  Continuous variable entanglement between magnon modes in Heisenberg
antiferromagnet with Dzyaloshinskii-Moryia (DM) interaction is examined.
Different bosonic modes are identified, which allows to establish a hierarchy
of magnon entanglement in the ground state. We argue that entanglement between
magnon modes is determined by a simple lattice specific factor, together with
the ratio of the strengths of the DM and Heisenberg exchange interactions, and
that magnon entanglement can be detected by means of quantum homodyne
techniques. As an illustration of the relevance of our findings for possible
entanglement experiments in the solid state, a typical antiferromagnet with the
perovskite crystal structure is considered, and it is shown that long wave
length magnon modes have the highest degree of entanglement.
