change in magnetic field due to its particular ground state. Consequently, an infinitesimally small magnetic field is enough to polarize the residual spin-a-half in the dot, which definitely hinders a full restoration of the un- derscreened Kondo effect by tuning the magnetic field. 

We acknowledge fruitful discussions with J. von Delft and R. ˇ Zitko. The authors acknowledge support from 

∗ Electronic address: weymann@amu.edu.pl 1 

W. J. de Haas and G. J. van den Berg, Physica 3 , 440 (1936). 2 

J. Kondo, Prog. Theor. Phys. 32, 37 (1964). 3 

A. C. Hewson, The Kondo Problem to Heavy Fermions (Cambridge University Press, Cambridge, 1993). 4 

D. Goldhaber-Gordon, H. Shtrikman, D. Mahalu, D. Abusch-Magder, U. Meirav, and M. A. Kastner, Nature (London) 391, 156 (1998). 5 

S. Cronenwett, T. H. Oosterkamp, and L. P. Kouwenhoven, Science 281, 182 (1998). 6 

M. R. Buitelaar, T. Nussbaumer, and C. Schnenberger, Phys. Rev. Lett. 89 , 256801 (2002). 7 

C. Buizert, A. Oiwa, K. Shibatam K. Hirikawa, and S. Tarucha, Phys. Rev. Lett. 99, 136806 (2007). 8 

A. N. Pasupathy, R. C. Bialczak, J. Martinek, J. E. Grose, L. A. K. Donev, P. L. McEuen, and D. C. Ralph, Science 306, 86 (2004). 9 

H. B. Heersche, Z. de Groot, J. A. Folk, L. P. Kouwen- hoven, H. S. van der Zant, A. A. Houck, J. Labaziewicz, and I. L. Chuang, Phys. Rev. Lett. 96, 017205 (2006). 10 

K. Hamaya, M. Kitabatake, K. Shibata, M. Jung, M. Kawamura, K. Hirakawa, T. Machida, T. Taniyama, S. Ishida and Y. Arakawa, Appl. Phys. Lett. 91 , 232105 (2007). 11 

K. Hamaya, M. Kitabatake, K. Shibata, M. Jung, M. Kawamura, S. Ishida, T. Taniyama, K. Hirakawa, Y. Arakawa, and T. Machida, Phys. Rev. B 77, 081302(R) (2008). 12 

J. Hauptmann, J. Paaske, P. Lindelof, Nature Phys. 4, 373 (2008). 13 

H. Yang, S.-H. Yang, S. S. P. Parkin, Nano Lett. 8 , 340 (2008). 14 

Rosa Lopez and David Sanchez, Phys. Rev. Lett. 90 , 116602 (2003). 15 

J. Martinek, Y. Utsumi, H. Imamura, J. Barna´s, S. Maekawa, J. K¨ onig, and G. Sch¨ on, Phys. Rev. Lett. 91 , 127203 (2003). 16 

J. Martinek, M. Sindel, L. Borda, J. Barna´s, J. K¨ onig, G. Sch¨ on, and J. von Delft, Phys. Rev. Lett. 91 , 247202 (2003). 17 

Mahn-Soo Choi, David Sanchez, and Rosa Lopez, Phys. Rev. Lett. 92 , 056601 (2004). 

## Acknowledgments 

the Alexander von Humboldt Foundation. I.W. acknowl- edges support from the Foundation for Polish Science and funds of the Polish Ministry of Science and Higher Education as research projects for years 2006-2009 and 2008-2010. Financial support by the Excellence Clus- ter ”Nanosystems Initiative Munich (NIM)” is grate- fully acknowledged. L.B. acknowledges the support from Hungarian Grants OTKA through projects K73361 and NNF78842. 

18 J. Martinek, M. Sindel, L. Borda, J. Barna´s, R. Bulla, J. K¨ onig, G. Sch¨ on, S. Maekawa, J. von Delft, Phys. Rev. B 72 , 121302(R) (2005). 19 

M. Sindel, L. Borda, J. Martinek, R. Bulla, J. K¨ onig, G. Sch¨ on, S. Maekawa, and J. von Delft, Phys. Rev. B 76 , 045321 (2007). 20 

P. Nozi`eres and A. Blandin, J. Phys. 41 , 193 (1980). 21 

Karyn Le Hur and B. Coqblin, Phys. Rev. B 56 , 668 (1997). 22 

P. Coleman and C. Pepin, Phys. Rev. B 68 , 220405(R) (2003). 23 

A. Posazhennikova and P. Coleman, Phys. Rev. Lett. 94 , 036802 (2005). 24 

P. Mehta, N. Andrei, P. Coleman, L. Borda, G. Zarand, Phys. Rev. B 72 , 014430 (2005). 25 

Nicolas Roch, Serge Florens, Theo A. Costi, Wolfgang Wernsdorfer, and Franck Balestro, Phys. Rev. Lett. 103 , 197202 (2009). 26 

Y. Utsumi, J. Martinek, G. Sch¨ on, H. Imamura, and S. Maekawa, Phys. Rev. B 71 , 245116 (2005). 27 

R. ´ Swirkowicz, M. Wilczy´ nski, M. Wawrzyniak, and J. Barna´s, Phys. Rev. B 73 , 193312 (2006). 28 

Daisuke Matsubayashi and Mikio Eto, Phys. Rev. B 75 , 165319 (2007). 29 

P. Simon, P. S. Cornaglia, D. Feinberg, and C. A. Balseiro, Phys. Rev. B 75 , 045310 (2007). 30 

K. G. Wilson, Rev. Mod. Phys. 47 , 773 (1975). 31 

R. Bulla, T. A. Costi, and T. Pruschke Rev. Mod. Phys. 80 , 395 (2008). 32 

A. I. T´ oth, C. P. Moca, O. Legeza, and G. Zar´ and, Phys. Rev. B 78 , 245109 (2008). 33 

O. Legeza, C. P. Moca, A. I. T´ oth, I. Weymann, G. Zar´ and, arXiv:0809.3143 (2008) (unpublished). 34 

We used the open access Budapest NRG code, http://www.phy.bme.hu/ ∼ dmnrg/ . 35 

A. Posazhennikova, B. Bayani, and P. Coleman, Phys. Rev. B 75 , 245329 (2007). 36 

M. Pustilnik and L. Borda, Phys. Rev. B 73 , 201301(R) (2006). 37 

D. E. Logan, Ch. J. Wright, and M. R. Galpin, arXiv:0906.3169 (unpblished). 

