Kondo Effect of a Vibrating Magnetic Impurity

Abstract

A generalized Anderson model for a magnetic ion in a harmonic potential is formulated. The model is investigated by the numerical renormalization group (NRG) method. In addition to the conventional swave screening, the model exhibits phonon assisted p-wave Kondo effect as well as Yu and Anderson type Kondo effect. It is shown that the s-wave Kondo and the Yu-Anderson Kondo belong to the same fixed point. At the boundary between the s-wave and p-wave Kondo regions line of fixed points of the two channel Kondo effect is identified. Filled skutterudite compounds RT 4 X 12 (R = rare earth or alkaline earth element; T = Fe, Ru, Pt, or Os; X = P, As, Ge, or Sb) are characterized by their specific structures which involve a network of cages filled by guest ions. When the radius of the guest ion is smaller than the diameter of the cage, the guest ion vibrates with larger amplitude and smaller frequency than conventional localized modes. Such anharmonic local vibrations are referred to as rattling modes and may lead to novel phenomena of the coupled electron-phonon systems. Recent experiments on SmOs 4 Sb 12 show a large electronic specific heat coefficient linear in T, which is robust against magnetic field. 1) One possible scenario of the unusual behavior is the effect of strong electron-phonon coupling.When a magnetic ion couples with conduction electrons we expect Kondo effect due to the localized moment. On the other hand, it has been shown by Yu and Anderson (YA) that when conduction electrons couple strongly with ionic vibrations a different type of Kondo effect is expected.2) In this letter we will study the interplay between the conventional Kondo effect and the YA type one. Concerning the effects of coupling between a magnetic ion and ionic vibrations, Hotta has studied effects of anharmonicity in the Holstein-Anderson model.3) A lattice version of the Holstein-Anderson model is also studied. 4) In this letter, we will discuss effects of transverse vibrations on the Kondo effect rather than the breathing type vibrations.Suppose electron orbitals of a magnetic ion are described by the '-spherical-wave functions. Then the hybridization with the conduction electrons is given by overlap integrals between the '-wave localized orbitals and plane waves. To include the effect of vibrations the origin of the localized orbitals is shifted by Q which is the coordinate of the ion position. We can expand the overlap integral with respect to Q. In the zeroth order the localized '-spherical-waves hybridize with the '-partial-waves of conduction electrons. In the first order of Q, they hybridize with the ' þ 1 and ' À 1 partial waves. In the present letter we will concentrate on the simplest case of s-wave localized orbital. Then the total Hamiltonian up to the order of Q is given by the sum of

The Intra- and Interband Phonon-Electron Potentials in a Two-Band Model of Interacting Lattice Fermions

“…3) [10][11][12][13][14][15][16]. However, the considerations were based on the single-impurity Anderson model which represents a dilute magnetic alloy.…”

“…However, the considerations were based on the single-impurity Anderson model which represents a dilute magnetic alloy. Moreover, s, p, and localized f-electrons were investigated in [12][13][14][15][16]. Electrons of s-type were mixed with f-ones via the conventional hybridization while p-electrons were hybridized with f-ones owing to phonons.…”

“…This was introduced to explain some anomalies in behavior of the A15 compounds, e.g., the violation of Mattheissen's rule. This idea was next undertaken in the series of papers [11][12][13][14][15][16] where the so called two-channel Kondo was investigated. One of reasons was the possibility of nonmagnetic Kondo effect in some materials, e.g., SmOs 4 Sb 12 that possesses a cage-like structure.…”

Electric dipolar susceptibility of the Anderson-Holstein model

“…Such oscillation with large amplitude is frequently called rattling and it is considered to play crucial roles for the formation of magnetically-robust heavy electron state in SmOs 4 Sb 12 [2]. This peculiar heavyelectron state has been theoretically investigated from various aspects by several groups [3][4][5][6][7][8][9][10][11][12][13][14][15][16][17].Recently, the Kondo effect of a vibrating magnetic ion in a cage has been theoretically discussed on the basis of a two-channel conduction electron system hybridized with a vibrating magnetic ion [18][19][20]. Note here that a vibrating ion inevitably induces electric dipole moment.…”

“…Recently, the Kondo effect of a vibrating magnetic ion in a cage has been theoretically discussed on the basis of a two-channel conduction electron system hybridized with a vibrating magnetic ion [18][19][20]. Note here that a vibrating ion inevitably induces electric dipole moment.…”