydride by x-ray powder diffraction reveals that the hydrogenation induces a pronounced anisotropic expansion of the unit cell. Moreover, $\mathrm{Ce}\mathrm{Ru}\mathrm{Si}{\mathrm{H}}_{1.0}$ presents two antiferromagnetic transitions at ${T}_{N1}=7.5(2)\phantom{\rule{0.3em}{0ex}}\mathrm{K}$ and ${T}_{N2}=3.1(2)\phantom{\rule{0.3em}{0ex}}\mathrm{K}$ evidenced by magnetization and specific heat measurements. Hydrogenation changes the moderate heavy-fermion compound CeRuSi, which has a $\ensuremath{\gamma}=220\phantom{\rule{0.3em}{0ex}}\mathrm{mJ}∕\mathrm{mol}\phantom{\rule{0.2em}{0ex}}{\mathrm{K}}^{2}$, to an antiferromagnet, which has a smaller electronic coefficient $\ensuremath{\gamma}=26\phantom{\rule{0.3em}{0ex}}\mathrm{mJ}∕\mathrm{mol}\phantom{\rule{0.2em}{0ex}}{\mathrm{K}}^{2}$. In other words, the hydrogen insertion diminishes the influence of the Kondo effect. The transition heavy-fermion $\text{behavior}\ensuremath{\rightarrow}\text{antiferromagnet}$ can be well understood in terms of the classical Doniach diagram where the hydrogenation plays a role opposite to the pressure. The expansion of the lattice induced by hydrogen insertion is here much more important than the role of Ce-H bonding observed in other hydrogenated compounds $\mathrm{Ce}\mathrm{Co}\mathrm{Si}{\mathrm{H}}_{1.0}$ or $\mathrm{Ce}\mathrm{Co}\mathrm{Ge}{\mathrm{H}}_{1.0}$, where an opposite transition ($\text{antiferromagnetic}\ensuremath{\rightarrow}\text{spin}$ fluctuation) was evidenced.

Chemical pressure and magnetic field effects in CePtGa

The antiferromagnetic Kondo compound CePtGa and theCe(Pt1−xNix)Ga and CePt(Ga1−yAly) alloy systems have been studied by resistivityρ(T), magnetoresistivityMR and susceptibility χ(T) measurements on polycrystalline samples to temperatures as low as 1.5 K and in magnetic fieldsup to 9 T. A Doniach diagram is presented of the volume dependences of the Néel temperatureTN and Kondotemperature TK of these alloys and the possible existence of a quantum critical point nearx = 0.38 isindicated. χ(T) measurements in different applied fields indicate a marked decrease inTN with field for the parent CePtGa compound and extrapolation of theresults suggests that magnetic order should disappear in a field of4.8 T. In contrast the Kondo energy scale, identified by a maximum inρ(T) at low temperatures, increases significantly with field.

Ferromagnetic Doniach diagram for the underscreened Kondo lattice

A coexistence between the Kondo effect and the ferromagnetic order has been observed in some Uranium compounds such as UTe or UCu 0.9Sb 2, which order ferromagnetically at roughly 100 K and present a Kondo resistivity decrease above it. Recently we have developed the underscreened Kondo lattice (UKL) model, where the competition between the ferromagnetic order and the underscreened Kondo effect is studied by considering a Kondo coupling J K of localized S f = 1 spins with a conduction band and an inter-site f–f ferromagnetic exchange interaction J H . Here we present a diagram for the UKL model, which appears to be significantly different from the Doniach diagram for the Kondo lattice model with localized spins S = 1 2 . We obtain that the ferromagnetic order exists for all values of the ratio J K / J H , while the Kondo-ferromagnetism coexistence takes place only for sufficiently large values of the ratio J K / J H . This new ferromagnetic diagram for the UKL model can, therefore, account for the strong Kondo-ferromagnetism coexistence observed in some Uranium compounds.

Underscreened Kondo lattice model applied to heavy fermion uranium compounds

We present theoretical results for the underscreened Kondo lattice model with localized $S=1$ spins coupled to a conduction band through a Kondo coupling, ${J}_{K}$, and interacting among them ferromagnetically. We use a fermionic representation for the spin operators and expand the Hamiltonian in terms of bosonic fields. For large values of ${J}_{K}$, we obtain a ferromagnetically ordered solution and a Kondo regime with a Kondo temperature, ${T}_{K}$, larger than the Curie temperature, ${T}_{C}$. This finding suggests a scenario for a coexistence of Kondo effect and ferromagnetic order. In some uranium compounds, such as UTe or $\mathrm{U}{\mathrm{Cu}}_{0.9}{\mathrm{Sb}}_{2}$, this kind of coexistence has been experimentally observed: they order ferromagnetically with a Curie temperature of order ${T}_{C}\ensuremath{\sim}100\phantom{\rule{0.3em}{0ex}}\mathrm{K}$ and exhibit a Kondo behavior for $T&gt;{T}_{C}$. The proposed underscreened Kondo lattice model accounts well for the coexistence between magnetic order and Kondo behavior and yields to a new ``ferromagnetic Doniach diagram.''

Pressure effect on antiferromagnetism in CeRhIn5−xSnx studied by thermal expansion

We present low-temperature thermal expansion measurements on the Sn-substituted heavy fermion antiferromagnet CeRhIn5−xSnx for 0⩽x⩽0.36 in which TN(x) is linearly suppressed from 3.8 K at x=0 to zero at xc≈0.4. The application of the Ehrenfest relation allows to calculate the initial uniaxial and hydrostatic pressure dependences dTN/dP at various x. The observed non-linear variation with x is interpreted in terms of the Doniach diagram by an increase of the 4f-conduction electron hybridization induced by Sn-doping. As no traces of superconductivity are observed close to xc, this system is ideally suited for the study of the magnetic quantum critical point.