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.
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