Effect of Spin–Orbit Coupling on Kondo Phenomena in f⁷-Electron Systems

Abstract

In order to promote our basic understanding on the Kondo behavior recently observed in europium compounds, we analyze an impurity Anderson model with seven f electrons at an impurity site by employing a numerical renormalization group method. The local part of the model consists of Coulomb interactions among f electrons, spin-orbit coupling λ, and crystalline electric field (CEF) potentials, while we consider the hybridization V between local f electrons and single-band conduction electrons with au symmetry. For λ = 0, we observe the underscreening Kondo behavior for appropriate values of V , characterized by the entropy change from ln 8 to ln 7, in which one of seven f electrons is screened by conduction electrons. When λ is increased, we obtain two types of behavior depending on the values of V . For large V , we find the entropy release of ln 7 at low temperatures, determined by the level splitting energy due to the hybridization. For small V , we also observe the entropy change from ln 8 to ln 2 by the level splitting due to the hybridization, but at low temperatures, ln 2 entropy is found to be released, leading to the Kondo effect. We emphasize that the Kondo behavior for small V is observed for realistic values of λ in the order of 0.1 eV. We also discuss the effect of CEF potentials and the multipole properties in the Kondo behavior found in this paper.

Europium mixed-valence, long-range magnetic order, and dynamic magnetic response in EuCu2(SixGe1−x)2Nemkovski1, Козленко2, Alekseev3 et al. 2016Phys. Rev. B301140View full textAdd to dashboardCite

“…Recently, the existence of a HF state in Eu-based compounds has attracted renewed interest. [23][24][25][26][27][28] This behavior has been clearly evidenced, in particular for the MV compound EuNi 2 P 2 (v = 2.45-2.55), from thermodynamic and transport, 25 as well as spectroscopic measurements.…”

“…In a recent paper, 28 Hotta has proposed an interesting theoretical basis to explain how the 4f 7 state of Eu 2+ can give rise to a Kondo phenomenology (including quantum criticality controlled by an external parameter) very similar to that found in nearly trivalent (4f 1 ) Ce compounds. The key argument is that, for realistic values of the spin-orbit coupling, a correct description of atomic 4f states cannot be achieved in terms of the standard Russel-Saunders scheme.…”

Europium mixed-valence, long-range magnetic order, and dynamic magnetic response in EuCu$_{2}$(Si$_{x}$Ge$_{1-x}$)$_{2}$

“…Recently, the existence of a HF state in Eu-based compounds has attracted renewed interest. [23][24][25][26][27][28] This behavior has been clearly evidenced, in particular for the MV compound EuNi 2 P 2 (v = 2.45-2.55), from thermodynamic and transport, 25 as well as spectroscopic measurements. 24,27 Hossain et al 23 have also reported the observation of Kondo effect with a HF behavior in the EuCu 2 (Si x Ge 1−x ) 2 series.…”

Magnetic, Transport, and Phonon Properties of the Trivalent Eu Metallic Compound EuBe13

“…The valence state of the Eu ion can be tuned easily by external parameters, such as temperature and pressure, because the energy difference between the two valence states is relatively small. 23) In this context, it will be useful to examine the relationship between the valence state and free space of the Eu ion in various Eu-based compounds, since the effective radii of Eu ions are different between the two valence states. EuBe 13 is a valuable material for studying not only the phonon property in MBe 13 systems but also characteristics of the Eu 3+ state.…”