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

Abstract

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 ${\ensuremath{\chi}}_{\ensuremath{\parallel}}^{*}$ [$\stackrel{\ensuremath{\rightarrow}}{\mathrm{H}}$ parallel to a (111) plane with $H=200$ Oe] from 4.2 to 700 K. From the behavior of ${\ensuremath{\chi}}_{\ensuremath{\parallel}}^{*}$ 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 ${\ensuremath{\chi}}_{p}=\frac{({\ensuremath{\chi}}_{\ensuremath{\parallel}}+{2\ensuremath{\chi}}_{\ensuremath{\perp}})}{3}$ and ${\ensuremath{\chi}}_{\ensuremath{\parallel}}^{*}=\frac{({\ensuremath{\chi}}_{\ensuremath{\parallel}}+{\ensuremath{\chi}}_{\ensuremath{\perp}})}{2}$ at various temperatures, the temperature variation of ${\ensuremath{\chi}}_{\ensuremath{\parallel}}$ and ${\ensuremath{\chi}}_{\ensuremath{\perp}}$, the principal susceptibilities, is determined. After correcting for ${\ensuremath{\chi}}_{\mathrm{vv}}$ and ${\ensuremath{\chi}}_{d}$ (the Van Vleck and diamagnetic susceptibilities) with ${\ensuremath{\chi}}_{\mathrm{vv}}+{\ensuremath{\chi}}_{d}=3.2\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}6}$ ${\mathrm{cm}}^{3}$/g, $\ensuremath{\chi}({T}_{N})=8.8\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}6}$ ${\mathrm{cm}}^{3}$/g, ${\ensuremath{\chi}}_{\ensuremath{\perp}}(0)=6.8\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}6}$ ${\mathrm{cm}}^{3}$/g, and ${\ensuremath{\chi}}_{\ensuremath{\parallel}}(0)=0$ are determined. It is shown that the spin-wave theory correctly gives the ratio $\frac{\ensuremath{\chi}({T}_{N})}{{\ensuremath{\chi}}_{\ensuremath{\perp}}(0)}$ and the temperature dependence of ${\ensuremath{\chi}}_{\ensuremath{\parallel}}$ to about 200 K if the experimental value of the spin reduction $\ensuremath{\Delta}S=0.19$ is used for ${\mathrm{Ni}}^{2+}$. From the experimental values of $\ensuremath{\chi}({T}_{N})$ and ${T}_{N}$ and the use of random-phase-approximation Green's-function theory, the magnitudes of exchange constants for NiO, viz. ${J}_{1}=34$ K and ${J}_{2}=202$ K, are determined.