Low-energy magnetoelectric control of domain states in exchange-coupled heterostructures

The electric manipulation of antiferromagnets has become an area of great interest recently for zero-stray-field spintronic devices, and for their rich spin dynamics. Generally, the application of antiferromagnetic media for information memories and storage requires a heterostructure with a ferromagnetic layer for readout through the exchange-bias field. In magnetoelectric and multiferroic antiferromagnets, the exchange coupling exerts an additional impediment (energy barrier) to magnetization reversal by the applied magnetoelectric energy. We proposed and verified a method to overcome this barrier. We controlled the energy required for switching the magnetic domains in magnetoelectric ${\mathrm{Cr}}_2{\mathrm{O}}_3$ films by compensating the exchange-coupling energy from the ferromagnetic layer with the Zeeman energy of a small volumetric spontaneous magnetization found for the sputtered ${\mathrm{Cr}}_2{\mathrm{O}}_3$ films. Based on a simplified phenomenological model of the field-cooling process, the magnetic and electric fields required for switching could be tuned. As an example, the switching of antiferromagnetic domains around a zero-threshold electric field was demonstrated at a magnetic field of 2.6 kOe.

Figure 1

(a) In contrast to the storage and readout using a single FM layer by a locally varying $H$ in FM-based recording media, in the ME-based media the information retention is in the ME-AFM by a local $E$ and a uniform $H$, whereas the readout is from an exchange-biased FM. If the FM is designed to have a coercivity smaller than the exchange bias field, a full switching for a practical readout is possible [14, 26, 27]. (b) Definitions of AFM domains of ${\mathrm{Cr}}_2{\mathrm{O}}_3$ with respect to the directions of applied fields. The AFM-staggered magnetization vector $l$ is defined as parallel to the spin sublattice beneath the smaller oxygen triangle (grayed triangle area). An angle $\theta =0\left(\pi \right)$ between $l$ and the positive $z$ axis, corresponds to the $L^{+}\left(L^{-}\right)$ domain. An $L^{+}\left(L^{-}\right)$ domain results from a parallel (antiparallel) magnetoelectric field cooling, and has a positive (negative) value of magnetoelectric susceptibility $\alpha$. (c) For a positive magnetic field, the Zeeman energy of ${\mathrm{Cr}}_2{\mathrm{O}}_3$ spontaneous volume magnetization $M_0$, which is parallel to $l$, prefers an $L^{+}$ domain (left). On the other hand, the interfacial exchange coupling with the Co ferromagnetic layer favors an $L^{-}$ domain (right).

Figure 2

(a) The magnetization areal density of ${\mathrm{Cr}}_2{\mathrm{O}}_3$ films shows a linear dependence on thickness, with a negligible surface component. The dashed line is the maximum expectation from a thickness-independent fully polarized surface magnetization. The magnetization values from Ref. [40] are also plotted, but not included in the fitting. (b), (c) The temperature dependence of (b) the thermoremnant magnetization (TRM), and (c) the magnetoelectric susceptibility $\alpha$ of the sample without an exchange bias (woEB) after cooling in a positive and a negative $H_{\mathrm{fr}}$. The inset in (c) shows coinciding transition temperatures from TRM and $\alpha$. (d) The temperature dependence of $\alpha$, for the sample wEB. (c), (d) For the same direction of $H_{\mathrm{fr}}$, the opposite ${\mathrm{Cr}}_2{\mathrm{O}}_3$ domains are generated in the samples woEB and wEB.

Figure 3

(a) The temperature dependence of $\alpha$ in the sample woEB, normalized by the maximum peak value for a cooling under the simultaneous application of a magnetic field $H_{\mathrm{fr}}=+10\mathrm{kOe}$ and a varying electric field $E_{\mathrm{fr}}$. An additional negative $E_{\mathrm{fr}}$ was needed to switch the ${\mathrm{Cr}}_2{\mathrm{O}}_3$ domains. (b) A comparison of the dependence of the average domain state $\langle L\rangle$ on $E_{\mathrm{fr}}$ between the samples woEB and wEB. The sample woEB shows a constant threshold electric field $E_{\mathrm{th}}$, irrespective of $H_{\mathrm{fr}}$. The sample wEB has a shift of $E_{\mathrm{th}}$ with changing $H_{\mathrm{fr}}$. At $H_{\mathrm{fr}}\approx 2.6$ kOe, the switching curve has a zero $E_{\mathrm{th}}$. (c) Plots of $E_{\mathrm{th}}\text{−}1/H_{\mathrm{fr}}$ with fits to the model outlined in Eq. (2). A single-crystal slab of ${\mathrm{Cr}}_2{\mathrm{O}}_3$ has a zero $E_{\mathrm{th}}$ regardless of $1/H_{\mathrm{fr}}$ (blue diamonds). The samples wEB and woEB have similar negative $y$-intercepts, due to the presence of $M_0$ (black circles and red squares, respectively). For the sample wEB, a slope results from exchange coupling to Co, and a zero $E_{\mathrm{th}}$ is found at $H_{E0}$. (d) The dependence of ${\lambda }_E$ on $1/H_{\mathrm{fr}}$ is linear with a slope ${\mathit{EH}}_T$ that is determined by $\alpha V$. For the deposited films, a nonzero ${\lambda }_E$ is still present even in the vanishing $1/H_{\mathrm{fr}}$ limit $\left(C\right)$.

Figure 4

(a) The dc (squares) and ac (circles) responses of the SQUID magnetometer along the position of the sample relative to the detection coils. The sample wEB was used, and the measurement was after MFC at $+500$ Oe. The dc and ac magnetizations correspond to Co's magnetization and ${\mathrm{Cr}}_2{\mathrm{O}}_3$ ME response, respectively. (b) The magnitude of $M_{\mathrm{ac}}$ increased linearly with sensing voltage, indicating that the ME response is linear. The negative sign of $\alpha$ indicates the formation of $L^{-}$ domains.

Figure 5

(a) The temperature dependence of exchange-bias field $H_{\mathrm{ex}}$ and coercivity $H_c$ of Co. (b) The change of $H_{\mathrm{ex}}$ and $H_c$ against $H_{\mathrm{fr}}$. The solid black line is a fitting to Eq. (B1), whereas the dashed red line is an eye guide. (c) The dependence of $\alpha$ of ${\mathrm{Cr}}_2{\mathrm{O}}_3$ on $H_{\mathrm{fr}}$, with a fitting to Eq. (B1). (b), (c) The fitting results from $H_{\mathrm{ex}}$ and $\alpha$ measurements are consistent, indicating that the AFM domains at the surface and inside the ${\mathrm{Cr}}_2{\mathrm{O}}_3$ film are highly correlated.

Figure 6

The relation between the AFM order parameter $l$ and ${\mathrm{Cr}}_2{\mathrm{O}}_3$ magnetization $M_0$ is parallel. (a) After initializing in one domain state, applying an opposing $H$ will switch the AFM domains through coupling to $M_0$, when anisotropy $K_u$ is low. (b) The protocols for measuring the switching of $l$ and $M_0$ are shown. (c) Applying $\mp 30$ kOe to a $L^{\pm }$ domain induces a sign reversal in $\alpha$ and $M_0$ at the same temperature $T_{\mathrm{sw}}$. Horizontal error bars correspond to temperature overshoots when $T^{\prime }$ is reached. (d) The temperature of switching at an applied field corresponds to the coercivity $H_c$ at that temperature. The large change of $H_c$ vs $T_{\mathrm{sw}}$ is due to a small $M$ and a large decrease in $K_u$ around $T_N$. (e) A schematic showing that $l$ is parallel to $M_0$.