Twofold and fourfold anisotropies in zinc ferrite thin films investigated by ferromagnetic resonance

By means of the ferromagnetic resonance (FMR) technique (at the $X$ band) we investigated the magnetic properties of ${\mathrm{ZnFe}}_2{\mathrm{O}}_4$ (ZFO) films grown on different substrates. Angular dependence of the FMR field showed the existence of twofold and fourfold anisotropies for the same material, grown on Si(111), MgO(100), and STO(100), respectively. By using a model that takes into consideration the relevant contributions to the energy, we were able to extract the following parameters: effective magnetization $M_{\mathrm{eff}}$, cubic magnetocrystalline anisotropy field, in-plane and out of plane uniaxial anisotropy fields, and the $g$ factor. The samples deposited on Si showed a twofold in-plane anisotropy while a fourfold magnetic anisotropy was observed for the ZFO/MgO and ZFO/${\mathrm{SrTiO}}_3$ samples. All samples showed a strong perpendicular uniaxial anisotropy above 1 kOe and low in-plane uniaxial and cubic anisotropy field, on the order of tens of oersteds. The FMR linewidth ($\mathrm{\Delta }H$) fitted from FMR data shows $\mathrm{\Delta }H$ values above 190 Oe for all samples, indicating high damping of this material to be $\sim {10}^{-2}$ for the ZFO/MgO. The present analysis compared the FMR data obtained for the in-plane and out of plane measurements. Likewise, the effective magnetization and perpendicular uniaxial anisotropy field by FMR were compared with the magnetic response obtained by a vibrating sample magnetometer.

Figure 1

Schematic illustration of the reference frame used in the calculation. The orientations of the magnetization vector M and the DC field H are given by the in-plane azimuthal angles, ${\phi }_{\mathrm{M}}$ and ${\phi }_{\mathrm{H}}$, and the out of plane polar angles, ${\theta }_{\mathrm{M}}$ and ${\theta }_{\mathrm{H}}$, respectively.

Figure 2

Ferromagnetic resonance field as a function of the in-plane azimuthal angle ${\phi }_{\mathrm{H}}$ for ZFO/Si, ZFO/MgO, and ZFO/STO. The red solid lines are theoretical fits to the experimental data (black spheres).

Figure 3

Out of plane dependence of the FMR field $H_R$ for zinc ferrite thin films grown on different substrates. Here the polar angle ${\theta }_{\mathrm{H}}$ is defined as the angle with the perpendicular axis. The left-hand column shows the data (black symbols) and the theoretical fits (red solid lines). Error bars are about the same size as the symbols. Representative absorption curves are shown in the insets for the in-plane angle $({\theta }_H={90}^{\circ }$). The right-hand column shows the FMR absorption derivative curves for representative angles as indicated by the color code.

Figure 4

Angular dependence of linewidth ($\mathrm{\Delta }H$) for ZFO45/MgO and ZFO90/MgO. The red solid line is numerically obtained with Eqs. (8) and (9). The inset shows the linewidth vs frequency at room temperature, measured by means of a broadband strip-line setup.

Figure 5

Room temperature in-plane (0°) and out of plane (90°) magnetic hysteresis loops of ${\mathrm{ZnFe}}_2{\mathrm{O}}_4$ thin films.