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Cu$_3$TeO$_6$, a three-dimensional antiferromagnet forming a unique spin-weblattice of spin-1/2 Cu2+ ions below the Neel temperature T$_N$ = 62 K, hasrecently been found to exhibit topological Dirac or nodal magnon dispersion. Inthis study, we report the discovery of the linear magnetoelectric (ME) effectsin Cu$_3$TeO$_6$ below TN. Our pyroelectric current measurements at a constantmagnetic field (H) reveal a linear increase of electric polarization (P) with Hfor both P // H and P $\perp$ H configurations; a maximum P // [110] = 20$\mu$C/m$^2$ is obtained at u0H // [1-10] = 14 T, corresponding to a linear MEcoefficient 1.8 ps/m. Magnetic point group analysis and Monte-Carlo simulationsconfirm that finite linear ME coefficients are allowed in the off-diagonal anddiagonal ME tensor components, consistent with the magnetic point group of$\bar{3}'$. As the parity-time symmetry can be broken in the presence of H orelectric field E in the linear ME materials, we envisage that Cu$_3$TeO$_6$should exhibit a H- or E-induced transformation in the topological magnondispersion from a Dirac point/nodal line type into two Weyl point types.

Observation of linear magnetoelectric effect in a Dirac magnon antiferromagnet Cu$_3$TeO$_6$