Charge-Driven Transtive Devices via Electric Field Control of Magnetism in a Helimagnet

The transtor and memtranstor are the fourth basic linear and memory elements, respectively, which allow direct coupling of charge (q) to magnetic flux (φ) via linear and nonlinear magnetoelectric (ME) effects, respectively. It is found here that a large variation of magnetization by an electric field is realized in both linear and nonlinear hysteretic styles in a magnetoelectric Y-type hexaferrite ${\mathrm{Ba}}_{0.5}{\mathrm{Sr}}_{1.5}{\mathrm{Zn}}_2({\mathrm{Fe}}_{0.92}{\mathrm{Al}}_{0.08}{)}_{12}{\mathrm{O}}_{22}$ single crystal. Moreover, based on the spin-current model, the underlying microscopic mechanisms for generating the two types of linear and nonlinear M versus E curves are understood to be E-induced changes to the cone angle and sign of P, respectively, establishing the charge-driven transtor and memtranstor in the Y-type hexaferrite system. This work points to a promising pathway to develop alternative circuit functionalities using magnetoelectric materials.

Figure 1

(a) Complete relational diagram of all possible fundamental two-terminal circuit elements, both linear and nonlinear, which correlate a particular pair of the four basic circuit variables, i.e., charge q, voltage v, current i, and magnetic flux φ. Nonlinear memory devices corresponding to the four linear fundamental elements, i.e., resistor (R), capacitor (C), inductor (L), and transtor (T), are accordingly termed as memristor (M_R), memcapacitor (M_C), meminductor (M_L), and memtranstor (M_T). (b) Schematic illustration of charge-driven transtive behavior, which is anticipated to directly correlate φ with q with positive or negative T values (or, equivalently, a linear change of M under E with either positive or negative α_C in ME materials). (c) Characteristic behavior of the charge-driven memtranstor, showing a butterfly hysteresis loop between q and φ. Butterfly-shaped loop in (c) occurs at sufficiently large input of q (or, equivalently, a butterfly shape of M under E in ME materials with a large enough E to induce a sign change in α_C).

Figure 2

(a) Schematic illustration of the crystal and transverse-cone magnetic structure of ${\mathrm{Ba}}_{0.5}{\mathrm{Sr}}_{1.5}{\mathrm{Zn}}_2({\mathrm{Fe}}_{0.92}{\mathrm{Al}}_{0.08}{)}_{12}{\mathrm{O}}_{22}$. Transverse-cone spin configuration propagates along a commensurate modulation vector, k₀= (0,0,3/2); µ_L and µ_S denote net magnetic moments in magnetic L and S blocks, respectively. According to the spin-current mechanism, ferroelectricity (FE) and an in-plane P perpendicular to both H and k₀ can be induced. Magnetic field dependence of (b) relative dielectric constant ε_r, (c) magnetization M, (d) polarization P, and (e) dP/dH of ${\mathrm{Ba}}_{0.5}{\mathrm{Sr}}_{1.5}{\mathrm{Zn}}_2({\mathrm{Fe}}_{0.92}{\mathrm{Al}}_{0.08}{)}_{12}{\mathrm{O}}_{22}$ at 15 K after magnetic field cooling processes. Measurement configuration is illustrated in the inset of (b). In the inset of (d), the cone opening angle, θ, is expected to be suppressed with increasing H between 3 and 19 kOe. Sign of P is directly correlated to spin-rotation directions. Above 19 kOe, spin configuration becomes collinear, that is, it is paraelectric (PE).

Figure 3

(a) Electric field (E) dependence of M under different low-dc magnetic fields (H) at 15 K. Clear hysteresis behavior can be seen in M-E loops for H = 100, 0, and −100 Oe. Strong quadratic ME behavior is clear for H = ±200 Oe. Data at H = 0 Oe are from Ref. [14]. (b) Nearly linear ME behavior for both +poled and −poled cases under H = 10 kOe. (c) Converted ϕ-q relationship [from (b)] of the transtor made from ${\mathrm{Ba}}_{0.5}{\mathrm{Sr}}_{1.5}{\mathrm{Zn}}_2({\mathrm{Fe}}_{0.92}{\mathrm{Al}}_{0.08}{)}_{12}{\mathrm{O}}_{22}$. (d) Schematic diagrams of the change in the cone opening angle under external E for +poled (upper panel) and −poled (lower panel) cases. Solid and dashed lines represent P and M of the cone under +E and −E, respectively.

Figure 4

(a) Nonlinear modulations of magnetization, M, at 18 kOe and 15 K by repeating triangular waves of E after +poled. From points 1 to 5, E is swept from 2.1 to −2.1 MV/m and back to 2.1 MV/m again. (b) Butterfly-shaped M-E loop, illustrating data in (a), spanning the range from points 1 to 5. (c) Schematic diagram of the P-E loop from points 1 to 5. Notably, point 1 and point 3 should have different cone-rotation directions. Accordingly, their signs of P and α_C are opposite. (d) Butterfly-shaped M-E loop in (b) can be directly converted into a memtranstive φ-q loop.