Energy of domain walls in ferrite films

MnZn Ferrite films were deposited by RF sputtering on (001) single crystal MgO substrates. AFM images show an increment in grain size with the film thickness. Grains with diameter between $\Phi$ $\sim $ 70 and 700 nm have been observed. The coercive field H$_{c}$ as a function of the grain size reaches a maximum value of about 80 Oe for $\Phi_{c} \sim $ 300 nm. The existence of a multidomain structure associated with a critical grain size was identified by Magneto-optical Kerr effect technique (MOKE). The transition of the one-domain regime to the two-domain regime was observed at a critical grain size of $D_{c} \sim $ 530 nm. This value agree with values predicted previously. The Jiles-Atherton model (JAM) was used to discuss the experimental hysteresis loops. The $k$ pinning parameter obtained from JAM shows a maximum value of $k$/$\mu _{o }$= 67 Am$^{2}$ for grains with $L_{c} \sim $ 529 nm. The total energy per unit area $E$ was correlated with $k$ and $D$. We found a simple phenomenological relationship given by $E \quad \alpha $ \textit{kD; }where $D$ is the magnetic domain width.