Exotic Kondo effects in metals: Magnetic ions in a crystalline electric field and tunnelling centres

The ordinary single-channel Kondo model consists of one or more spin-½ local moments interacting antiferromagnetically with conduction electrons in a metal. This model has provided a paradigm for understanding many phenomena of strongly correlated electronic materials, ranging from the formation of heavyfermion Fermi liquids to the mapping of a one-band model in the cuprate superconductors. The simplest extension of this ordinary Kondo model in metals which yields exotic non-Fermi-liquid physics is the multichannel Kondo impurity model in which the conduction electrons are given an extra quantum label known as the channel or flavour index. In the overcompensated regime of this model, nonFermi-liquid physics is possible, in contrast with the single-channel model. We overview here the multichannel Kondo impurity model candidates most extensively studied for explaining real materials, specifically the two-level system Kondo model relevant for metallic glasses, nanoscale devices and some doped semiconductors, and the quadrupolar and magnetic two-channel Kondo models developed for rare-earth and actinide ions with crystal-field splittings in metals. We provide an extensive justification for the derivation of the theoretical models, noting that, whenever the local impurity degree of freedom is non-magnetic, a two-channel Kondo model must follow by virtue of the magnetic spin degeneracy of the conduction electrons. We carefully delineate all energy and symmetry restrictions on the applicability of these models. We describe the various methods used to study these models along with their results and limitations (multiplicative renormalization group, numerical renormalization group, non-crossing approximation, conformal field theory and Abelian bosonization), all of which provide differing and useful views of the physics. We pay particular attention to the role that scale invariance plays in all these theoretical approaches. We point out in each case how various perturbing fields (magnetic, crystalline electric, electric field gradients and uniaxial stress) may destabilize the non-Fermi-liquid fixed point. We then provide an extensive discussion of the experimental evidence for the relevance of the two-level system Kondo model to metallic glasses and nanoscale devices, and of the quadrupolar and magnetic two-channel models to a number of heavyfermion-based alloys and compounds. We close with a discussion of the extension of the single-impurity models which comprise the main focus of this review to other systems (Coulomb blockade), multiple impurities and lattice models. In the latter case, we provide an overview of the relevance of the two-channel Kondo lattice model to non-Fermi-liquid behaviour and exotic superconductivity in heavy-fermion compounds and to the theoretical possibility of odd-frequency superconductivity, which is realized (for the first time) in the limit of infinite spatial dimensions for this model.     

Crystal potential model for the description of crystalline electric field effects in rare earth metals and intermetallics

A crystal potential model is suggested. It allows us to interpret crystalline electric field effects in optical, EPR, NMR, NGR and neutron spectroscopy measurements in rare earth metals and intermetallics. The crystal potential character and space distribution are discussed. The model is used for the theoretical interpretation of the effects of the crystalline field in the compound PrAl₃.     

Additional crystalline electric field potentials for heavy rare earth metals

A derivation is given of additional crystalline potential energy terms due to the interaction of conduction electrons with the localised electrons of ions in pure heavy rare earth metals. Explicit expressions for theA ₄ ⁰ andA ₆ ⁰ coefficients are given to supplement those ofA ₂ ⁰ andA ₆ ⁶ given in a recent paper. Additional contributions which arise from the unfilledf shells of the neighbours of any particular ion under consideration, are derived but shown to be of such a magnitude that, for most purposes, they can be neglected. The use of Slater orbitals in calculating enhancement factors forA ₄ ⁰ andA ₆ ⁰ is discussed with particular reference to those contributions which involve resonance amplitudes and mainly involve thef orbitals.     

Magnetic field effects on positron annihilation in metals

It is shown that the positron annihilation rate from a state with momentum k parallel to the magnetic field is periodic in $\text{1}\text{B}$, and that the periodicity is determined by the area of the section of the fermi surface whose z component of momentum is k.     

