Crystalline Electric Field Research Articles

Van Vleck excitons in Ca2RuO4

A framework is presented for modeling and understanding magnetic excitations in localized, intermediate coupling magnets where the interplay between spin-orbit coupling, magnetic exchange, and crystal field effects are known to create a complex landscape of unconventional magnetic behaviors and ground states. A spin-orbit exciton approach for modeling these excitations is developed based upon a Hamiltonian which explicitly incorporates single-ion crystalline electric field and spin exchange terms. This framework is then leveraged to understand a canonical Van Vleck $j\rm{_{eff}}=0$ singlet ground state whose excitations are coupled spin and crystalline electric field levels. Specifically, the anomalous Higgs mode [Jain et al. Nat. Phys. 13, 633 (2017)], spin-waves [S. Kunkem\"{o}ller et al. Phys. Rev. Lett. 115, 247201 (2015)], and orbital excitations [L. Das et al. Phys. Rev. X 8, 011048 (2018)] in the multiorbital Mott insulator Ca$_2$RuO$_4$ are captured and good agreement is found with previous neutron and inelastic x-ray spectroscopic measurements. Furthermore, our results illustrate how a crystalline electric field-induced singlet ground state can support coherent longitudinal, or amplitude excitations, and transverse wavelike dynamics. We use this description to discuss mechanisms for accessing a nearby critical point.

Crystalline electrical field effects on powdered [formula omitted] Cu4Al8 ([formula omitted] = Tb, Dy, Ho and Er) intermetallic compounds

In this work, structural and magnetic properties RE Cu4Al8 (RE = Tb, Dy, Ho and Er) family of compounds are reported. Measurements of X-ray diffraction, temperature (T) and magnetic field (H) dependencies of magnetization are presented for each compound. The analysis of X-ray diffraction patterns shows a small variation in a (8.705824–8.734991 Å) and c (5.123802–5.135258 Å) lattice parameters as a function of the rare earth. The T-dependent magnetic susceptibility reveals the Curie-Weiss-like behavior at high-T evolving to antiferromagnetic transitions at low-T (6 <TN< 28 K) for all studied materials. Measurements of magnetization as a function of magnetic field show field-induced transitions for RE = Dy, Ho and Er, which present larger magnetic moments, though no magnetic saturation is attained (4.4 <Mmax< 7.3 μB) for none of the studied compounds. This fact is an indicative of strong crystalline electrical field (CEF) effects. We have conducted a detailed analysis, based on a mean-field spin model, in order to determine the CEF parameters from the macroscopic data of the studied powdered samples. Finally, to show the reliability of our calculations, the obtained CEF energy levels and wave functions are compared with previous CEF studies in single crystalline samples of ErCu4Al8, including results obtained from inelastic neutron scattering data.

Time-Controlling the Latent Heat Release of Fatty Acids using Static Electric Field

Latent heat released during freezing of phase change material (PCM), which occurs at a constant temperature, can be modified using an electric field, through a process called electrofreezing. To date, the effects of the electric field on the freezing of salt solutions or salt hydrates of inorganic PCM, such as reduction of the supercooling degree, increase of nucleation rate, and reduction of the induction time due to changes in the Gibbs free energy, have been the focus. In this paper, we describe the electrofreezing of stearic acid and lauric acid of fatty acid PCM. Because common organic PCM has relatively small or even zero supercooling, the effect of the DC electric field on the time of latent heat release at a constant temperature and crystallization time was more pronounced. A comparison was also done with inorganic CaCl2⋅6H2O PCM using previously published data. We propose that the two time parameters are closely related to the electrical and thermal conductivities. Different nucleation mechanisms for fatty acids and CaCl2⋅6H2O with interactions between the crystalline sample and electric field, as well as dissimilar Joule heating effects, have been proposed. Changes in the chemical structure and thermal stability due to electric field treatment are evaluated using the Fourier-transform infrared spectra, the decomposition and melting temperatures, and the calculation of the latent heat of fusion. We also discuss the potential applications of lauric and stearic acids as phase change composites in thermoresponsive devices for high electrical to thermal energy conversion efficiencies.

