Ferroelectric $p$-wave magnets

Abstract

Couplings between ferroelectric and magnetic orders offer promising routes toward low-dissipation electronics. However, such couplings are notably rare, largely due to the poor compatibility between insulating band structures and ferromagnetism. Here, we study a different strategy: we identify previously overlooked time-reversal-symmetric $p$- and $f$-wave spin-polarized insulating electronic states in ferroelectrics with noncollinear magnetic sublattices. We show that combining spin and magnetic group theory enables a systematic classification of the origin of polar symmetry breaking. We distinguish crystallographic, exchange-, or spin-orbit-driven mechanisms. Furthermore, we identify more than 50 candidate materials. Using first-principles calculations, we demonstrate a pristine, time-reversal-symmetric $p$-wave spin-polarized electronic structure in the well-known multiferroic $\mathrm{GdMn_2O_5}$. We further show that its $p$-wave order can be switched electrically, opening alternative paths toward spintronic and multiferroic functionalities in this class of materials.

Figures (3)

• Figure 1: (a) Altermagnetic $d$-wave spin polarization with highlighted nodal plane on top of constant-energy isosurface at energy $0.5~\mathrm{eV}$ below the Fermi level, and (b) Magnetic structure of ultrathin $\mathrm{BiFeO_3}$fratian2026topologicaltexturesemergentaltermagnetic. (c) Time-reversal $\mathcal{T}$ symmetric $p$-wave spin polarization on top of constant-energy isosurface at energy $0.1~\mathrm{eV}$ below the Fermi level calculated for $\mathrm{GdMn_2O_5}$ with a ferroelectric polarization $P$ along the $z$-axis. Color indicates the $z$-component of the spin polarization. (d) Coplanar magnetic structure of $\mathrm{GdMn_2O_5}$. O atoms are located on the vertices of the grey-shaded polyhedra.
• Figure 2: Band structures showing $p$-wave spin splitting in Type-I multiferroic $\mathrm{Ni_2Mo_3O_8}$ and Type-II multiferroic $\mathrm{GdMn_2O_5}$, without and with SOC. High-symmetry points are located at $\Gamma = (0, 0, 0)$, $X = (\pi/a, 0, 0)$.
• Figure 3: Ferroelectric switching of $p$-wave magnetism: $p$-wave-magnetoelectric coupling. (a) Four coplanar magnetic structures of $\mathrm{GdMn_2O_5}$ (only parts of the unit cell displayed) with combinations of spin (S) and electric (P) polarization signs, energetically degenerate without SOC. SOC splits the four states into two pairs of degenerate states -- states (i) and (iii) become ground states. State (i) is experimentally reported in MAGNDATA. (b) First-principles-calculated dependence of electric polarization from the electrons $P$ and spin splitting strength $\Delta$ of the valence band at high-symmetry point $X = (\pi/a, 0, 0)$ vs. relative rotation of the magnetic moments $\phi = \phi_1 - \phi_2$. The four states are indicated by vertical solid (i, iii) and dashed (ii, iv) lines.