Low-Temperature Mössbauer Study of a Nickel-Zinc Ferrite: ${\mathrm{Zn}}_x{\mathrm{Ni}}_{1-x}{\mathrm{Fe}}_2{\mathrm{O}}_4$

The Yafet-Kittel angles of the disordered system ${\mathrm{Zn}}_x{\mathrm{Ni}}_{1-x}{\mathrm{Fe}}_2{\mathrm{O}}_4$ for $0\le x\le 1$ have been determined using ${\mathrm{Fe}}^{57}$ Mössbauer spectroscopy with and without an external magnetic field. It is found that for $x\le 0.5$ the resultant $A$- and $B$-site Fe-spin moments have a collinear arrangement, whereas for $x>\mathrm{}0.5\mathrm{}$ a noncollinear arrangement of $A$- and $B$-site Fe spin moments exists. The canting angles of the $B$-site Fe moments determined from the applied-field Mössbauer spectra are smaller than those deduced from the neutron-diffraction data. An explanation based on the relative strength of the exchange constants $J_{\mathrm{AB}}$ and $J_{\mathrm{BB}}$ is given to account for this difference. The cation distributions are shown to correspond within experimental error limits to $\left({\mathrm{Zn}}_x{\mathrm{Fe}}_{1-x}\right)\left[{\mathrm{Ni}}_{1-x}{\mathrm{Fe}}_{1+x}\right]{\mathrm{O}}_4$ for all values of $x$ in the interval $0\le x\le 1.0$. The systematics of the dependence of the isomer shifts on Zn content are consistent with the variations in crystal chemical-structural parameters and with an increase in the covalence of the ${\mathrm{Fe}}^{2+}$-${\mathrm{O}}^{2-}$ bond with decreasing internuclear separation. The variations in the magnetic hyperfine fields at the $A$ -site Fe ions can be understood on the basis of a molecular-field model with distant-neighbor exchange interactions being important at low temperatures. A significant contribution from supertransferred hyperfine interactions must be invoked to understand the systematics of the magnetic hyperfine field at the $B$ -site Fe ions.