Imprint of charge and oxygen orders on Dy ions in DyBa2Cu3O6+x thin films probed by resonant x-ray scattering

We used resonant elastic x-ray scattering at the Cu $L_3$ and Dy $M_5$ edges to investigate charge order in thin films of underdoped DyBa$_2$Cu$_3$O$_{6+x}$ (DyBCO) epitaxially grown on NdGaO$_3$ (110) substrates. The films show an orthorhombic crystal structure with short-range ortho-II oxygen order in the charge-reservoir layers. At the Dy $M_5$ edge we observe diffraction peaks with the same planar wavevectors as those of the two-dimensional charge density wave in the CuO$_2$ planes and of the ortho-II oxygen order, indicating the formation of induced ordered states on the rare-earth sublattice. The intensity of the resonant diffraction peaks exhibits a non-monotonic dependence on an external magnetic field. Model calculations on the modulation of the crystalline electric field at the Dy sites by charge and oxygen order capture the salient features of the magnetic field, temperature, and photon energy dependence of the scattering intensity.

Synthesis, crystal chemistry, and magnetic properties of Ce3-xRhGa10+3x (x = 0.36): A new member of the [BaAl4]m[CaF2]n[AlB2]p homologous series

Ce3-xRhGa10+3x (x = 0.36) is a new member of the linear intergrowth structure series built up from segments of the BaAl4, AlB2 and CaF2 structure types. The compound crystallizes with a disordered variant of the Pr3NiGa10 type structure. Unlike the prototype, Ce3-xRhGa10+3x exhibits notable deficiency in rare-earth content, accompanied with significant excess of Ga atoms, corresponding to additional Ga environment of one of the Ce atoms. The novel compound is a Curie-Weiss paramagnet and orders antiferromagnetically at low temperatures. The electrical transport in Ce3-xRhGa10+3x has a metallic character, and bears contributions due to crystalline electric field, Kondo and magnetic exchange interactions.

Evolution of the magnetic properties in the antiferromagnet Ce2RhIn8 simultaneously doped with Cd and Ir.

We report the evolution of the magnetic properties of single crystals. In particular, for () and (), we have solved the magnetic structure of these compounds using single-crystal neutron magnetic diffraction experiments. Taking the magnetic structure of the heavy-fermion antiferromagnet as a reference, we have identified no changes in the magnetic wave vector; however, the direction of the ordered Ce3+ moments rotates toward the plane, under the influence of both dopants. By constraining the analysis of the crystalline electric field (CEF) with the experimental ordered moment's direction and high-temperature magnetic-susceptibility data, we have used a mean-field model with tetragonal CEF and exchange interactions to gain insight into the CEF scheme and anisotropy of the CEF ground-state wave function when Cd and Ir are introduced into . Consistent with previous work, we find that Cd doping in tends to rotate the magnetic moment toward the plane and lower the energy of the CEF excited states' levels. Interestingly, the presence of Ir also rotates the magnetic moment towards the plane although its connection to the CEF overall splitting evolution for the y = 0 samples may not be straightforward. These findings may shed light on the origin of the disordered spin-glass phase on the Ir-rich side of the phase diagram and also indicate that the compounds may not follow exactly the same Rh-Ir CEF effects trend established for the compounds.

Quantum Critical Point between Two-Channel Kondo and Fermi-Liquid Phases

We investigate the emergence of quantum critical points near a two-channel Kondo phase by evaluating an $f$-electron entropy of a seven-orbital impurity Anderson model hybridized with three ($\Gamma_7$ and $\Gamma_8$) conduction bands with the use of a numerical renormalization group method First we consider the case of Pr$^{3+}$ ion, in which quadrupole two-channel Kondo effect is known to occur for the local $\Gamma_3$ doublet state. When we control crystalline electric field (CEF) potentials so as to change the local CEF ground state from $\Gamma_3$ doublet to $\Gamma_1$ singlet or $\Gamma_5$ triplet, we commonly observe a residual entropy of $\log \phi$ with the golden ratio $\phi=(1+\sqrt{5})/2$, which is equal to that for three-channel Kondo effect. This peculiar residual entropy is also observed for the case of Nd$^{3+}$ ion, in which magnetic two-channel Kondo phase is found to occur for the local $\Gamma_6$ doublet state. We envisage a scenario that the quantum critical point characterized by $\log \phi$ generally appears between two-channel Kondo and Fermi-liquid phases.

