Journal of Magnetism and Magnetic Materials 310 (2007) e343–e345 Kondo effect in single-molecule spintronic devices J. Martinek a,b,c,Ã , L. Borda d , Y. Utsumi e,c , J. Ko¨nig f , J. von Delft g , D.C. Ralph h , G. Scho¨n c , S. Maekawa b a Institute of Molecular Physics, Polish Academy of Sciences, 60-179 Poznan´, Poland b Institute for Materials Research, Tohoku University, Sendai 980-8577, Japan c Theoretische Festko¨perphysik, Universita ¨ t Karlsruhe, 76128 Karlsruhe, Germany d Theory of Condensed Matter, Hungarian Academy of Science, TU Budapest, Budapest H-1521, Hungary e Condensed Matter Theory Laboratory, RIKEN, Wako 351-0198, Saitama, Japan f Institut fu ¨ r Theoretische Physik III, Ruhr-Universita ¨ t Bochum, 44780 Bochum, Germany g Sektion Physik and Center for Nanoscience, LMU Mu ¨ nchen, 80333 Mu ¨ nchen, Germany h Laboratory of Atomic and Solid State Physics, Cornell University, Ithaca 14853, USA Available online 3 November 2006 Abstract We study the Kondo effect in a quantum dot or a single molecule coupled to ferromagnetic leads. Spin-dependent quantum charge fluctuations in the dot induce the lifting of the spin degeneracy of the dot. It leads to the dot’s level spin splitting observed in the nonequilibrium transport as a splitting of a zero-bias anomaly in the differential conductance. We discuss basic properties of this effect and its temperature dependence using numerical renormalization group technique. Recent experimental results fit well to our theoretical consideration. r 2006 Elsevier B.V. All rights reserved. PACS: 75.20.Hr; 72.15.Qm; 72.25.b; 73.23.Hk Keywords: Kondo effect; Molecular spintronics; Quantum dot; Ferromagnetism; Spin-dependent transport 1. Introduction Spintronics has recently become a mature branch of mesoscopic physics and nanotechnology. There is also significant progress in development of the molecular electronics. The intersection of these two fields namely molecular spintronics is just a rising topic. Here we discuss some first investigations in this direction and new experi- mental results obtained recently. We study a spin- dependent transport in a quantum dot or a single molecule attached to ferromagnetic leads. We investigate the low- temperature properties, where one can expect the many- body Kondo effect due to the presence of the strong correlations. 2. Model We model a dot or single molecule, which is coupled to ferromagnetic leads by means of the Anderson model described by the Hamiltonian: H ¼ X rks e rks a y rks a rks þ X s  0 d y s d s þ Ud y " d " d y # d # þ X rks V r d y s a rks þ h:c:; ð1Þ where a rks ðd s Þ are annihilation operators of electrons with spin-s ðs ¼"; #Þ in the lead r ¼ L; R (dot). The energy of the single dot level  0 may be tuned by a gate voltage V g , and U is the onsite Coulomb interaction. The ferromagnet- ism in the leads is accounted for by the spin-dependent dispersion e rks and, hence, spin-dependent density of states n rs ðeÞ¼ P k dðe  e rks Þ. The spin-dependent coupling strength between the dot and the leads is given by G rs ¼ 2pjV r j 2 n s ðeÞ. ARTICLE IN PRESS www.elsevier.com/locate/jmmm 0304-8853/$ - see front matter r 2006 Elsevier B.V. All rights reserved. doi:10.1016/j.jmmm.2006.10.322 Ã Corresponding author. Institute of Molecular Physics, Polish Academy of Sciences, 60-179 Poznan´ , Poland. Tel.: +48 61 8695223; fax: +48 61 8684524. E-mail address: martinek@ifmpan.poznan.pl (J. Martinek).