Ferroelectricity-driven altermagnetism in two-dimensional van der Waals multiferroics

TL;DR

This work leverages the spin space group framework to design electrically tunable altermagnetism in two-dimensional van der Waals multiferroics. By combining ferroelectric polarization and interlayer sliding, the authors realize momentum-dependent spin splitting in FeCuP$_2$S$_6$, with monolayer AFE–AFM order protected by a nonsymmorphic screw axis and bilayer sliding enabling reversible control of spin splitting. The study provides concrete predictions for spin-split band structures, shift-current responses, and anomalous Hall signals as experimental probes, establishing 2D FeCuP$_2$S$_6$ as a platform for electrically reconfigurable altermagnetism. This approach offers a general design principle for tunable spin-split states in next-generation spintronic devices and magnetoelectric technologies.

Abstract

Altermagnets (AMs) are a recently identified class of unconventional collinear compensated antiferromagnets that exhibit momentum-dependent spin splitting despite having zero net magnetization. This unconventional magnetic order gives rise to a range of phenomena, including the anomalous Hall effect, chiral magnons, and nonlinear photocurrents. Here, using spin space group (SSG) symmetry analysis and first-principles calculations, we demonstrate an efficient strategy to control altermagnetism in two-dimensional multiferroics through ferroelectric polarization and interlayer sliding. For material realization, we find that monolayer and bilayer FeCuP2S6 exhibit finite spin splitting when ferroelectric sublattices are connected by nonsymmorphic screw-axis operations rather than pure translation or inversion symmetry. Interlayer sliding further enables reversible switching or suppression of spin splitting through modifications of the SSG. Our calculations further reveal that the anomalous Hall response serves as a direct probe of these spin-split states. These findings establish two-dimensional van der Waals multiferroics as promising platforms for realizing electrically controllable altermagnetism and advancing next-generation spintronic and magnetoelectric technologies.

Figures (16)

• Figure 1: Schematics of two FE sublattices with opposite spins in (a) AFEAFM and (b) FEAFM structures. Arrows indicate the transformation between them, where in AFEAFM the lattice part is connected by $C_2$ rotation and in FEAFM it is connected by translation. Spin splittings can be observed in AFEAFM band structure, while degenerated in the FEAFM bands. (c) Schematics of switching spin splitting through bilayer sliding. $\sigma$ stands for the inverse Berry-curvature related properties.
• Figure 2: (a) Top view of antiferroelectric monolayer (AFE-ML) FeCuP$_2$S$_6$ structure, the orange, blue, light purple, and yellow balls stand for Fe, Cu, P, and S atoms, respectively. (b) Side view of the AFE-ML FeCuP$_2$S$_6$ (up) and the corresponding FE-ML configuration (down), respectively. (c) The transition pathways between two FE states (positive and negative polarization P) through PE state (red dashed line) and through AFE state (black line). The energy barriers of the FE-to-AFE, AFE-to-FE and FE-to-FE are denoted as E$_{B1}$, E$_{B2}$, and E$_{B3}$, respectively. (e) and (f) are the band structures of FE- and AFE-ML FeCuP$_2$S$_6$, respectively. The Brillouin zone and the high-symmetry $k$-path are shown in the inset of (d). (d) Shift current tensor for AFE-ML FeCuP$_2$S$_6$. (g) The $\sigma_{xyy}$ component of the charge shift current and the spin current tensor for AFE-ML FeCuP$_2$S$_6$, respectively. (h) The spin up and down channels of the spin shift current component $\sigma_{xyy}$.
• Figure 3: (a) Three possible stacking configurations for BL FeCuP$_2$S$_6$and the corresponding MSG. Type-I and -II exhibit altermagnetism, while type-III shows trivial compensated ferromagnetism; The corresponding band structures along the spin-splitting $k$-path are shown in (b); (c) Side views of AA' stacking mode of FeCuP$_2$S$_6$. (d) Schematics for the minimal symmetry requirement for AM. Open circles and double-ring circles are symmetry equivalent sites, respectively. Red and blue colors represent different spin up and spin down, respectively.
• Figure 4: (a) The top view of the AA stacking BL FeCuP$_2$S$_6$ (left) and a sliding configuration along x-y plane (right). (b) The sliding potential energy surface of AA BL stacking, number of the space group is marked at the high-symmetry points. (c) spin-splitting energy $\Delta E$ upon sliding along $\vec{a}$ direction, with $\vec{b}$ at $\vec{b}/b_0 = 1$ (blue) and $\vec{b}/b_0 = \frac{1}{2}$ (red); (d) Reversed spin splittings observed in the bands at 0.75 eV below $E_F$ in Type II BL at (top) $\vec{a}/a_0 = \vec{b}/b_0 = 1$ and (bottom) $\vec{a}/a_0 = \vec{b}/b_0 = \frac{1}{2}$. The corresponding spin-splitting energy heat maps on $k_z = 0$ plane are shown on the right.
• Figure 5: AHC $\sigma_{xy}$ as a function of Fermi energy for (a) AFEAM-ML (blue line) and FEAFM-ML (red line), respectively. (b) AHC for AA-stacked type-II FEAFM-BL FeCuP$_2$S$_6$. The orange, green, and blue lines show the different slding vectors.