Neutron Diffraction Measurement of the Effective Magnetic Moment of Ni2+ in KNiF3

Two main effects reduce the apparent moment associated with a cation in an ordered antiferromagnet. Covalency tends to spread the moment onto the adjacent anions resulting in a loss due to cancellation at the ligand,¹ and the nature of the antiferromagnetic ground state gives rise to zero point deviations from fully aligned spins.² The latter effect has proved very difficult to measure experimentally with accuracy. In principle the moment associated with the cation may be measured using neutron diffraction by extrapolation of the magnetic Bragg peak intensities to forward scattering. The present measurements were carried out on an ideal antiferromagnet, KNiF₃, in order to test the current theories of covalency and spin deviations. The magnitude of both effects may be predicted in this compound^1,2 as the covalency parameters are known from NMR work.³ From powder diffraction at 4.2°K we find a value of 1.495 (±0.020) for ${\mathrm{[g〈S}}_z{〉}_0{\mathrm{\hspace{0.17em}f(\tau }}_{111}{\mathrm{)/F}}_{200}]$ giving a value of 0.851 (±0.050) for the effective value of ${\mathrm{〈S}}_z{〉}_0$ . The error in ${\mathrm{〈S}}_z{〉}_0$ here includes both the random error of the experiment (0.011), and possible systematic errors (0.039) due to the uncertainties in the current values of the Ni²⁺ g factor, the form factor, and the nuclear scattering lengths. This value for ${\mathrm{〈S}}_z{〉}_0$ may be compared with 0.803 calculated using the molecular orbital theory of covalency and spin wave theory, and 0.832 calculated using covalency parameters determined from a configuration interaction approach⁴ and perturbation calculations of the spin deviation.⁵ The experiments thus confirm the order‐of‐magnitude of the theoretical prediction, but the current systematic errors preclude an exact test of the theoretical approach at the present time. The measurements illustrate the difficulties in obtaining precise values of either covalency parameters or the spin deviation using this technique.