Quantum and classical dynamics in complex one-dimensional antiferromagnets

Of great recent interest in condensed matter physics are phenomena of coexistence of quantum and classical properties in the same material. Such duality occurs in certain mixed-spin antiferromagnets composed of quantum spin chains interacting through ``auxiliary'' magnetic ions. In this category are linear-chain rare earth nickelates that exhibit a seemingly paradoxical co-existence of long-range magnetic order and one-dimensional gapped quantum spin excitations at low temperatures. In the present paper we propose a unified physical description of these compounds, supported by recent neutron diffraction and inelastic scattering studies. Our basic concept is the effective separation between low-frequency classical and high-frequency quantum spin correlations. This interpretation enables experimental measurements of some previously inaccessible fundamental properties of quantum spin chains, and predicts new exotic magnetic excitations and mechanisms of long-range ordering in complex quantum magnets.