Figure 1

Characterization of Fe${}_3$O${}_4$ thin films. (a) and (b) are RHEED patterns for 50 nm Fe${}_3$O${}_4$ on MgO(001) along the [100] and [110] in-plane directions, respectively. (c) HRXRD $\theta –2\theta$ scans (arb. units) measured around the location of the MgO(002) peak with Kiessig fringes. Inset: LEED pattern with incident energy of 160 eV. (d) Temperature dependence of resistance measured by four-point probe (blue solid line) and magnetization measured by MOKE (red symbols). The vertical dashed line indicates the Verwey transition. Inset: geometry for the resistance and magnetization measurements. (e) $I$-$V$ curve for Fe${}_3$O${}_4$ channel at 115 K. (f) MOKE hysteresis loop for Fe${}_3$O${}_4$ at 113 K. The right axis shows absolute magnetization based on SQUID measurements on corresponding samples.Reuse & Permissions

Figure 2

Electrical gating of Fe${}_3$O${}_4$ and manipulation of the Verwey transition. (a) A schematic of the sample device structure. The dielectric layer consists of PMMA(900 nm)/Al${}_2$O${}_3$(50 nm)/MgO(10 nm). Positive electric field corresponds to the application of positive voltage to the top gate electrode. (b) Temperature dependence of resistance for applied electric fields of $+$1.8 MV/cm (blue), $+$0.9 MV/cm (orange), 0 MV/cm [black; from Fig. 1d], $-$0.9 MV/cm (green), and $-$1.8 MV/cm (red). The arrows show $T_V$ for each electric field, which is summarized in the inset.Reuse & Permissions

Figure 3

Electrostatic gate dependence of resistance. (a) Gate-dependent resistance for Fe${}_3$O${}_4$ at a temperature of 115 K. (b) and (c) show the symmetric and antisymmetric components of the gate-dependent resistance change, respectively.Reuse & Permissions

Figure 4

Electrostatic gate dependence of magnetization. (a) MOKE loops measured at 113 K with applied electric fields of 0 MV/cm (black) and $-$1.8 MV/cm (red), showing a decrease in magnetization with the application of an electric field. (b) Magnetization as a function of electric field, demonstrating a magnetoelectric effect induced by electric field control of the Verwey transition.Reuse & Permissions