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

We propose a new form of the frustrated Heisenberg antiferromagnetic Hamiltonian with spatially anisotropic exchange parameters Jc, Ja, and Jac extended along the c, a, and a +/- c lattice directions and apply it to describe fascinating physics of copper carbodiimide CuNCN in the assumption of resonating valence bond (RVB) type of its phases. These are invoked to explain the intriguing absence of magnetic order in CuNCN down to 4 K. We show that the quasiparticle spectrum of the RVB model of the proposed Hamiltonian has three principal regimes: (i) one with two pairs of lines of nodes, (ii) one with a pair of lines of nodes (termed as 1D- and Q1D-RVB states), (iii) and one with two pseudogaps and four nodal points (2D-RVB). We present a complete parameters-temperature phase diagram of the model constructed with use of the high-temperature expansion of the free energy. The phase diagram thus obtained contains eight different phases whose magnetic behavior includes Curie and Pauli paramagnetism (respectively, in disordered and 1D- or Q1D-RVB phases), and gapped (quasi-Arrhenius) paramagnetism (2D-RVB phases). Adding magnetostriction and elastic terms to the free energy we derive possible structural manifestations of transitions between RVB phases. Assuming a sequence of transitions between RVB phases to occur in CuNCN while temperature decreases explains the features observed in the temperature runs of the magnetic susceptibility and lattice constants. Confronting these with the magnetic susceptibility and structure data measured as functions of temperature in the range between ca. 20 and 200 K we show a remarkably good agreement between our theoretical predictions and the experiment as reached by ascribing the model parameters values which are intuitively acceptable both in terms of their absolute and relative magnitudes and of the character of their geometry dependence.