Kondo quantum dot coupled to ferromagnetic leads: Numerical renormalization group study

Abstract

We systematically study the influence of ferromagnetic leads on the Kondo resonance in a quantum dot tuned to the local moment regime. We employ Wilson's numerical renormalization group method, extended to handle leads with a spin asymmetric density of states, to identify the effects of (i) a finite spin polarization in the leads (at the Fermi-surface), (ii) a Stoner splitting in the bands (governed by the band edges) and (iii) an arbitrary shape of the leads density of states. For a generic lead density of states the quantum dot favors being occupied by a particular spin-species due to exchange interaction with ferromagnetic leads leading to a suppression and splitting of the Kondo resonance. The application of a magnetic field can compensate this asymmetry restoring the Kondo effect. We study both the gate-voltage dependence (for a fixed band structure in the leads) and the spin polarization dependence (for fixed gate voltage) of this compensation field for various types of bands. Interestingly, we find that the full recovery of the Kondo resonance of a quantum dot in presence of leads with an energy dependent density of states is not only possible by an appropriately tuned external magnetic field but also via an appropriately tuned gate voltage. For flat bands simple formulas for the splitting of the local level as a function of the spin polarization and gate voltage are given.

Keldysh effective action theory for universal physics in spin-12Kondo dots

“…16 The whole temperature range can be comprehensively numerically described in equilibrium by the numerical renormalization group (NRG) method, 17 which is quite flexible with respect to different physical setups and has been used, e.g., for QDs coupled to ferromagnetic contacts. 18 In nonequilibrium the recently developed semianalytical realtime renormalization group (RTRG) method 19 is a promising theory.…”

Dimensionality effects in the local density of states of ferromagnetic hosts probed via STM: Spin-polarized quantum beats and spin filtering

“…(3) and on the bottom band D σ = D + σ with D as the unpolarized half-width and as the Stoner splitting. 35 In particular, for a small polarization P , Eq. (27) results in slightly different Fermi wave numbers and, consequently, in spin-polarized quantum beats in the full LDOS as we will see.…”

“…24 In the condensed-matter literature on scanning microscopy, there is a profusion of work discussing spin-dependent phenomena employing ferromagnetic leads coupled to quantum dots or adatoms in the Kondo regime. 4,6,7,[25][26][27][28][29][30][31][32][33][34][35][36][37][38][39][40][41][42][43][44] Here, we mention those with metallic samples and buried impurities in which the anisotropy of the Fermi surface plays an important role in electron tunneling. [45][46][47][48][49][50] According to the experiment of Prüser et al, 45 such anisotropy allows atoms of Fe and Co beneath the Cu(100) surface to scatter electrons in preferential directions of the material due to an effect called "electron focusing."…”

Sources of negative tunneling magnetoresistance in multilevel quantum dots with ferromagnetic contacts

“…The leads are described byĤ l = σ q lqĉ † lσ qĉ lσ q , witĥ c lσ q annihilating an electron of energy lq and of spin σ in lead l. The density of states in lead l, D lσ (ω), is assumed to be constant over an energy range set by a spin-dependent bandwidth: 12,13 …”

“…Both can be explained in terms of charge fluctuations, 10 whereby electron-electron interactions are responsible for the logarithmic gate dependence, 11 while a Stoner splitting of the energy bands of the magnetically polarized leads accounts for the almost gate-independent part. 12,13 While the effects of the energy level shifts in the Kondo regime are by now well understood, a thorough understanding of their influence on the TMR phenomenon in interacting quantum dots is still missing. The negative TMR data 1 have been satisfactorily fitted in terms of a generalized Anderson model already including gate-independent level shifts.…”