Converse magnetoelectric effects in Fe${}_3$O${}_4$/BaTiO${}_3$ multiferroic hybrids

The quantitative understanding of converse magnetoelectric effects, i.e., the variation of the magnetization as a function of an applied electric field, in extrinsic multiferroic hybrids is a key prerequisite for the development of future spintronic devices. We present a detailed study of the strain-mediated converse magnetoelectric effect in ferrimagnetic Fe${}_3$O${}_4$ thin films on ferroelectric BaTiO${}_3$ substrates at room temperature. The experimental results are in excellent agreement with numerical simulation based on a two-region model. This demonstrates that the electric field induced changes of the magnetic state in the Fe${}_3$O${}_4$ thin film can be well described by the presence of two different ferroelastic domains in the BaTiO${}_3$ substrate, resulting in two differently strained regions in the Fe${}_3$O${}_4$ film with different magnetic properties. The two-region model allows to predict the converse magnetoelectric effects in multiferroic hybrid structures consisting of ferromagnetic thin films on ferroelastic substrates.

Figure 1

Intensity evolution of the RHEED $\left(00\right)$ reflection monitored during the deposition of a 64-nm-thick Fe${}_3$O${}_4$ film on a 0.5-mm-thick BTO substrate. The intensity was integrated within the red rectangle marked in the RHEED patterns, which are shown in the insets. The time stamps at which the RHEED patterns were recorded are marked by (I)–(IV). The growth process can be subdivided into three main steps: (a) highly disordered growth (0 s $\le t\lesssim$ 25 s), (b) three-dimensional growth mode (300 s $\lesssim t\lesssim$ 3000 s), and (c) layer-by layer growth mode (3000 s $\lesssim t\lesssim$ 3950 s).

Figure 2

Magnetic hysteresis of a 45-nm-thick Fe${}_3$O${}_4$ film grown on a (001)-oriented BTO substrate measured at 300 K with the magnetic field applied in the film plane. The magnetic field dependence of the magnetization can be fitted by a $(1-b/\sqrt{H})$ behavior using $b=(0.045\pm 0.005)\sqrt{\mathrm{T}}$ (red solid line). (a) The $M\left(H\right)$ loop reveals a coercive field of 35 mT and a saturation magnetization of $M_{\mathrm{s}}=438$ kA/m at $\mu H=7$ T. (b) The normalized remanent magnetization as a function of temperature measured after field cooling the sample with ${\mu }_{0}H=7$ T discloses a Verwey transition at 121 K.

Figure 3

Converse magnetoelectric effects measured at 300 K for a Fe${}_3$O${}_4$(38 nm)/BTO multiferroic hybrid. The magnetic field was applied in the film plane along the $y$ direction. A miscut BTO substrate was used for the experiment with a misalignment of $1^{\circ }$ ($7^{\circ }$) of the [001] ([100]) direction of the ferroelastic unit cell with respect to the $z$ ($x$) direction describing the surface of the BTO substrate. The variation of the ferroelastic domain configuration as a function of the electric field is illustrated in the bottom part of the figure. At high positive and negative fields, a ferroelastic single $c$ domain state is expected, while at low-electric fields a $c$/$a_2$ multidomain state is present in the BTO crystal. The blue arrows indicate the orientation of the ferroelectric polarization and the blue regions denote ferroelastic domain walls. Polarization rotation induced by the electric field is neglected for simplicity.

Figure 4

X-ray diffraction around the asymmetric BTO (204) reflection of a Fe${}_3$O${}_4$(38 nm)/BTO hybrid recorded in the (a) $q_{H00}-q_{00L}$ plane and (b) $q_{0K0}-q_{00L}$ plane at 0 kV/m using a miscut BTO crystal (yellow/red: high intensity, light blue/dark blue: low intensity). Only reflections caused by ferroelastic $c$ domains and tilted $a_2$ domains are visible. The expected positions of the reflections caused by diffraction from tilted ferroelastic $a_1$ domains are marked by dashed circles.

Figure 5

(a) X-ray diffraction around the BTO (002) reflection recorded at an electric field of 400 kV/m (black full symbols) and subsequently of $-$28 kV/m (red full symbols) applied across a Fe${}_3$O${}_4$/BTO hybrid structure. The measurements were performed at the BM28 beamline at the European Synchrotron Facility (ESRF). Upon increasing the electric field from $-$28 kV/m to 400 kV/m again (black open symbols), the initial measurement at 400 kV/m is reproduced. The effect of the strain imposed on the Fe${}_3$O${}_4$ film is shown in more detail in (b) and (c). In the case of 400 kV/m, the (004) reflection of the Fe${}_3$O${}_4$ thin film (black symbols) can be well fitted using a single peak profile (black solid line). At 0 kV/m, two peak profiles (dashed lines) are needed to fit the measured reflection (red solid line). The gray lines display the difference between the experimental data (symbols) and the fits (solid lines), and the blue arrows mark the $q_{00L}$ positions of the reflections.

Figure 6

Determination of the volume fraction of ferroelastic $c$ domains $x_c\left(E\right)$ using x-ray diffraction. (a) and (b) Mesh scans around the BTO (002) reflection recorded while applying an electric field of 400 and 0 kV/m across the Fe${}_3$O${}_4$(38 nm)/BTO hybrid. To obtain $x_c$, the ratio of the integrated intensities for $q_{00L}\le 2.01$ rlu and $q_{00L}>2.01$ rlu is calculated. (c) $x_c$ as a function of the applied electric field.

Figure 7

Magnetization $M$ plotted vs the angle $\varphi$ defining the in-plane orientation of the applied magnetic field. $\varphi =0^{\circ }$ corresponds to the $x$ direction. The data are taken at an electric field of $E_z=400$ kV/m and an external magnetic field of 25 mT (black symbols) and 20 mT (red symbols). The $M\left(\varphi \right)$ curves can be fitted using a cubic anisotropy field of $K_c/M_{\mathrm{s}}=(-19\pm 1)$ mT (solid lines), assuming a misalignment of $4^{\circ }$ between the sample normal and the rotation axis.

Figure 8

Measurement (symbols) and simulation (lines) of the converse magnetoelectric effect in a Fe${}_3$O${}_4$(38 nm)/BTO multiferroic hybrid for different magnetic field strengths. The magnetic field was aligned in the film plane along the $y$ direction of the BTO crystal and the temperature was set to 300 K. For better visibility, the curves are vertically shifted with respect to each other. The best fit between experiment and simulation was obtained by assuming a magnetoelastic coupling efficiency of 55$\%$ ($\chi =0.55$). A misalignment of the sample surface with respect to the magnetic field of $5^{\circ }$ was assumed for the calculation.