Disorder‐induced local magnetic moments in weakly correlated metallic systems

Abstract

Abstract. We consider the formation and the Kondo effect of local magnetic moments in the Anderson-Hubbard model with off-diagonal disorder. The existence of moments at sites weakly coupled to the environment is deduced in effective medium approximation. The distribution of moments is calculated both deep in the metallic phase and near the metal-insulator transition. We discuss the Kondo quenching of the moments and derive a distribution of local Kondo temperatures. Recent experimental studies of metallic samples of doped semiconductors have indicated that localized magnetic moments are formed in the metallic phase as these systems approach the metal-insulator transition [ 1 -71. In fact the contribution of these moments dominates the magnetic and thermodynamic properties at low temperatures. The moments are thought to be intrinsic, i.e formed by the same dopant atoms that form the impurity conduction band, rather than being due to additional magnetic ions. There are two issues involved here: (i) the formation of moments, (ii) the eventual quenching of the moments due to coupling to the environment or among each other at low temperature. According to the conventional picture of moment formation [8], a spindegenerate atomic level of an impurity placed sufficiently below the Fermi energy is split by the Coulomb interaction into two levels. There is a level at the original position involving single occupancy and an upper level above the Fermi energy involving double occupancy. Provided the coupling of the conduction electrons to the local impurity is sufficiently weak, the impurity will be occupied by a single electron to a good approximation, and will hence form a spin + local magnetic moment. In the case of doped semiconductors the levels forming the conduction band and the magnetic impurity belong to the same system of dopant atoms, which therefore may be described by a one-band model. The atomic levels are the same at each dopant site, but the hopping elements are not, as the dopant atoms occupy random lattice sites in the host crystal lattice (we neglect possible short-range order correlation). In the metallic regime, i.e. for sufficiently large doping concentration, an impurity conduction band is formed, the Fermi energy lying in the center of the band, at the position of the atomic levels, for the uncompensated materials. Even though at first sight there appears to be no close similarity with above-described picture of the Anderson magnetic impurity, since

Disorder-quenched Kondo effect in mesoscopic electronic systems

“…Thus, for a sample containing many magnetic impurities, T K may be distributed due to fluctuations of the microscopic exchange coupling. 6,7,8 Impurities (magnetic or nonmagnetic) and lattice defects also cause fluctuations in the local density of states (LDOS) of the conduction electrons at the magnetic impurity site. Thus, the distributions of the Kondo temperature and of the LDOS are related in a disordered metal.…”

Disorder, electron-electron interactions and the metal-insulator transition in heavily doped Si:P

“…This clearly indicates that the Bhatt-Lee model is unsuited for the metallic state although its validity has often been tacitly assumed in this range. The origin of localized moments in the metallic state has been investigated in a numberof approaches [22,23,24,25,20], most of them starting with an AndersonHubbard model which is the simplest model Hamiltonian featuring the essential elements of disorder, through random hopping integrals t/j, and on-site Coulomb interaction U:…”

“…The various approaches differ in the type of mean-field model employed. In the approach taken by Langenfeld and WSlfle [25] the starting point is the observation that the fraction of dopant atoms carrying a localized moment in the metallic state is relatively small, of the order of several percent at Nc (see Fig. 3).…”

Electron‐electron interactions and the metal‐insulator transition in heavily doped silicon

“…The origin of localized moments in the metallic state has been investigated in a number of approaches [27,[30][31][32][33], most of them starting with an Anderson-Hubbard model which is the simplest model Hamiltonian featuring the essential elements of disorder, through random hopping integrals t ij , and on-site Coulomb repulsion U :…”

“…The various approaches differ in the type of mean-field model employed. In the approach taken by Langenfeld and Wölfle [33] the starting point is the observation that the fraction of dopant atoms carrying a localized moment in the metallic state is relatively small, of the order of several percent at N c [26]. The donor sites i are assumed to be on a regular simple-cubic lattice and the disorder is introduced through a variation of t ij .…”