Ground state of magnetic dimers on metal surfaces

We present model studies of the ground state for magnetic dimers on metal surfaces. We find it can be neither ferromagnetic nor antiferromagnetic, but is often canted for nearest neighbors. Thus, the system cannot be described using bilinear exchange. We give a criterion which can be used quite generally to interrogate the local stability of ferromagnetically or antiferromagnetically aligned dimers, and which also may be used to infer the canting angle when canted states are stable.