arXiv:1102.1154v1 [cond-mat.mes-hall] 6 Feb 2011 Kondo screening regimes of a quantum dot with a single Mn ion E. Vernek, 1 Fanyao Qu, 2 F. M. Souza, 1 J. C. Egues, 3 and E. V. Anda 4 1 Instituto de F´ ısica - Universidade Federal de Uberlˆ andia - Uberlˆ andia, MG 38400-902 - Brazil 2 Instituto de F´ ısica - Universidade de Bras´ ılia - Bras´ ılia, DF 70919-970 - Brazil 3 Departamento de F´ ısica e Inform´ atica, Instituto de F´ ısica de S˜ ao Carlos, Universidade de S˜ ao Paulo, 13560-970 S˜ ao Carlos, S˜ ao Paulo, Brazil 4 Departamento de F´ ısica, Pontif´ ıcia Universidade Cat´ olica, Rio de Janeiro-RJ, Brazil (Dated: October 14, 2013) We study the Kondo and transport properties of a quantum dot with a single magnetic Mn ion connected to metallic leads. By employing a numerical renormalization group technique we show that depending on the value of ferromagnetic coupling strength between the local electronic spin and the magnetic moment of the Mn, two distinct Kondo regimes exist. In the weak coupling limit, the system can be found in a completely screened Kondo state describing a local magnetic moment decoupled from the rest of the system. In contrast, in the strong coupling regime the quantum dot spin and the local magnetic moment form a single large-spin entity partially Kondo screened. A crossover between these two regimes can be suitably tuned by varying the tunnel coupling between the quantum dot electron and the leads. The model investigated here is also suitable to study magnetic molecules adsorbed on a metallic surface. The rich phenomenology of these systems is reflected in the conductance across the system. PACS numbers: 72.20-i, 73.23.Hk, 75.50.Pp, 71.21.La, 72.10.-d, 73.21.La, 75.50.Xx Spin manipulation of localized impurities is of great interest in spintronics and quantum computation[1]. In this context, diluted magnetic semiconductor quantum dots (DMSQDs) could play a prominent role as they al- low the control of the spins of the magnetic ions[2, 3]. In general DMSQDs are grown in II-VI semiconductor composites with a few Mn atoms in each quantum dot (QD)[4]. In these systems, the coupling between the spins of the electrons in the QD and those of the manganese arises from the sp − d exchange interaction. More recently, the successful fabrication of QDs doped with a single Mn 2+ ion[5–7] has stimulated many optical and transport measurements[8–10], demanding a great deal of theoretical efforts[11–14]. Recent investigations of these systems have uncovered many interesting physical phenomena[5, 7–10, 15–18]. For instance, the exchange interaction makes single photon emitters active at six dif- ferent frequencies, thus serving as the basic framework for the six-state qubit[12]. In this context, a very exotic system composed of an “impurity” with spin degrees of freedom coupled to a QD containing electrons (the impu- rity is outside the QD) has been proposed and studied, recently[17]. Fewer theoretical works, however, have ad- dressed the transport properties in these systems[19]. In this work we investigate the low temperature prop- erties of a quantum dot with a single magnetic Mn ion connected to leads. The study could be applied as well to analyze a magnetic molecules containing sites with correlated electrons, adsorbed on a metallic sur- face or connected to independent leads. Although the ideas have this general scope, to be concrete, we re- strict our discussion to a system composed of a Mn 2+ ion implanted in a small QD, coupled to two metallic (source and drain) leads, schematically represented in Fig. 1. It is well known that a QD connected to leads possesses a Kondo ground state similarly to what hap- pens in magnetic impurities embedded in metals under temperature below the characteristic Kondo temperature (T K )[21]. At the same time the electrons in the QD cou- ple to the Mn 2+ magnetic moment by a ferromagnetic exchange interaction, J , that can be optically or electri- cally tunned[14, 15]. The antiferromagnetic case will be discussed in detail elsewhere[23]. In our case, T K can be modified by tuning the hopping matrix element V that connects the localized and the lead states, while J in turn can be tailored by properly choosing the size of the QD[18]. Based on a numerical renormalization group (NRG) technique[24], our theoretical study shows two-distinct Kondo regimes: 1) T K /|J |≫ 1, where the QD spin is completely screened by the conduction spins comprising a Kondo state and the Mn 2+ is decoupled from the rest of the system and 2) T K /|J |≪ 1, in which the spins of the electrons in the QD strongly couples to the Mn 2+ spin, forming a large-spin local magnetic impurity that is partially screened by the conduction electrons: the un- derscreened Kondo state. A crossover between these two regimes is achieved by suitably tuning the parameters of the system. Our system is described by the Hamiltonian H = H imp + H bands + H T where H imp =  σ ε dσ c † dσ c dσ + Un d↑ n d↓ + J M · s (1) corresponds to the single-level QD and the Mn 2+ ion, in which the operator c † dσ (c dσ ) creates (annihilates) an electron of spin σ with energy ε d , U is the local Coulomb repulsion and M and s are the spin operators of the Mn 2+ ion and of the QD, respectively. The Hamilto-