Yafet-Kittel Angles in Zinc-Nickel Ferrites

Abstract

The chemical and magnetic structures of the ${\mathrm{Zn}}_{x}{\mathrm{Ni}}_{1\ensuremath{-}x}{\mathrm{Fe}}_{2}{\mathrm{O}}_{4}$ system have been determined using neutron diffraction for $x=0, 0.25, 0.50, \mathrm{and} 0.75$. The data yield a cation distribution (${{\mathrm{Zn}}_{x}}^{2+}{{\mathrm{Fe}}_{1\ensuremath{-}x}}^{3+}$) [${{\mathrm{Ni}}_{1\ensuremath{-}x}}^{2+}{{\mathrm{Fe}}_{1+x}}^{3+}$]. 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 $x=0.25 \mathrm{and} 0.50$, there is a transition from the YK to N\'eel type of ordering prior to the paramagnetic transition. The N\'eel region decreases with increasing $x$; thus, for $x=0.75$, there is no N\'eel region, while Ni${\mathrm{Fe}}_{2}$${\mathrm{O}}_{4}$ has the N\'eel 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 N\'eel and Brochet.