A new paradigm for two-dimensional spin liquids

Motivated by the geometry of the materials Na2Ti2As2O and Na2Ti2Sb2O, we study a square-lattice Heisenberg antiferromagnet, with spins located at the bond centers. The largest exchange constant J couples neighboring spins in a given row or column. This leads to a mesh of isolated spin chains running along the X and Y axes. A weaker exchange constant J′ couples the nearest-neighbor spins on the lattice. Classically, J′ fails to fix the relative spin orientation for different chains and hence the ground state is highly degenerate. Quantum order by disorder effect is studied by spin-wave theory and numerical methods. It is shown that a four-sublattice order is favored by quantum fluctuations. However, several arguments are presented that suggest that the ground state of the system remains disordered, thus providing us with a paradigm for a two-dimensional spin liquid.