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CuNCN is a very special member of a novel class of materials, the transition-metal carbodiimides M(NCN) which may be looked upon as nitrogen-based analogs of the corresponding oxides with the rock-salt structure [1]. Although CuNCN is quite similar to the other family members in terms of stoichiometry and crystal structure, it strikingly differs from them with respect to its magnetic behavior. Indeed, while all other known transition-metal carbodiimides manifest more or less standard antiferromagnetic ground states, the nonmetallic CuNCN exhibits no magnetic scattering of polarized neutrons at either temperature down to several Kelvin [1,2]. At intermediate temperatures (between 80 and 350 K which, in fact, defines the upper limit of chemical stability of the material) CuNCN shows temperature-independent paramagnetism, which changes to a fair Arrhenius decay below 80 K [3] but without any signs of magnetic ordering as found from various spectroscopic techniques (ESR, NMR, SR). We have conjectured [3,4] that the above features may be related to the formation of resonating valence bond (RVB) – spin-liquid – phases of unpaired electrons residing on Cu2+ ions on an anisotropic triangular lattice. More specifically, the Arrhenius decay is tentatively attributed to the transition from a medium-temperature non-gapped 1D-RVB state to the low-temperature 2D-RVB gapped state. Following this idea, we have suggested [5] tentative structural manifestations of the aforementioned 1D- to 2D-RVB transition. A recent synchrotron structural study [6] is in harmony with the theoretical predictions [5]. This work is supported by DFG and by RFBR through the grant no. 10-03-00155. [1] X. Liu, R. Dronskowski, R. K. Kremer, M. Ahrens, C. Lee, M.-H. Whangbo, J. Phys. Chem. C 2008, 112, 11013 [2] H. Xiang, X. Liu, R. Dronskowski, J. Phys. Chem. C 2009, 113, 18891. [3] A. Zorko, P. Jeglič, A. Potočnik, D. Arčon, A. Balčytis, Z. Jagličić, X. Liu, A. L. Tchougréeff, R. Dronskowski, Phys. Rev. Lett. 2011, 107, 047208 [4] A. L. Tchougréeff, R. Dronskowski, arXiv:1008.0182. [5] A. L. Tchougréeff, R. Dronskowski, arXiv:1111.7210 [6] A. L. Tchougréeff, X. Liu, P. Müller, W. van Beek, U. Ruschewitz, R. Dronskowski, in preparation.