Long range ordered, dimerized, large-D and Haldane phases in spin 1 chain compounds

In 1983, F. Duncan M. Haldane predicted a singlet ground state for isolated integer-spin one-dimensional antiferromagnets with low single-ion anisotropy D. Since then, a lot of species containing chains of integer spin ions were tested to check the basic conjecture on an energy gap separating the continuum of the excited states from the ground state. As a result of these studies, it has been established that there are numerous states competing with the Haldane phase, namely long-range ordered, dimerized, and large-D phases. The long-range magnetic order takes place due to sufficiently strong exchange interactions between adjacent chains. Dimerization results from the alternation of the exchange interactions within the chains. Both uniaxial and rhombic single-ion anisotropies can suppress the Haldane phase, which is robust only until some critical values. The choice between the competing phases depends also on exchange anisotropy. Excellent reviews on the basic results obtained during the first 20 years of investigation of these phenomena provided solid background for the future studies. Here, we present some developments in this field obtained over the next two decades of research on spin-1 chain systems.