Competition between Hund-Rule Coupling and Kondo Effect

Abstract

We investigate a problem about the competition between the hybridization and the Hundrule coupling by applying the Wilson numerical renormalization-group method to the extended Kondo model where the impurity spin interacts via the Hund-rule coupling, with an extra spin which is isolated from the conduction electrons. It is shown that the Hund-rule coupling is an irrelevant perturbation against the strong coupling fixed point. However, the Hund-rule coupling decreases the characteristic energy TK drastically to the lower side and the irrelevant operator, which describes the low energy physics, takes a form of ferromagnetic exchange interaction between the extra spin and the Kondo resonance states because of the existence of the Hundrule coupling.KEYWORDS: Hund-rule coupling, Kondo effect, numerical renormalization-group, anisotropic hybridization, plural electrons at localized orbitals, transition between high-spin and low-spin state, Uranium based heavy fermion, Ni-doped High-Tc cuprate §1. IntroductionOne of the most important question concerning heavy fermion systems 1) , which exhibit the exotic phenomena such as anisotropic superconductivity and extremely weak anitiferromagnetism is to understand how the low energy quasipartile states are formed, in other words, how the high energy incoherent states are reflected in the low energy physics. Many theoretical attempts have been made to include higher Crystalline Electric Field (CEF) effects both in single impurity 2,3,4,5) and lattice case 6,7,8) . When the degenerate orbitals are deformed by CEF, the hybridizations between the deformed orbitals and conduction electrons become anisotropic in general. The anisotropic hybridization produces different characteristic energies for each CEF orbitals. As a result, the orbital which concerns the Kondo effect changes depending on the temperature range.For Ce based compounds this anisotropy is reflected in the formation of highly renormalized quasiparticle band only through the one-body effect: its typical example has been put forward in Ref. 9 to explain anomalous properties observed in CeNiSn. On the other hand, for U based compounds, where (5f ) 2 or (5f ) 3 configuration is realized, the anisotropic hybridizations may be reflected on the quasiparticles through a many-body effect, because at least two characteristic energy scales and the Hund-rule coupling are involved in the problem. The "spin of localized electron" tends to be quenched by the Kondo effect, while the Hund-rule coupling stabilizes the high-spin state. Then a competition between the two effects plays a crucial role in determining the low energy physics.Such a competition is likely to be realized in a variety of physical situations: For example, (i) the magnetic susceptibility in UPd 2 Al 3 can be fitted by a certain CEF scheme under the tetravalent U state ((5f ) 2 configuration) 10) while the Fermi surface measured by dHvA effect is in good agreement with the band structure calculation with the trivalent state ((5f ) 3 configuration) 11) , and the pho...

Strong Correlations from Hund’s Coupling

“…This is quite transparently seen, following Refs. [8,9,10,11,13], by considering a 'composite spin' Kondo (CSK) hamiltonian as a starting point:…”

“…The second is a low-energy effect, revealed in early studies of a single impurity atom coupled to a conduction electron gas (the Kondo problem). For a multi-orbital shell, the characteristic temperature below which screening of the atomic degrees of freedom takes place is considerably lowered by Hund's coupling [7,8,9,10,11,12,13]. This is due to the quenching of orbital momentum and associated loss of exchange energy, and explains the sensitive dependence of the Kondo temperature on the size of the impurity spin [14,15,16].…”

Low-energy physics of three-orbital impurity model with Kanamori interaction

“…The effects of the Hund's rule coupling were explored for several simpler (mostly two-orbital) models [14][15][16][17][18][19][20][21][22] . The common conclusion of these works is that the Hund's rule coupling suppresses the Kondo temperature through reduced exchange coupling of the low-lying impurity spin degrees of freedom with conduction electrons.…”

Quantum criticality associated with dimensional crossover in the iso-electronic series Ca2−x Sr x RuO4

“…There are, however, MO systems such as Ruthenates [3,4], iron pnictides [5,6] and chalcogenides [7] which are strongly correlated metals not at the border of a Mott insulating phase. The role of Hund's coupling [8][9][10][11][12] in single and two-particle responses in many such MO materials have now been extensively investigated. The Hund's coupling leads to an exponential suppression of the coherence scale of a MO metal and leads to a large spinfrozen non Fermi-liquid phase.…”