Nonvolatile Electrical Control of Spin via Sliding Fractional Quantum Multiferroics

Abstract

We propose a fractionally quantized polarization induced by interlayer sliding in bilayer altermagnets, unveiling a previously unrecognized multiferroic phase termed sliding fractional quantum multiferroicity (SFQM). This unconventional magnetic phase uniquely integrates sliding ferroelectricity with fractional quantum ferroelectricity, enabling highly efficient switching and nonvolatile electrical control of spin.~Unlike conventional multiferroics, SFQM simultaneously exhibits lattice-scale atomic displacements, ultralow switching barriers, and spin splitting, giving rise to a large fractionally quantized polarization and strong magnetoelectric coupling. Through symmetry analysis and first-principles calculations, we identify bilayer altermagnet Ca(CoN)$_2$ and its family materials as promising candidates hosting SFQM. In contrast to gate-controlled schemes, the spin-layer coupling in SFQM is intrinsically induced by spontaneous electrical and layer polarization, requiring no sustained gate field and exhibiting nonvolatile character. This mechanism enables nonvolatile electrical control of spin through biaxial sliding, where displacements along the \textit{x}- and \textit{y}-axes generate opposite polarization directions in the layer-dependent electrical polarization. Furthermore, SFQM exhibits a fully switchable anomalous Hall effect and a pronounced magneto-optical response, which can be utilized for its detection and distinction. These findings highlight the promising role of sliding-mediated couplings among unconventional magnetism, fractional quantum ferroelectricity, and stacking order in realizing electrically controllable two-dimensional multiferroics.

Figures (4)

• Figure 1: Concept of sliding fractional quantum multiferroicity (SFQM). (a),(b) Comparison of conventional ferroelectricity (FE) and the proposed fractional quantum ferroelectricity (FQFE). (c) In altermagnets, sliding induces fractionally quantized polarization for a SFQM state. Grey, green, red, and blue spheres denote ligand ions, movable nonmagnetic ions, and magnetic ion clusters with opposite spins, respectively. (d) Underlying structure and symmetry of the altermagnetic bilayer. The top layer $S'$ is obtained by applying an operation to the bottom layer $S$. Here, $\hat{\tau}_z=${$E|\tau_z$} is a trivial out-of-plane translation operator which does not change the symmetry of the bilayer, and $\hat{O}=\{E|\tau_{o}\}$ is the sliding operator, where $\tau_{o}$ is the in-plane sliding part.
• Figure 2: Sliding pathway and fractional polarization in bilayer Ca(CoN)$_2$. Top and side views of the bilayer structure in the (a) $L_1$, (b) $H$, and (c) $L_2$ phases, with the in-plane sliding displacement of $\frac{1}{2}\mathbf{a} + \frac{1}{2}\mathbf{b}$ indicated. (d) The phase transition pathway characterized by the energy barrier from nudged elastic band (NEB) calculations and the evolution of the polarization. The primitive cells for the $L_1$, $H$, and $L_2$ phases are depicted, showing the fractional polarizations $|\mathbf{P}_1| = |\mathbf{P}_2| = \frac{1}{2}\mathbf{Q}$.
• Figure 3: (a),(b) Band structures of $L_1$, and $L_2$ phase of the bilayer Ca(CoN)$_2$ (without SOC), with red/blue indicating opposite spin polarities. The Fermi level is set to zero. (c),(d) Differential charge density of $L_1$ and $L_2$, where the yellow and cyan regions correspond to charge accumulation and depletion.
• Figure 4: (a) The schematic illustration of two transition pathways between the $L_1$ and $L_2$ phases. (b) Energy distribution of bilayer Ca(CoN)$_2$ with the ground state energy ($L_{1(2)}$) as the reference. (c),(d) The anomalous Hall conductivities for the $L_1$ phase and $L_2$ phase of bilayer Ca(CoN)$_2$. (e),(f) The magneto-optical response of the $L_1$ and $L_2$ phases for bilayer Ca(CoN)$_2$, characterized by Kerr angle and Kerr ellipticity.