  Materials with strong spin-orbit interactions are presently a main target in
the search for systems with novel magnetic properties. Magnetic anisotropies
can be very large in such compounds, ranging from strongly frustrated Kitaev
exchange in honeycomb iridates and the associated spin-liquid states to robust
antisymmetric couplings in square-lattice Sr_2IrO_4 . Here we predict from ab
initio quantum chemistry calculations that another highly unusual regime is
realized in pyrochlore iridium oxides: the nearest-neighbor Heisenberg
interaction can vanish whilst the antisymmetric Dzyaloshinskii- Moriya exchange
reaches values as large as 5 meV, a result which challenges common notions and
existing phenomenological models of magnetic superexchange. The resulting spin
excitation spectra reveal a very flat magnon dispersion in the Nd- and Tb-based
pyrochlore iridates, suggesting the possibility of using these modes to store
magnetic information. Indeed the magnetization dynamics indicates that these
modes are unable to propagate out of the excitation region.