Magnetothermal properties of [formula omitted] ([formula omitted] 0.25, 0.50 and 0.75)

We describe magnetic, thermal, and magnetocaloric properties of rare earth intermetallic compounds TmxDy1−xAl2 with x= 0.25, 0.5 and 0.75. Using model Hamiltonian we consider contributions of the crystalline electric field anisotropy in both Tm and Dy magnetic sublattices, disorder in exchange interactions among Tm-Tm, Dy-Dy and Tm-Dy magnetic ions, and the Zeeman effect. Employing earlier reported and new experimental measurements, we first determine a single free variable – the intersublattice magnetic exchange parameter – to properly model the temperature and magnetic field dependencies of heat capacity and magnetization, and then use the modeling results to explain the emergence of an anomalous spin reorientation transition and its influence on the magnetocaloric effect in the title compounds. Theoretical results agree with experimental data reasonably well.

Tuning the crystalline electric field and magnetic anisotropy along the CeCuBi2−xSbx series

We have performed X-ray powder diffraction, magnetization, electrical resistivity, heat capacity and inelastic neutron scattering (INS) to investigate the physical properties of the intermetallic series of compounds CeCuBi$_{2-x}$Sb$_{x}$. These compounds crystallize in a tetragonal structure with space group $P4/nmm$ and present antiferromagnetic transition temperatures ranging from 3.6 K to 16 K. Remarkably, the magnetization easy axis changes along the series, which is closely related to the variations of the tetragonal crystalline electric field (CEF) parameters. This evolution was analyzed using a mean field model, which included anisotropic nearest-neighbor interactions and the tetragonal CEF Hamiltonian. The CEF parameters were obtained by fitting the magnetic susceptibility data with the constraints given by the INS measurements. Finally, we discuss how this CEF evolution can affect the Kondo physics and the search for a superconducting state in this family.

Channel-selective non-Fermi liquid behavior in the two-channel Kondo lattice model under a magnetic field

Stimulated by anomalous behaviors found in non-Kramers $f$-electron systems in an applied magnetic field, we study a two-channel Kondo lattice model by using a cluster extension of the dynamical mean-field theory combined with the continuous-time quantum Monte Carlo method. We include the effect of the external magnetic field in two ways: the Zeeman coupling to conduction electron spins and an effective coupling to the quadrupole degree of freedom through the crystalline electric field splitting. We show that the magnetic field suppresses the antiferroic-spin order (physically, corresponding to the antiferroic-quadrupole order), and yields a channel-selective non-Fermi liquid state where one of the two channels (physically, spin-up or -down) exhibits non-Fermi liquid behavior while the other shows Fermi liquid behavior, before entering the Fermi liquid regime in higher fields. This anomalous state appears in a dome-shaped region which extends from inside the antiferroic-spin ordered phase to the paramagnetic phase. We find that the composite correlation, which is a measure of differentiation in the Kondo coupling between the two channels, is enhanced in this dome-shaped region. We also find that the specific heat coefficient is enhanced in this region in the paramagnetic side, indicating heavy fermion behavior not only in the vicinity of the critical field where the antiferroic-spin order vanishes but also in a certain region of the field and temperature. We discuss the results in comparison with the ordinary Kondo lattice model. We also discuss the implication of our findings to the peculiar behavior observed in the 1-2-20 compounds such as $\rm{PrIr_2Zn_{20}}$, $\rm{PrRh_2Zn_{20}}$, and $\rm{PrV_2Al_{20}}$ under a magnetic field.

EPR Spectroscopy of $$^{53}\hbox {Cr}^{3+}$$ Monoisotopic Impurity Ions in a Single Crystal of Scandium Orthosilicate $$\hbox {Sc}_{2}\hbox {SiO}_{5}$$

Monoisotopic $$^{53}\hbox {Cr}^{3+}$$ impurity ions in scandium orthosilicate single crystal ( $$\hbox {Sc}_2\hbox {SiO}_5$$ ) are studied by the method of electron paramagnetic resonance in the X-band frequencies. The directions of the main principal magnetic axes and the parameters of the effective spin Hamiltonian that describe the magnetic characteristics of the impurity centers of chromium, which replaces scandium in two structurally nonequivalent positions, are determined. It is shown that the orientation dependencies of the EPR spectra are well described by the second-order spin Hamiltonian corresponding to the orthorhombic symmetry of the local crystal field acting on the impurity ion. It was assumed that the g-tensor and the A-tensor determining the Zeeman energy of electronic levels in a magnetic field and the hyperfine interaction of electron and nuclear spins are isotropic, and the entire anisotropy of the EPR spectra is due to the anisotropy of the D-tensor, which describes the fine structure of electronic levels in a crystalline electric field. A strong dependence of the probability of “forbidden” transitions between hyperfine sublevels of electronic levels on the orientation of an external magnetic field is established. Moreover, for some orientations, the probability of “forbidden” transitions exceeds the probability of “allowed” transitions.

