Figure 1

(a) Hysteresis loop of pinned CoPd thin film after magnetoelectric annealing of the sample. The dashed line illustrates positive exchange bias. (${\mathrm{a}}^{\prime }$) Hysteresis loop of pinned CoPd thin film after electrically switching the spin configuration of chromia. The dashed line illustrates negative exchange bias. (b) Hysteretic behavior of equilibrium exchange bias with respect to applied electric field, a constant magnetic field of 100 mT is simultaneously applied. (c) Diagrams of the spin structure (up and down arrows) of the AFM bulk (bottom layer), FM boundary magnetization at the AFM interface (middle layer), and FM spins (top layer) in the positive exchange bias state (c), and in the negative exchange bias state (${\mathrm{c}}^{\prime }$).Reuse & Permissions

Figure 2

(a) Example of the hysteretic behavior of exchange bias with respect to the electric field applied in steps of $30\mathrm{kV}/\mathrm{m}$. The initial exchange bias is illustrated with solid symbols and the equilibrium exchange bias is illustrated with open symbols. The arrow indicates the history of the measurements. (b) Example of the hysteretic behavior of exchange bias with respect to the applied electric field with one large step of $226\mathrm{kV}/\mathrm{m}$. The resulting initial and equilibrium exchange bias fields are displayed by large solid and open circles. The arrow indicates the history of measurements. (c) Circles show the exchange bias training series after initialization in a step from $E=300$ to $E=526\mathrm{kV}/\mathrm{m}$. The first and fifteenth exchange bias values are also illustrated in (b) by a closed ($n=1$) and open circle ($n=15$), respectively. Squares show three exchange training series after initialization in a step from $E=340$ to $E=370\mathrm{kV}/\mathrm{m}$, from $E=370$ to $E=400\mathrm{kV}/\mathrm{m}$, and from $E=400$ to $E=430\mathrm{kV}/\mathrm{m}$, respectively from bottom to top. First and fifteenth exchange bias values can be found in (a). (d) $K$ vs $H_{\mathrm{EB}}^{\infty }(E)$ for the training events arising from best fits of Eq. (1) to various training series corresponding to the squares in (a) and circles in (b). Solid and dashed lines are plots of Eq. (2) using $H_{\mathrm{EB}}^{\max /\min }$ from the saturation values in (a) and (b). (e) Diagram of the spin structure (up and down arrows) in a domain state after electric field initialization before training (i), and in equilibrium (ii). The dashed line separates two domains with opposite order parameter.Reuse & Permissions