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Register a new userKondo temperature and crystal field levels of Ce systems within a finite U Non-Crossing Approximation
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Pablo Roura-Bas Mr.
Publication date
2007
fields
Physics
and research's language is
English
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We calculate the Kondo temperature ($T_K$) and crystal-field levels of strongly correlated multiorbital systems solving the Anderson Impurity Model with the finite U Non-Crossing Approximation (UNCA) in its simplest scheme, that is, considering the self energies at lowest order in the 1/N diagrammatic expansion. We introduced an approximation to the vertex function that includes the double energy dependence and investigate its effect on the values of $T_K$ for simple electronic models. We also analyze the competition between the two spin flip mechanisms, involving virtual transitions to empty and doubly occupied states, in the determination of the ground state symmetry by including an extra diagram of higher order in $1/N.$ We finally combine the resulting simple formalism with {it ab initio} calculated electronic structures to obtain $T_K$s, ground states, and crystal field splittings in excellent agreement with experimental results for two particular Ce compounds, namely CeIn$_3$ and CeSn$_3$.
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We present a high-resolution photoemission study on the strongly correlated Ce-compounds CeCu_6, CeCu_2Si_2, CeRu_2Si_2, CeNi_2Ge_2, and CeSi_2. Using a normalization procedure based on a division by the Fermi-Dirac distribution we get access to the spectral density of states up to an energy of 5 k_BT above the Fermi energy E_F. Thus we can resolve the Kondo resonance and the crystal field (CF) fine-structure for different temperatures above and around the Kondo temperature T_K. The CF peaks are identified with multiple Kondo resonances within the multiorbital Anderson impurity model. Our theoretical 4f spectra, calculated from an extended non-crossing approximation (NCA), describe consistently the observed photoemission features and their temperature dependence. By fitting the NCA spectra to the experimental data and extrapolating the former to low temperatures, T_K can be extracted quantitatively. The resulting values for T_K and the crystal field energies are in excellent agreement with the results from bulk sensitive measurements, e.g. inelastic neutron scattering.
We present a simple approach to calculate the thermodynamic properties of single Kondo impurities including orbital degeneracy and crystal field effects (CFE) by extending a previous proposal by K. D. Schotte and U. Schotte [Physics Lett. A 55, 38 (1975)]. Comparison with exact solutions for the specific heat of a quartet ground state split into two doublets shows deviations below $10%$ in absence of CFE and a quantitative agreement for moderate or large CFE. As an application, we fit the measured specific heat of the compounds CeCu$_2$Ge$_2$, CePd$_{3}$Si$_{0.3}$, CePdAl, CePt, Yb$_2$Pd$_2$Sn and YbCo$_2$Zn$_{20}$. The agreement between theory and experiment is very good or excellent depending on the compound, except at very low temperatures due to the presence of magnetic correlations (not accounted in the model).
Quantum magnets with spin $J=2$, which arise in spin-orbit coupled Mott insulators, can potentially display multipolar orders. We carry out an exact diagonalization study of a simple octahedral crystal field Hamiltonian for two electrons, incorporating spin-orbit coupling (SOC) and interactions, finding that either explicitly including the $e_g$ orbitals, or going beyond the rotationally invariant Coulomb interaction within the $t_{2g}$ sector, causes a degeneracy breaking of the $J!=!2$ level degeneracy. This can lead to a low-lying non-Kramers doublet carrying quadrupolar and octupolar moments and an excited triplet which supports magnetic dipole moments, bolstering our previous phenomenological proposal for the stabilization of ferro-octupolar order in heavy transition metal oxides. We show that the spontaneous time-reversal symmetry breaking due to ferro-octupolar ordering within the non-Kramers doublet leads to electronic orbital loop currents. The resulting internal magnetic fields can potentially explain the small fields inferred from muon-spin relaxation ($mu$SR) experiments on cubic $5d^2$ osmate double perovskites Ba$_2$ZnOsO$_6$, Ba$_2$CaOsO$_6$, and Ba$_2$MgOsO$_6$, which were previously attributed to weak dipolar magnetism. We make further predictions for oxygen NMR experiments on these materials. We also study the reversed level scheme, where the $J!=!2$ multiplet splits into a low-lying magnetic triplet and excited non-Kramers doublet, presenting single-ion results for the magnetic susceptibility in this case, and pointing out its possible relevance for the rhenate Ba$_2$YReO$_6$. Our work highlights the intimate connection between the physics of heavy transition metal oxides and that of $f$-electron based heavy fermion compounds.
Starting with the heavy fermion compound CeNi$_9$Ge$_4$, the substitution of nickel by copper leads to a dominance of the RKKY interaction in competition with the Kondo and crystal field interaction. Consequently, this results in an antiferromagnetic phase transition in CeNi$_{9-x}$Cu$_x$Ge$_4$ for $x>0.4$, which is, however, not fully completed up to a Cu-concentration of $x=1$. To study the influence of single-ion effects on the AFM ordering by shielding the $4f$-moments, we analyzed the spin diluted substitution series La$_{0.5}$Ce$_{0.5}$Ni$_{9-x}$Cu$_x$Ge$_4$ by magnetic susceptibility $chi$ and specific heat $C$ measurements. For small Cu-amounts $xleq 0.4$ the data reveal single-ion scaling with regard to the Ce-concentration, while for larger Cu-concentrations the AFM transition (encountered in the CeNi$_{9-x}$Cu$_x$Ge$_4$ series) is found to be completely depressed. Calculation of the entropy reveal that the Kondo-effect still shields the 4$f$-moments of the Ce$^{3+}$-ions in CeNi$_8$CuGe$_4$.
We apply our recently developed, selfconsistent renormalization group (RG) method to STM spectra of a two-impurity Kondo system consisting of two cobalt atoms connected by a one-dimensional Cu chain on a Cu surface. This RG method was developed to describe local spin screening in multi-impurity Kondo systems in presence of the Ruderman-Kittel-Kasuya-Yosida (RKKY) interaction. Using the RKKY interaction of a one-dimensional chain, we explain the experimentally observed suppression and oscillation of the Kondo temperature, $T_K(y)$, as a function of the length of the chain and the corresponding RKKY interaction parameter $y$, regardless of the RKKY coupling being ferromagnetic or antiferromagnetic.
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