Tuning the crystalline electric field and magnetic anisotropy along the series.

We have performed X-ray powder diffraction, magnetization, electrical resistivity, heat capacity and inelastic neutron scattering (INS) to investigate the physical properties of the intermetallic series of compounds . These compounds crystallize in a tetragonal structure with space group and present antiferromagnetic transition temperatures ranging from 3.6 K to 16 K. Remarkably, the magnetization easy axis changed along the series, which is closely related to the variations of the tetragonal crystalline electric field (CEF) parameters. This evolution was analyzed using a mean field model, which included an anisotropic nearest-neighbor interactions and the tetragonal CEF Hamiltonian. We obtained the CEF parameters by fitting the magnetic susceptibility data with the constraints given by the INS measurements. More broadly, we discuss how this CEF evolution can affect the Kondo physics and the search for a superconducting state in this family.

Evolution of the Kondo lattice electronic structure above the transport coherence temperature

The temperature-dependent evolution of the Kondo lattice is a long-standing topic of theoretical and experimental investigation and yet it lacks a truly microscopic description of the relation of the basic f-c hybridization processes to the fundamental temperature scales of Kondo screening and Fermi-liquid lattice coherence. Here, the temperature dependence of f-c hybridized band dispersions and Fermi-energy f spectral weight in the Kondo lattice system CeCoIn5 is investigated using f-resonant angle-resolved photoemission spectroscopy (ARPES) with sufficient detail to allow direct comparison to first-principles dynamical mean-field theory (DMFT) calculations containing full realism of crystalline electric-field states. The ARPES results, for two orthogonal (001) and (100) cleaved surfaces and three different f-c hybridization configurations, with additional microscopic insight provided by DMFT, reveal f participation in the Fermi surface at temperatures much higher than the lattice coherence temperature, [Formula: see text] K, commonly believed to be the onset for such behavior. The DMFT results show the role of crystalline electric-field (CEF) splittings in this behavior and a T-dependent CEF degeneracy crossover below [Formula: see text] is specifically highlighted. A recent ARPES report of low T Luttinger theorem failure for CeCoIn5 is shown to be unjustified by current ARPES data and is not found in the theory.

Effect of structural and magnetic disorder on the 3d−5d exchange interactions in La2−xCaxCoIrO6

The delicate balance between spin-orbit coupling, Coulomb repulsion and crystalline electric field interactions observed in Ir-based oxides is usually manifested as exotic magnetic behavior. Here we investigate the evolution of the exchange coupling between Co and Ir for partial La substitution by Ca in La$_{2}$CoIrO$_6$. A great advantage of the use of Ca$^{2+}$ as replacement for La$^{3+}$ is the similarity of its ionic radii. Thus, the observed magnetic changes can more easily be associated to electronic variations. A thorough investigation of the structural, electronic and magnetic properties of the La$_{2-x}$Ca$_{x}$CoIrO$_6$ system was carried out by means of synchrotron x-ray powder diffraction, muon spin rotation and relaxation ($\mu$SR), AC and DC magnetization, XAS, XMCD, Raman spectroscopy, electrical resistivity and dielectric permittivity. Our XAS results show that up to 25% of Ca substitution at the La site results in the emergence of Co$^{3+}$, possibly in high spin state, while the introduction of larger amount of Ca leads to the increase of Ir valence. The competing magnetic interactions resulting from the mixed valences lead to a coexistence of a magnetically ordered and an emerging spin glass (SG) state for the doped samples. Our $\mu$SR results indicate that for La$_{2}$CoIrO$_6$ a nearly constant fraction of a paramagnetic (PM) phase persists down to low temperature, possibly related to the presence of a small amount of Ir$^{3+}$ and to the anti-site disorder at Co/Ir sites. For the doped compounds the PM phase freezes below 30 K, but there is still some dynamics associated with the SG. The dielectric data obtained for the parent compound and the one with 25% of Ca-doping indicate a possible magnetodielectric effect, which is discussed in terms of the electron hopping between the TM ions, the anti-site disorder and the distorted crystalline structure.

