JETP Letters: issues online

In this Letter we address a challenging problem of a competition of charge and spin orders for high-T_c cuprates within a simplified 2D spin-pseudospin model which takes into account both conventional Heisenberg Cu²⁺-Cu²⁺ antiferromagnetic spin exchange coupling (J) and the on-site (U) and inter-site (V) charge correlations in the CuO₂ planes with the on-site Hilbert space reduced to only three effective charge states (nominally Cu^1+;2+;3+). We performed classical Monte-Carlo calculations for large square lattices implying the mobile doped charges and focusing on a case of a small inter-site repulsion $V\ll J$ . The on-site attraction (U<0) does suppress the antiferromagnetic ordering and gives rise to a checkerboard charge order with the doped charge distributed randomly over a system in the whole temperature range. However, under the on-site repulsion (U>0) the homogeneous ground state antiferromagnetic solutions of the doped system found in a mean-field approximation are shown to be unstable with respect to a phase separation with the charge and spin subsystems behaving like immiscible quantum liquids. Puzzlingly, with lowering the temperature one can observe two sequential phase transitions: first, an antiferromagnetic ordering in the spin subsystem diluted by randomly distributed charges, then, a charge condensation in the charge droplets. The effects are illustrated by the Monte-Carlo calculations of the specific heat and longitudinal magnetic susceptibility.