Coexistence of Haldane gap excitations and long range antiferromagnetic order in mixed-spin nickelates R₂ Ba Ni O₅

The spin dynamics of the S=1 Ni-chains in mixed-spin antiferromagnets Pr_2 Ba Ni O_5 and Nd_x Y_2-x Ba Ni O_5 is described in terms of a simple Ginzburg-Landau Lagrangian coupled to the sublattice of rare-earth ions. Within this framework we obtain a theoretical explanation for the experimentally observed coexistence of Haldane gap excitations and long-range magnetic order, as well as for the increase of the Haldane gap energy below the Neel point. We also predict that the degeneracy of the Haldane triplet is lifted in the magnetically ordered phase. The theoretical results are consistent with the available experimental data.