Crystalline field effects in metals: Thermoelectric power

We study the thermoelectric power of metals containing magnetic impurities with crystal-field split energy levels. Of special interest is the case where the ground state is a nonmagnetic singlet. It is shown that anomalous contributions arise, whose size can be nearly comparable with that found in the Kondo problem. However the mechanism leading to these effects is very different in the present problem, since it results from differences in the thermal population of the impurity levels. Also the anomalous contributions appear in a lower order of perturbation theory than they do in the corresponding Kondo problem calculations.     

Magnetic field effects on the nonohmic impurity conduction of uncompensated crystalline silicon

The impurity conduction of a series of crystalline silicon samples with the concentration of major impurity N ≈ 3 × 10¹⁶ cm^?3 and with a varied, but very small, compensation K was measured as a function of the electric field E in various magnetic fields H-σ(H, E). It was found that, at K < 10^?3 and in moderate E, where these samples are characterized by a negative nonohmicity (dσ(0, E)/dE < 0), the ratio σ(H, E)/σ(0, E) > 1 (negative magnetoresistance). With increasing E, these inequalities are simultaneously reversed (positive nonohmicity and positive magnetoresistance). It is suggested that both negative and positive nonohmicities are due to electron transitions in electric fields from impurity ground states to states in the Mott-Hubbard gap.     

Electric field effects in freely suspended liquid crystalline (FSLC) films of 5CB

Electric field effects on FSLC films of p-pentyl cyano biphenyl (5CB) have been optically studied. Due to the initial alignment of the molecules, initially formed transition layers grow with increasing field and merge to form a linear wall at the middle of the sample. This linear wall splits into two disclinations at relatively high fields. But a sudden application of relatively high electric field results in the formation of closed metastable walls. The wall orientation shows interesting behaviour with the field frequency. At high field, the closed walls undergo distortion and division into two or more parts.     

Electric field gradients in amorphous metals

The⁵⁷Fe-Mössbauer spectroscopy has been used in order to study the quadrupole splitting E_Q at the Fe-site and its dependence on temperature in Fe_85–XCr_XB₁₅ and Fe_80–XMo_XB₂₀ amorphous alloys. In all investigated compositions the local symmetry was lower than cubic with room temperature values of E_Q in the range of 0.4–0.5 mm/s. In all cases relatively broad distributions of E_Q and therefore of the EFG have been obtained. The EFG of the investigated compounds changes reversibly with temperature up to about 650 K according to the relation E_Q (T)=E_Q (O)·(1-BTV^3/2) as in the case of crystalline noncubic metals. Assuming that the same dependence of B on the Debye temperature as in crystalline non-cubic metals holds for amorphous alloys, values of have been obtained in good agreement with those determined from the temperature dependence of the Mössbauer f-factor.     

Theory of shear magnetostriction in amorphous and crystalline ferromagnetic metals

The theory of shear magnetostriction (SMS) in ferromagnetic metallic systems is formulated in terms of Green functions in real space for a tight binding model. This is general enough to include amorphous (“glassy”) alloys, as well as crystalline materials. It is shown that the SMS coefficient λ_s(E_F) must have at least four zeros as a function of band filling E_F through the d-band, which explains the change in sign between Fe alloys and Co, Ni alloys. A method is presented for computing the indefinite integral of the imaginary part of the product of two Green functions expressed as continued fractions, not necessarily over the same band width, and some preliminary calculations explore the importance of various terms.     

Aspherical 4f-shell effects in rare-earth metals: Electric field gradient at Dy probe nuclei

Systematic DPAC measurements of the electric field gradient at Dy in very low concentration in pure Pr, Nd, Gd, Tb, Dy, Ho and Er metals in the paramagnetic phase have shown for the first time the host associated aspherical 4f-shell effects. The results are compared with the presently available first-principles based calculations of the electric field gradient and crystalline electric field parameters of rare-earth ions in rare-earth metals and alloys. The observed 4f-spin relaxation time of Dy ion in rare-earth metals is of the order of 2 ps. This revised version was published online in August 2006 with corrections to the Cover Date.