Electric field control of multiple switching regimes in a multiferroic

Abstract

Controlling magnetic moments by electric fields has been an everlasting goal for fundamental research. Achieving such control promises to substantially improve the efficiency of data storage and processing devices. A peculiar magnetoelectric behavior recently demonstrated in multiferroic \GdMn showing a switching through a cycle of four states when the magnetic field is ramped up and down through a critical field. Here we show that an external electric field can direct such switching to follow a predetermined sequence of magnetic states. By tuning electric and magnetic fields, large changes in the magnetic state can be achieved by relatively small external field variations. The material thus presents an exciting pradigm of an electrically controlled single crystal magnetic data storage device.

Figures (7)

• Figure 1: $E$-field modification of topological switching (A) Magnetic unit cell of GdMn$_2$O$_5$. Mn$^{4+}$ ions (red spheres) and Mn$^{3+}$ ions (green spheres) form zigzag antiferromagnetic chains (blue dashed lines) running along the $a$-axis. $\mathbf{L}_1$ and $\mathbf{L}_2$ are the Néel vectors of the two inequivalent chains. Arrows indicate a ground state spin configuration, which doubles the crystallographic unit cell along $a$, with opposite spins in the neighbouring cells. (B) Magnetic field ramp protocol (left) and schematic energy landscape in the space spanned by the angles $\phi_{1,2}$ between the $a$-axis and $\mathbf{L}_{1,2}$ vectors. Yellow (green) puddles represent local energy minima at $H$ field below (above) the spin reorientation transition. $\mathbf{L}_1$ and $\mathbf{L}_2$ are indicated by blue and red arrows in each puddle. Purple boxes indicate the possible transition paths when $H$ field is applied at a positive angle to the $a$-axis ($\Phi_H > 0$), driving the switching along vertical valleys, while orange boxes show the path followed for $\Phi_H < 0$, where horizontal valleys are formed. Black arrows illustrate the single switching events occurring when the $H$ field is ramped across the spin reorientation field $H_{sp}$. Switching at zero $E$-field goes along these vertical (horizontal) valleys when $\Phi_H$ is inside the magic angle region, $\Phi_H = + \Phi_H^*$ ( $\Phi_H = - \Phi_H^*$), while outside an external $E$-field is necessary to drive these transitions. Blue boxes highlight the state deformation in which the former local minimum shifts into the following one where $\mathbf{L}_1$ and $\mathbf{L}_2$ are symmetrical with respect to the $a$-axis when the $H$ field is applied along the $a$-axis. Here, again, a degree of control of the transition path is possible under a relatively small $E$-field (cf. Fig. \ref{['fig:fig3']} A,B,E,F).
• Figure 2: E-field switching of magnetoelectric states in GdMn$_2$O$_5$. (A-D) E-field controlled switching between single unit states of the system. (A) Switching from state 1 to states 2 and 4 at positive and negative applied voltage, respectively. (B) Switching from state 2 to states 1 and 3. (C) Switching from state 3 to states 2 and 4. (D) Switching from state 4 to states 3 and 1. (E, F) Combined four-state switching sequence with winding controlled through external electric fields: (E): clockwise cycle 1-2-3-4-1. (F): anti-clockwise cycle 1-4-3-2-1. Magnetic field is applied parallel to the a-axis (nominal deviation $\sim 1^\circ$).
• Figure 3: Energy landscape probed by electric field and resulting in a rich switching diagram (A) The trajectory in the space of order parameter orientation $(\phi_1(t),\phi_2(t))$, corresponding to topological switching at $\Phi_H=-11^\circ$ and $E_b=0$, overlaid on the potential energy surface for $H=4.5$ T. The low-energy valleys run vertically. The numbers mark the four states, connected by $L_2$ rotation by $90^\circ$. (B) An applied $E_b$ field leads to diagonal valleys and breaks the topological switching sequence. (C) Simulated switching regimes starting from state 1 when the magnetic field at $\Phi_H$ to $a$-axis is swept up and down across the spin reorientation transition in the presence of an electric field $E_b$. The state sequences are indicated, with periodically repeating states underlined (e.g. $1\to \underline{ 2\to 3}$ implies the sequence 1232323…).
• Figure 4: Simulated switching between magnetoelectric states under $H$ sweeps and a low constant $E$-field. Color encodes the magnitude of $E_b$. (A,B) Switching driven by magnetic field sweeps at $\Phi_H = 0^{\circ}$. (A) At low $E$-field switching follows $1\to 4$, at high --- $1\to 2$. (B) Switching starting from state 2. Continuous deformation of $P(H)$ curves with increasing $E$-field indicates that the final magnetic state resembles state 3, strongly polarized by $E$-field. (C, D) $E$-field controlled switching starting from states 1 and 2, respectively, when the $H$-field angle $\Phi_H = -18^{\circ}$ is above the magic angle interval. (E-J) Switching paths below (E,F), within (G,H) and above (I,J) the magic angle interval $7.7^{\circ} \leq |\Phi_H^*| \leq 17.7^{\circ}$. Switching paths starting in states 3 and 4 are obtained by a mirror $P\to -P, E\to -E, \bm L_1\to -\bm L_1$.
• Figure S1: Estimating the spin reorientation field: (a) Magnetic exchange constants and a spin configuration for a single chain. (b) A collinear spin configuration.