Basic concept of multiferroic materials
Fig.1 Multiferroic family tree[1]
Multiferroics exhibit more than one primary ferroic ordering, including ferromagnetism, ferroelectricity, or ferroelasticity in the same phase[1,2]. The terminology is usually extended to include non-primary orderings such as antiferromagnetism, antiferroelectricity, as well as composites of individual ferroics. The concept often used today is referred to magnetoelectric materiasl combing ferroelectric and magnetic behaviors (Fig. 1);. Such a combination of ferroic orders in multiferroics can lead to coupling between them and provide an efficient route to control magnetism by electric fields or vice versa.
Types of multiferroics
Fig.2 Types of multiferroicity[3]
Multiferroics can be classified into two categories: type-I mulitferroics refer to the ferroelectricity does not have magnetic origin, which usually leads to an indirect and weak magnetoelectric coupling; Type-II multiferroics are induced by some specific magnetic orders with a strong magnetoelectric coupling but a small electric polarization and thus low transition temperature (TC). The two types are depicted in Fig. 2[3]
Several mechanisms in multiferroics
Ferroelectricity may be driven by electronic lone pairs, geometric effects, charge order or magnetism. In the first three classes, electric polarization and magnetism occur independently, i.e. the Type-I. In the last one, electric polarization and magnetic order emerge jointly, i.e. the Type-II.
Fig.3 Mechanisms in multiferroics[3]
The lone-pairs mechanism is based on spatial asymmetry caused by anisotropic distribution of unbonded valance electrons around the host ion (see Fig. 3a). In this case the material is a single-phase, containing two cations, with one provides the ferroelectricity and the other the magnetism. This mechanism originates from room-temperature ferroelectricity in BiFeO3. A pair of Bi3+ valance electrons in the 6s orbital in BiFeO3 is not involved in sp hybridization and creates a local dipole, which yields a spontaneous polarization[4] of ~100 μC/cm
In geometrically driven ferroelectrics, a small A-site cation permits rotations of its surrounding coordination polyhedral (Fig. 3b), which are either polar in their own right (for example, in BaNiF4[6]) or couple to a secondary polar distortion (as in YMnO3[7]). In this case, the polarization is both robust and small in magnitude. In h-RMnO3 (R=Sc, Y, In or Dy-Lu[8,9]), unit-cell tripling drives the emergence of a ferroelectric order at Tc ≥ 1,200 K with a polarization of 5.6 μC/cm2, followed by a magnetic ordering at the Neel temperature (TN ≤ 120 K).
Valance electrons can be distributed non-uniformly around their host ions in the crystal lattice to form a periodic superstructure (Fig. 3c). For example, the Fe atoms in LuFe2O4 may form a superlattice with an alternating sequence of Fe2+ and Fe3+ ions[10]. This kind of charge ordering might be the source of an electric polarization.
In magnetically induced ferroelectrics, a non-collinear magnetic ordering, such as a spin spiral, breaks the inversion symmetry and induces a spontaneous polarization. These magnetically induced, so-called improper ferroelectric materials are totally different from displacive ferroelectrics, in which magnetic ordering is inhibited. The most intensely discussed mechanism is the inverse Dzyaloshinskii–Moriya (DM) interaction. Spin-orbit coupling (SOC) is crucial for the inverse DM interaction. The polarization is essentially determined by the optimization of the spin configuration from the point of view of anitsymmetry exchange, expressed by the antisymmetric product Si × Sj of neighboring spins Si,j (see Fig. 3d). The polarization vector is P ∝ eij × ( Si × Sj), where eij is the unit vector connecting neighboring spins. Multiferroicity of this type was first found in Cr2BeO4[11].
Multiferroicity in NiI2
Fig.4 Layer-dependent magnetic groundstate of NiI2
Arxiv
Varied competition among three multiferroic phases of NiI2 from the bulk to the monolayer limit
Bulk NiI2 undergoes two successive magnetic phase transitions from a para-magnetic (PM) phase to an interlayer antiferromagnetic (AFM) phase at TN1 = 76 K and then to a spiral magnetic phase below TN2 = 59.5 K [12]. The AFM-to-spiral transition is accompanied by both rotational symmetry and inversion symmetry breaks, resulting in electric polarization through inverse DM interaction, as reflected in second harmonic generation (SHG) [13] and birefringence signals [14]
The monolayer (ML) of NiI2 was recently suggested to be a type-II multiferroic material, based on a presumed magnetic configuration and a supposed origin of the enhanced SHG signal. We found that such an assumption is flawed at the monolayer limit where a freestanding ML NiI2 showing broken C3 symmetry prefers to a striped antiferromagnetic order (AABB-AFM) along with an intralayer antiferroelectric (AFE) order[15]. However, the C3 symmetry of the monolayer may preserve under a substrate confinement, which leads to a spiral magnetic order (Spiral-V), a different spiral order from that of the bulk counterpart (Spiral-B). The Spiral-V order persists up to 2L thickness with the C3 symmetry and shows ferroelectricity (FE) ascribed to the inversed DM interaction. Thus, those three type-II multiferroic phases, namely Spiral-B+FE, Spiral-V+FE and AABB-AFM+AFE, emerge for NiI2 with different layer numbers and structural symmetries.
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Ji Group@Renmin University