Magnetic susceptibilities, their temperature variation, and exchange constants of NiO

The temperature variation of the magnetic susceptibilities of NiO for a powder sample and a single crystal has been measured from 4.2 to 700 K. The single crystal was stressed along a $〈111〉$ direction on cooling through $T_N$ (=524 K) with successive stress magnitudes of 7, 30, and 42 bars, followed in each case by measurements of ${\chi }_{\parallel }^{*}$ [$\overrightarrow{\mathrm{H}}$ parallel to a (111) plane with $H=200\mathrm{}$ Oe] from 4.2 to 700 K. From the behavior of ${\chi }_{\parallel }^{*}$ with stress, a stress of 30 bars was found to be sufficient to completely remove the $T$ domains. With the use of the data of initial powder susceptibility ${\chi }_p=\frac{({\chi }_{\parallel }+{2\chi }_{\perp })}{3}$ and ${\chi }_{\parallel }^{*}=\frac{({\chi }_{\parallel }+{\chi }_{\perp })}{2}$ at various temperatures, the temperature variation of ${\chi }_{\parallel }$ and ${\chi }_{\perp }$, the principal susceptibilities, is determined. After correcting for ${\chi }_{\mathrm{vv}}$ and ${\chi }_d$ (the Van Vleck and diamagnetic susceptibilities) with ${\chi }_{\mathrm{vv}}+{\chi }_d=3.2\mathrm{}\times {10}^{-6\mathrm{}}$ ${\mathrm{cm}}^3$/g, $\chi \left(T_N\right)=8.8\mathrm{}\times {10}^{-6\mathrm{}}$ ${\mathrm{cm}}^3$/g, ${\chi }_{\perp }\mathrm{}\left(0\right)=6.8\mathrm{}\times {10}^{-6\mathrm{}}$ ${\mathrm{cm}}^3$/g, and ${\chi }_{\parallel }\mathrm{}\left(0\right)=0\mathrm{}$ are determined. It is shown that the spin-wave theory correctly gives the ratio $\frac{\chi \left(T_N\right)}{{\chi }_{\perp }\mathrm{}\left(0\right)\mathrm{}}$ and the temperature dependence of ${\chi }_{\parallel }$ to about 200 K if the experimental value of the spin reduction $\Delta S=0.19\mathrm{}$ is used for ${\mathrm{Ni}}^{2+}$. From the experimental values of $\chi \left(T_N\right)$ and $T_N$ and the use of random-phase-approximation Green's-function theory, the magnitudes of exchange constants for NiO, viz. $J_1=34\mathrm{}$ K and $J_2=202\mathrm{}$ K, are determined.