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We propose a new form of the frustrated Heisenberg antiferromagneticHamiltonian with spatially anisotropic exchange parameters Jc, Ja, and Jacextended along the c, a, and a +/- c lattice directions and apply it todescribe fascinating physics of copper carbodiimide CuNCN in the assumption ofresonating valence bond (RVB) type of its phases. These are invoked to explainthe intriguing absence of magnetic order in CuNCN down to 4 K. We show that thequasiparticle spectrum of the RVB model of the proposed Hamiltonian has threeprincipal regimes: (i) one with two pairs of lines of nodes, (ii) one with apair of lines of nodes (termed as 1D- and Q1D-RVB states), (iii) and one withtwo pseudogaps and four nodal points (2D-RVB). We present a completeparameters-temperature phase diagram of the model constructed with use of thehigh-temperature expansion of the free energy. The phase diagram thus obtainedcontains eight different phases whose magnetic behavior includes Curie andPauli paramagnetism (respectively, in disordered and 1D- or Q1D-RVB phases),and gapped (quasi-Arrhenius) paramagnetism (2D-RVB phases). Addingmagnetostriction and elastic terms to the free energy we derive possiblestructural manifestations of transitions between RVB phases. Assuming asequence of transitions between RVB phases to occur in CuNCN while temperaturedecreases explains the features observed in the temperature runs of themagnetic susceptibility and lattice constants. Confronting these with themagnetic susceptibility and structure data measured as functions of temperaturein the range between ca. 20 and 200 K we show a remarkably good agreementbetween our theoretical predictions and the experiment as reached by ascribingthe model parameters values which are intuitively acceptable both in terms oftheir absolute and relative magnitudes and of the character of their geometrydependence.

c-a-ca Mean Field RVB Model of CuNCN Physics. Structure Manifestations of the RVB Transitions