  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.
