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Unconventional magnetic properties of the low-dimensional ruthenates Sergey Streltsov, Institute of Metal Physics, Ekaterinburg, Russia On the example of several Ru oxides we will discuss such effects as Effective reduction of the dimensionality due to orbital degrees of freedom (Tl2Ru2O7 [1]); Suppression of the magnetic moments in the 4d and 5d transition metal oxides (Ba4Ru3O10 [2], Ba3CoRu2O9 [3]); Competition between the conventional double exchange, leading to ferromagnetism, and the tendency for electrons with strongly overlapping orbitals and large intersite hopping to form a nonmagnetic singlet molecular orbitals on a dimer (Ba3NaRu2O9) [4]; Orbital-selective behavior, valence bond liquid state and other consequences of the molecular orbitals formation (Li2RuO3) [4-7]; References [1] S. Lee, J.-G. Park, D. T. Adroja, D. Khomskii, S. Streltsov, K. A. McEwen, H. Sakai, K. Yoshimura, V. I. Anisimov, D. Mori, R. Kanno, and R. Ibberson, Nat. Mater. 5, 471 (2006). [2] S. V. Streltsov and D. I. Khomskii, Phys. Rev. B 86, 064429 (2012). [3] S. V. Streltsov, Phys. Rev. B 88, 024429 (2013). [4] S. V Streltsov and D. I. Khomskii, Phys. Rev. B 89, 161112 (2014). [5] S. A. J. Kimber, I. I. Mazin, J. Shen, H. O. Jeschke, S. V Streltsov, D. N. Argyriou, R. Valenti, and D. I. Khomskii, Phys. Rev. B 89, 081408 (2014). [6] J. C. Wang, J. Terzic, T. F. Qi, F. Ye, S. J. Yuan, S. Aswartham, S. V. Streltsov, D. I. Khomskii, R. K. Kaul, and G. Cao, Phys. Rev. B 90, 161110 (2014). [7] Z. Pchelkina, A. Pitman, A. Moewes, E. Kurmaev, T.-Y. Tan, D. Peets, J.-G. Park, and S. V. Streltsov, Phys. Rev. B 91, 115138 (2015).