Low-temperature structure anomalies in CuNCN. Manifestations of RVB phase transitions?

We propose a new frustrated Heisenberg antiferromagnetic model with spatially anisotropic exchange parameters Jc, Ja, and Jac, extending along the c, a, and a ± c (c-a-ca model) lattice directions, and apply it to describe the fascinating physics of copper carbodiimide, CuNCN, assuming the resonating valence bond (RVB) type of its phases. This explains within a unified picture the intriguing absence of magnetic order in CuNCN. We further present a parameters-temperature phase diagram of the c-a-ca-RVB model in the high-temperature approximation. Eight different phases including Curie and Pauli paramagnets (respectively, in disordered and 1D- or Q1D-RVB phases) and (pseudo)gapped (quasi-Arrhenius) paramagnets (2D-RVB phases) are possible. By adding magnetostriction and elastic terms to the model, we derive possible structural manifestations of RVB phase transitions. Assuming a sequence of RVB phase transitions to occur in CuNCN with decreasing temperature, several anomalies observed in the temperature course of the lattice constants are explained.