Type-II Antiferroelectricity

Abstract

Antiferroelectricity (AFE) is a fundamental concept in physics and materials science. Conventional AFEs have the picture of alternating local electric dipoles defined in real space. Here, we discover a new class of AFEs, termed type-II AFEs, which possess opposite polarizations defined in momentum space across a pair of symmetry decoupled subspaces. Unlike conventional AFEs, the order parameter of type-II AFEs is rigorously formulated through Berry-phase theory and can be quantitatively extracted from the electronic band structure. Focusing on a subclass of type-II AFEs that preserve spin-rotation symmetry, we establish the relevant symmetry constraints and identify all compatible spin point groups. Remarkably, we find that type-II AFE order intrinsically coexists with antiferromagnetism, revealing a robust form of magnetoelectric coupling. We construct an altermagnetic model and identify several concrete antiferromagnetic/altermagnetic materials, such as FeS, Cr2O3, MgMnO3, monolayer MoICl2 and bilayer CrI3, that exhibit this novel ordering. Furthermore, we uncover unique physical phenomena associated with type-II spin-AFE systems, including spin current generation upon AFE switching and localized spin polarization at boundaries and domain walls. Our findings reveal a previously hidden class of quantum materials with intertwined ferroic orders, offering exciting opportunities for both fundamental exploration and technological applications.

Figures (5)

• Figure 1: (a) Illustration of conventional AFE. The green and yellow dots represent two kinds of ions. The AFE order is associated with opposite local electric dipoles defined in real space, as indicated by the red and blue arrows. (b) Illustration of type-II AFE. The AFE order is connected to opposite polarization $P^\pm$ defined in $k$ space for two decoupled sectors $V_\pm$ of the total Hilbert space.
• Figure 2: (a) Illustration of the spin-AFE lattice model (\ref{['eq:ham1']}). The red and blue arrows denote the magnetic moments on the sites. (b) Band structure of the model, showing altermagnetic spin splitting. The Brillouin zone is presented in Supplemental Material (SM) SM. The resulting AFE order $\bm{\mathcal{Q}}$ is along $z$ axis, as shown in (a). (c) The AFE order $\mathcal{Q}_3$ vs the AFM order $\Delta_0$. Here, we set $t_{1}=-0.9$ eV, $t_{2} =0.8$ eV, and $\chi=-0.8$ in (b-c) and $\Delta_{0}=-1$ eV in (b).
• Figure 3: (a) Crystalline structure of $\mathrm{FeS}$, where the red and blue spheres represent the $\mathrm{Fe}$ atoms with opposite magnetic moments. It is an altermagnetic type-II AFE. (b) Band structure of $\mathrm{FeS}$ without SOC. Red and blue lines denote the spin-up and spin-down bands, showing altermagnetic spin splitting. (c) The $k$ resolved polarization $P_z=\int_{0}^{2\pi}{\cal A}_z(k_x,k_y) dk_z$ in the $k_x$-$k_y$ plane. It takes opposite values for the two spin subspaces, leading to AFE.
• Figure 4: (a) Crystalline structure of monolayer $\mathrm{MoICl_2}$, where the red and blue spheres represent $\mathrm{Mo}$ atoms with opposite magnetic moments. Its AFE order $\bm{\mathcal{Q}}$ is along $b$ axis. (b) Band structure of monolayer $\mathrm{MoICl_2}$ without SOC, which are spin-degenerate.
• Figure 5: (a) Schematic of a possible junction geometry for detection of spin-AFE. A pure spin current is generated by reversing the spin-AFE order, and it flows into an adjacent heavy-metal layer and produces a transverse voltage signal via the inverse spin Hall effect. (b) Domain wall between two spin-AFE domains hosts a local spin polarization. (c) Calculated band structure for such a domain wall based on model (\ref{['eq:ham1']}). The red and blue dots are respectively the spin-up and spin-down domain wall modes. (d) The real-space distribution of spin-down domain wall mode at $\Gamma$ point in (c).