Ground-state phases in a system of two competing square-lattice Heisenberg antiferromagnets

We study a two-dimensional (2D) spin-half Heisenberg model related to the quasi 2D antiferromagnets (Ba,Sr)2Cu3O4Cl2 by means of exact diagonalization and spin-wave theory. The model consists of two inequivalent interpenetrating square-lattice Heisenberg antiferromagnets A and B. While the antiferromagnetic interaction JAA within the A subsystem is strong the coupling JBB within the B subsystem is much weaker. The coupling JAB between A and B subsystems is competing giving rise for interesting frustration effects. In dependence of the strength of JAB we find a collinear Neel phase, non-collinear states with zero magnetizations as well as canted and collinear ferrimagnetic phases with non-zero magnetizations. For not too large values of frustration JAB, which correpond to the situation in (Ba,Sr)2Cu3O4Cl2, we have Neel ordering in both subsystems A and B. In the classical limit these two Neel states are decoupled. Quantum fluctuations lead to a fluctuational coupling between both subsystems ('order from disorder') and select the collinear structure. For stronger JAB we find evidence for a novel spin state with coexisting Neel ordering in the A subsystem and disorder in the B subsystem.