Crystal structure and magnetic properties of novel La(Ce, Pr)R’PbSi2S8 (R’ = Ce, Pr, Sm, Tb, Dy, Y, Ho and Er) compounds

The formation of the La2-xR’xPbSi2S8 (R’ ​= ​Ce, Pr, Sm, Tb, Dy, Y, Ho, Er), Ce2-xR’xPbSi2S8 (R’ ​= ​Pr, Sm, Tb, Dy, Y, Ho, Er), and Pr2-xR’xPbSi2S8 (R’ ​= ​Sm, Tb, Dy, Y, Ho, Er) (x ​= ​1.5, 1.0, 0.5) solid solutions was established. The crystal structures of LaR’PbSi2S8 (R ​= ​Ce, Sm, Tb, Dy, Y, Ho, Er), CeR’PbSi2S8 (R’ ​= ​Pr, Sm, Tb, Dy, Y, Ho, Er) and PrR’PbSi2S8 (R’ ​= ​Sm, Tb, Dy, Y, Ho, Er) (La2PbSi2S8 structure type, space group R3¯c, Pearson symbol hR78) were determined by means of single crystal X-ray diffraction. Rare-earth and lead atoms are located in split positions inside bi-capped trigonal prisms made by chalcogen atoms. The Si atoms are located in tetrahedra. The crystal structure of the La2PbSi2S8 type can be derived from the Eu3As2S8 type by random substitution of the Eu atoms by the R, R′, and Pb atoms at their 18e site. The magnetic properties of LaR’PbSi2S8 (R ​= ​Ce, Sm, Tb, Dy, Y, Ho, Er), CeR’PbSi2S8 (R’ ​= ​Pr, Sm, Tb, Dy, Y, Ho, Er) and PrR’PbSi2S8 (R’ ​= ​Sm, Tb, Dy, Y, Ho, Er) were studied in wide temperature and magnetic field strength ranges. All these materials but weakly diamagnetic LaYPbSi2S8 were characterized as Curie-Weiss paramagnets due to the magnetic moments carried on trivalent rare-earth ions. At low temperatures, each compound exhibits distinct crystalline electric field effect, while in none of them any magnetic ordering emerges down to 1.72 ​K.

Magnetic properties and magnetic structures of R2PdGe6 (R = Pr, Nd, Gd-Er) and R2PtGe6 (R = Tb, Ho, Er)

Polycrystalline samples of the intermetallic compounds R2PdGe6 (R = Pr, Nd, Gd-Er) and R2PtGe6 (R = Tb, Ho, Er) have been studied using X-ray diffraction as well as magnetometric and neutron diffraction measurements. All compounds have an orthorhombic crystal structure of the Yb2PdGe6-type (space group Cmca) and are antiferromagnetic with the Néel temperatures ranging from 4.9 K for Er2PtGe6 up to 48 K for Tb2PdGe6. The magnetic properties and specific heat data collected for Nd2PdGe6 show the presence of an additional phase transition below TN at T = 4 K. Based on the neutron diffraction data, the magnetic structures have been determined for R2PdGe6 (R = Pr, Nd, Tb, Dy, Ho) and R2PtGe6 (R = Tb and Er). Both the magnetic properties and neutron diffraction data indicate that the magnetic moment is localized on rare earth atoms. The magnetic unit cell is equal to the crystal one, however, individual compounds show different types of magnetic orderings. Magnetic moments in Pr2PdGe6 form a non-collinear antiferromagnetic structure at low temperatures with magnetic moments confined to the (001) plane. The low temperature magnetic structure in Nd2PdGe6 is a collinear antiferromagnetic one with moments parallel to the b-axis and coupled ferromagnetically within the (001) plane, while along the c-axis the moments follow the +−−+ sequence. With increasing temperature, atransition to a modulated magnetic structure is observed in Nd2PdGe6 at T = 4 K. The magnetic moments in R2PdGe6 (R = Tb, Dy, Ho) and Tb2PtGe6 assume a non-collinear antiferromagnetic order within the (001) plane with the +−+− sequence of signs of the moments in the neighboring planes along the c-axis. The Er moments in Er2PtGe6 form a collinear magnetic structure with magnetic moments oriented along the a-axis and coupled ferromagnetically within the (001) plane. Along the c-axis the moments follow the +−+− sequence. The magnetic structures determined here are discussed on the basis of the competition between the RKKY-type interactions and influence of Crystalline Electric Field.

