Yafet-Kittel Angles in Zinc-Nickel Ferrites

The chemical and magnetic structures of the ${\mathrm{Zn}}_x{\mathrm{Ni}}_{1-x}{\mathrm{Fe}}_2{\mathrm{O}}_4$ system have been determined using neutron diffraction for $x=0, 0.25, 0.50, \mathrm{and} 0.75$. The data yield a cation distribution (${{\mathrm{Zn}}_x}^{2+}{{\mathrm{Fe}}_{1-x}}^{3+}$) [${{\mathrm{Ni}}_{1-x}}^{2+}{{\mathrm{Fe}}_{1+x}}^{3+}$]. All the mixed ferrites show a noncollinear, Yafet-Kittel (YK) type of magnetic ordering. The YK angles increase with the zinc content and for a given composition decrease with increasing temperature. For $x=0.25\mathrm{} \mathrm{and} 0.50$, there is a transition from the YK to Néel type of ordering prior to the paramagnetic transition. The Néel region decreases with increasing $x$; thus, for $x=0.75\mathrm{}$, there is no Néel region, while Ni${\mathrm{Fe}}_2$${\mathrm{O}}_4$ has the Néel type of ordering at all temperatures. The YK angle can be analytically related to $x$, using the molecular-field theory. The angles predicted in this manner are consistent with a three-sub-lattice molecular-field analysis of the paramagnetic susceptibility data of Néel and Brochet.