Doping-Tunable Ferrimagnetic Phase with Large Linear Magnetoelectric Effect in a Polar Magnet ${\mathrm{Fe}}_2{\mathrm{Mo}}_3{\mathrm{O}}_8$

The magnetoelectric (ME) effect, i.e., cross control of magnetization (electric polarization) by an external electric (magnetic) field, may introduce a new design principle for novel spin devices. To enhance the ME signal, control of a phase competition has recently been revealed as a promising approach. Here, we report the successful chemical-doping control of the distinct ME phases in a polar magnet ${\mathrm{Fe}}_2{\mathrm{Mo}}_3{\mathrm{O}}_8$, in which an antiferromagnetic state is competing with a ferrimagnetic state. We demonstrate that Zn doping stabilizes the metamagnetic state to realize the spontaneous ferrimagnetic state and varies the ME coefficients from large negative to large positive values; for instance, the diagonal component of the ME coefficients under the magnetic field perpendicular to the polar axis varies from $\text{−}142\mathrm{ps}/\mathrm{m}$ to $107\mathrm{ps}/\mathrm{m}$ by doping Zn from 12.5% to 50%. This remarkable doping control of the ME property originates from coexisting distinct ME mechanisms, which are selectively tunable by substituting one of the two distinct magnetic sites in the unit cell with nonmagnetic Zn.

Popular Summary

The magnetoelectric effect, which enables cross-control of magnetization (electric polarization) by an electric (magnetic) field, promises to inform novel spintronic devices. However, it has been a long-standing challenge to enhance the magnetoelectric effect. There are two known magnetoelectric effects: a conventional linear magnetoelectric effect in a centrosymmetry-broken magnet and a recently explored nonlinear magnetoelectric effect associated with a magnetic phase transition. Although the former is rather simple and ubiquitous, as typified by the room-temperature antiferromagnet ${\mathrm{Cr}}_2{\mathrm{O}}_3$ reported in the early 1960s, a guiding principle for controlling the magnitude and sign of the linear magnetoelectric coefficient has remained elusive. One possible strategy is a systematic control of magnetism via chemical doping. However, this control often results in a significant reduction in the magnetoelectric signal. Here, we report the systematic control of the magnitude and sign of a large linear magnetoelectric effect by site-selective nonmagnetic doping in the noncentrosymmetric magnet ${\mathrm{Fe}}_2{\mathrm{Mo}}_3{\mathrm{O}}_8$ that is magnetically frustrated.

We consider the origin of the magnetoelectric effect from a microscopic perspective. We consider a single crystal of the $3d$ transition metal ${\mathrm{Fe}}_2{\mathrm{Mo}}_3{\mathrm{O}}_8$, which has a large linear magnetoelectric coefficient that is 3 times larger than that of magnetite, a known giant-magnetoelectric material. This coefficient originates from competing magnetoelectric mechanisms. Furthermore, as long as the ferromagnetic order and noncentrosymmetry are preserved, a finite linear magnetoelectric signal can be expected. We demonstrate chemical doping control of magnetoelectric phases in ${\mathrm{Fe}}_2{\mathrm{Mo}}_3{\mathrm{O}}_8$; nonmagnetic Zn doping encourages the ferromagnetic state. Doped Zn selectively occupies a distinct magnetic site while maintaining the basal ferromagnetic structure and noncentrosymmetry, which makes it possible to systematically study the competing magnetoelectric mechanisms.

Our results provide new guiding principles to understand and improve the linear magnetoelectric effect.

Figure 1

(a) A unit cell of $M_2{\mathrm{Mo}}_3{\mathrm{O}}_8$ ($M:\mathrm{Fe}$). (b, c) Schematic illustrations of antiferromagnetic and ferrimagnetic orders, respectively. Spin-induced $P$ ($P_{\mathrm{AF}}$ and $P_{\mathrm{FM}}$) are also indicated. Although the sign of $P$ with respect to the $c$ axis has not been determined, it is provisionally defined in this work. The numbers 1 and 2 are the indices for bonds of magnetic interaction.

Figure 2

(a, b) $T$ dependence of (a) $M/H$ and (b) change of $P$ ($\mathrm{\Delta }P$) under various magnitudes of $H$ along the $c$ axis. (c, d) Field dependence of $M$ and $\mathrm{\Delta }P$ at various $T$. The dashed curve is the fit to the $P\text{−}H$ curve for $H>H_{\mathrm{cr}}$ at 45 K with the function $P=P_0+{\alpha }_{3}H+\beta H^2$, where $P_0$, ${\alpha }_3$, and $\beta$ are constants. Zero points of $\mathrm{\Delta }P$ are taken at (b) $T=140\mathrm{K}$ and (d) ${\mu }_{0}H=0\mathrm{T}$.

Figure 3

(a–d) The $H\text{−}T$ phase diagrams for $({\mathrm{Fe}}_{1-y}{\mathrm{Zn}}_y{)}_2{\mathrm{Mo}}_3{\mathrm{O}}_8$ with various values of $y$ under $H\parallel c$, as determined by $M$ and $P$ measurements. PM, AF, and FM indicate the paramagnetic, antiferromagnetic, and ferrimagnetic phases, respectively. Shaded areas indicate hysteretic regions.

Figure 4

(a, b) $T$ and (c–e) $H$ dependence of $M$ for $({\mathrm{Fe}}_{1-y}{\mathrm{Zn}}_y{)}_2{\mathrm{Mo}}_3{\mathrm{O}}_8$ with various values of $y$ under $H\parallel c$. (c–e) Each scan starts after cooling to the target $T$ without a field. The horizontal scale of ${\mu }_{0}H$ for data above the gray horizontal bars in (d) and (e) is appended at the top of each panel. Data for (a) and (c–e) are shifted for clarity.

Figure 5

(a–c) $H$ dependence of (a) $M$, (b) $\mathrm{\Delta }P$ along the $c$ axis under $H\parallel c$, and (c) $\mathrm{\Delta }P$ along the $b^{\prime }$ axis under $H\parallel b^{\prime }$. The $b^{\prime }$ axis is the axis intersecting at a right angle with one of the $a$ axes and the $c$ axis. The colored solid and dashed curves for each $y$ indicate the scans for $+H\to -H$ and $-H\to +H$, respectively. The black solid curve for $y=0.125$ in (b) is the scan from ${\mu }_{0}H=0\mathrm{T}$ to 14 T after the cooling without a field. Data of $\mathrm{\Delta }P$ for each $y$ are shifted for clarity. Black dashed lines are linear fits to $P\text{−}H$ curves. (d) $y$ dependence of ME coefficients ${\alpha }_1$ and ${\alpha }_3$ measured at 2 K, and saturated magnetization estimated from data in Figs. 4 and Fig. 5. Solid lines are linear fits. The open square indicates the value of ${\alpha }_3$ for ${\mathrm{Fe}}_2{\mathrm{Mo}}_3{\mathrm{O}}_8$ at 45 K, obtained from the data in Fig. 2.