LAUSR

Using single-crystal neutron diffraction we show that the magnetic structure ${\mathrm{Ni}}_{3}{\mathrm{TeO}}_{6}$ at fields above 8.6 T along the $c$ axis and low temperature changes from a commensurate collinear antiferromagnetic structure with spins along $c$ and ordering vector ${Q}_{\mathrm{C}}=(0\phantom{\rule{0.28em}{0ex}}0\phantom{\rule{0.28em}{0ex}}1.5)$ to a conical spiral with propagation vector ${Q}_{\mathrm{IC}}=(0\phantom{\rule{0.28em}{0ex}}0\phantom{\rule{0.28em}{0ex}}1.5\ifmmode\pm\else\textpm\fi{}\ensuremath{\delta}), \ensuremath{\delta}\ensuremath{\sim}0.18$, having a significant spin component in the $(a,b)$ plane. We determine the phase diagram of this material in magnetic fields up to 10.5 T along $c$ and show the phase transition between the low field and conical spiral phases is of first order by observing a discontinuous jump of the ordering vector. ${Q}_{\mathrm{IC}}$ is found to drift both as a function of magnetic field and temperature. Preliminary inelastic neutron-scattering data reveal that the spin-wave gap in zero field has minima exactly at ${Q}_{\mathrm{IC}}$ and a gap of about 1.1 meV consisting with a crossover around 8.6 T. Further, a simple magnetic Hamiltonian accounting in broad terms for these is presented. Our findings confirm the exclusion of the inverse Dzyaloshinskii-Moriya interaction as a cause for the giant magnetoelectric due to symmetry arguments. In its place we advocate for the symmetric exchange striction as the origin of this effect.