Fig. 2: Spin-electric potential and driven magnetoelectric coupling mechanism.
Schematic diagrams of (a) electric dipole potential, (b) magnetic potential, and (c) spin-electric potential. P, M, Ɛ and B represent electric dipole moment, magnetic moment, electric field intensity and magnetic field intensity, respectively. PSAP and PSP represent electric dipole moments of spin-antiparallel (SAP) and spin-parallel (SP) states, respectively. Red and blue arrows represent electron spins. Green arrows represent electric dipole moments. d Schematic diagram of electric-field switching of interlayer magnetic order driven by spin-electric potential. Ɛz represents the out-of-plane electric field, Ɛc represents the coercive electric field required to switch the interlayer magnetic order. e Tight-binding dimer model for the origin of spin-order-dependent electric dipole moment. Δdd represents the on-site energy difference between magnetic atoms. Light green arrows indicate electric dipole moments (p) contributed by bonding and antibonding orbitals. f Energy difference between SP and SAP orders (Eex = ESAP – ESP) as a function of external electric fields with Δdd = 0, − 0.1, − 0.3 and − 0.5 eV derived from the tight-binding model. Inset: PSAP and PSP, and their difference (Pex = PSAP – PSP) for the magnetic dimer as a function of Δdd.