Magnetic structure and crystalline electric field effects in the triangular antiferromagnet CePtAl4Ge2

Kondo metal $\mathrm{CePtA}{\mathrm{l}}_{4}\mathrm{G}{\mathrm{e}}_{2}$ exhibits long-range antiferromagnetic order below 2.3 K. Neutron powder-diffraction experiments reveal that Ce moments order antiferromagnetically with an incommensurate ordering wave vector $\mathbit{k}=(1.39,0,0.09)$. Inelastic neutron powder scattering experiments show a magnetic excitation at 14.5 meV, which corresponds to the first excited state due to the crystalline electric field splitting of the ground-state multiplet of $\mathrm{C}{\mathrm{e}}^{3+}$. The temperature and field dependence of the magnetization of $\mathrm{CePtA}{\mathrm{l}}_{4}\mathrm{G}{\mathrm{e}}_{2}$ is consistent with a doublet ground state with a dominant $|{j}_{\mathrm{z}}=1/2\ensuremath{\rangle}$ character and a first excited doublet $|{j}_{\mathrm{z}}=3/2\ensuremath{\rangle}$ at 14.5 meV.

Crystal structure and complex magnetic properties of R11Pd4In9 compounds (R = Y, Gd–Er)

Magnetic properties of the R11Pd4In9 compounds (R = Y, Gd–Er) were investigated by means of X-ray diffraction and magnetic measurements. Three of these compounds, namely those with R = Y, Ho and Er, are newly synthesized. The compounds crystallize in the orthorhombic Nd11Pd4In9-type crystal structure (oC48, Cmmm) in which the rare earth atoms occupy five nonequivalent sublattices. Magnetic properties of the investigated compounds are related mainly to the R3+ ions, except the case of Y11Pd4In9 which is a Pauli paramagnet. For R = Gd-Er, the values of effective magnetic moments in the paramagnetic state are close to the free R3+ ion values while the moments in the ordered state at T = 2 K and H = 90 kOe are lower than the respective R3+ moments. The compounds have complex magnetic properties. All paramagnetic Curie temperatures are positive suggesting that the ferromagnetic interactions are predominant. However, the low temperature data indicate an antiferromagnetic order. With increase of temperature the magnetic properties change from antiferro-to ferrimagnetic and finally to paramagnetic ones. The critical temperatures of magnetic ordering do not fulfill the de Gennes scaling, indicating a crystalline electric field contribution to stabilization of the magnetic order at low temperatures. The neutron diffraction measurements, performed for Ho11Pd4In9, reveal a coexistence of two magnetic phases at low temperatures: the antiferromagnetic with propagation vector k = [0,0,½] and the ferrimagnetic one with k = [0,0,0]. The antiferromagnetic order is predominant at low temperatures while the ferrimagnetic one dominates at intermediate temperatures.

Large anisotropic magnetocaloric effect in ferromagnetic semimetal PrAlSi

We report on the large anisotropic magnetocaloric effect of PrAlSi, a ferromagnetic semimetal of current interest with a probable topologically nontrivial electronic structure. The maximum magnetic entropy change amounts to −ΔSM=22.6J/kgK near the Curie temperature TC=17.8K under a magnetic field change of μ0ΔH=5T along the magnetic easy c axis. A highly relevant feature is the small crystalline electric field splitting of the Pr3+ (J=4) multiplet, which appears to be comparable with the effective exchange interaction in the magnetic ordering. This leads to the full saturation moment of the Pr3+ ion in small fields and an accumulation of magnetic entropy in the vicinity of the magnetic ordering. The weakly first-order nature of the ferromagnetic transition and the subsequent reentrant spin-glass transitions below TC are features further enhancing the magnetocaloric effect. Given the strong magnetic anisotropy, a large rotating magnetocaloric effect becomes achievable in this material.

Dependence of transport coefficients of Yb(Rh1−xCox)2Si2 intermetallics on temperature and cobalt concentration

Dependence of transport coefficients of the Yb(Rh$_{1-x}$Co$_x$)$_2$Si$_2$ series of alloys on temperature and cobalt concentration is explained by an asymmetric Anderson model which takes into account the exchange scattering of conduction electrons on ytterbium ions and the splitting of 4$f$-states by the crystalline electric field (CEF). The substitution of rhodium by cobalt is described as an increase of chemical pressure which reduces the exchange coupling and the CEF splitting. The scaling analysis and numerical NCA solution of the model show that the effective degeneracy of the 4$f$-state at a given temperature depends on the relative magnitude of the Kondo scale and the CEF splitting. Thus, we find that dependence of the thermopower, $S(T)$, on temperature and cobalt concentration can be understood as an interplay of quantum fluctuations, driven by the Kondo effect, and thermal fluctuations, which favor a uniform occupation of the CEF states. The theoretical model captures all the qualitative features of the experimental data and it explains the evolution of the shape of $S(T)$ with the increase of cobalt concentration.