Measurement of Spin-Wave Dispersion in NiO by Inelastic Neutron Scattering and Its Relation to Magnetic Properties

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Inelastic neutron scattering techniques have been used to measure the spin-wave dispersion relations at 78\ifmmode^\circ\else\textdegree\fi{}K in the fcc antiferromagnet NiO. The energy dispersion has a steep initial slope (\ensuremath{\sim}250 meV \AA{}) and a high maximum energy (\ensuremath{\sim}117 meV) and is further characterized by a relatively low zone boundary energy in certain directions. The exchange parameters defined by ${\mathcal{H}}^{1,2}={J}_{j}{\stackrel{\ensuremath{\rightarrow}}{\mathrm{S}}}^{(1)}\ifmmode\cdot\else\textperiodcentered\fi{}{\stackrel{\ensuremath{\rightarrow}}{\mathrm{S}}}^{(2)}$ were determined by fitting the theoretical expression for the spin-wave energies to the experimental data corrected for instrumental resolution effects. The predominant interaction is a large antiferromagnetic exchange ${J}_{2}=221\ifmmode^\circ\else\textdegree\fi{}$K (19.01 meV) between next-nearest neighbors, which are linked by a 180\ifmmode^\circ\else\textdegree\fi{} superexchange path. The interaction between nearest neighbors, linked by a 90\ifmmode^\circ\else\textdegree\fi{} ${\mathrm{Ni}}^{2+}$---${\mathrm{O}}^{2\ensuremath{-}}$---${\mathrm{Ni}}^{2+}$ configuration, is much smaller and ferromagnetic in sign, ${J}_{1}=\ensuremath{-}15.9\ifmmode^\circ\else\textdegree\fi{}$K (-1.37 meV). A consequence of the relatively small value of ${J}_{1}$ is that the spin waves from the four domains present in the sample can only be resolved in a limited region of reciprocal space. These values of exchange interactions are in accord with simple ideas of covalency and overlap, and the results emphasize the behavior of NiO as a weakly covalent insulator. The density of magnon states, estimates of the transition temperature, and several thermomagnetic properties of NiO have been calculated from the measured exchange parameters using molecular field and random-phase-approximation Green's-function formulas.