type-II Multiferroics Research Articles

First-principles investigation of the magnetoelectric properties of Ba7Mn4O15

Type-II multiferroics, in which the magnetic order breaks inversion symmetry, are appealing for both fundamental and applied research due their intrinsic coupling between magnetic and electrical orders. Using first-principles calculations we study the ground state magnetic behaviour of Ba7Mn4O15 which has been classified as a type-II multiferroic in recent experiments. Our constrained moment calculations with the proposed experimental magnetic structure shows the spontaneous emergence of a polar mode giving rise to an electrical polarisation comparable to other known type-II multiferroics. When the constraints on the magnetic moments are removed, the spins self-consistently relax into a canted antiferromagnetic ground state configuration where two magnetic modes transforming as distinct irreducible representations coexist. While the dominant magnetic mode matches well with the previous experimental observations, the second mode is found to possess a different character resulting in a non-polar ground state. Interestingly, the non-polar magnetic ground state exhibits a significantly strong linear magnetoelectric (ME) coupling comparable to the well-known multiferroic BiFeO3, suggesting strategies to design new linear MEs.

Realistic Spin Model for Multiferroic NiI_{2}.

A realistic first-principle-based spin Hamiltonian is constructed for the type-II multiferroic NiI_{2}, using a symmetry-adapted cluster expansion method. Besides single ion anisotropy and isotropic Heisenberg terms, this model further includes the Kitaev interaction and a biquadratic term, and can well reproduce striking features of the experimental helical ground state, that are, e.g., a proper screw state, canting of rotation plane, propagation direction, and period. Using this model to build a phase diagram, it is demonstrated that, (i)the in-plane propagation direction of ⟨11[over ¯]0⟩ is determined by the Kitaev interaction, instead of the long-believed exchange frustrations and (ii)the canting of rotation plane is also dominantly determined by Kitaev interaction, rather than interlayer couplings. Furthermore, additional MonteCarlo simulations reveal three equivalent domains and different topological defects. Since the ferroelectricity is induced by spins in type-II multiferroics, our work also implies that Kitaev interaction is closely related to the multiferroicity of NiI_{2}.

Symmetry-based prediction of the type-II multiferroics with pyrochlore structure

Symmetry-based prediction of the type-II multiferroics with pyrochlore structure

Can the ferroelectric soft mode trigger an antiferromagnetic phase transition?

Type-II multiferroics, where spin interactions induce a ferroelectric polarization, are interesting for new device functionalities due to large magnetoelectric coupling. We report on a new type of multiferroicity in the quadruple-perovskite BiMn3Cr4O12, where an antiferromagnetic phase is induced by the structural change at the ferroelectric phase transition. The displacive nature of the ferroelectric phase transition at 125 K, with a crossover to an order-disorder mechanism, is evidenced by a polar soft phonon in the THz range and a central mode. Dielectric and pyroelectric studies show that the ferroelectric critical temperature corresponds to the previously reported Néel temperature of the Cr3+ spins. An increase in ferroelectric polarization is observed below 48 K, coinciding with the Néel temperature of the Mn3+ spins. This increase in polarization is attributed to an enhanced magnetoelectric coupling, as no change in the crystal symmetry below 48 K is detected from infrared and Raman spectra.

Observation of magnetic field-induced second magnetic ordering and peculiar ferroelectric polarization in L-type ferrimagnetic Fe2(MoO4)3

${\mathrm{Fe}}_{2}{({\mathrm{MoO}}_{4})}_{3}$ was synthesized and characterized as a prototype of L-type ferrimagnets (L-FiM) with an ordering temperature ${T}_{\mathrm{N}1}\ensuremath{\sim}12\phantom{\rule{0.28em}{0ex}}\mathrm{K}$ using magnetic susceptibility $(\ensuremath{\chi})$, specific heat $({C}_{\mathrm{p}})$, and dielectric $({\ensuremath{\varepsilon}}^{\ensuremath{'}})$ anomaly. Two remarkable findings are magnetic field $(H)$ induced (i) an additional magnetic phase transition at ${T}_{\mathrm{N}2}$ below ${T}_{\mathrm{N}1}$; and (ii) the emergence of flexible ferroelectric polarization $(P)$ with the tuning parameters $H$ and $T$ below ${T}_{\mathrm{N}2}$. Thus, the H-T phase diagram for spin-induced type-II multiferroics was established. In contrast to some known multiferroics with a critical field-induced spin-flip $P$ below ${T}_{\mathrm{N}1}$, the observed multiferroic nature is exotic. The origin of the profound multiferroic nature may be hidden in the complex $T$-and $H$-dependent spin and lattice structures. Consequently, the schematic picture of $H$-induced possible change of lattice symmetry and conical spin structure has been proposed. More experimental and theoretical works providing solid evidence and interpretations have been suggested to explore these peculiar multiferroic phenomena.

Evidence for a single-layer van der Waals multiferroic.

Multiferroic materials have attracted wide interest because of their exceptional static1-3 and dynamical4-6 magnetoelectric properties. In particular, type-II multiferroics exhibit an inversion-symmetry-breaking magnetic order that directly induces ferroelectric polarization through various mechanisms, such as the spin-current or the inverse Dzyaloshinskii-Moriya effect3,7. This intrinsic coupling between the magnetic and dipolar order parameters results in high-strength magnetoelectric effects3,8. Two-dimensional materials possessing such intrinsic multiferroic properties have been long sought for to enable the harnessing of magnetoelectric coupling in nanoelectronic devices1,9,10. Here we report the discovery of type-II multiferroic order in a single atomic layer of the transition-metal-based van der Waals material NiI2. The multiferroic state of NiI2 is characterized by a proper-screw spin helix with given handedness, which couples to the charge degrees of freedom to produce a chirality-controlled electrical polarization. We use circular dichroic Raman measurements to directly probe the magneto-chiral ground state and its electromagnon modes originating from dynamic magnetoelectric coupling. Combining birefringence and second-harmonic-generation measurementswith theoretical modelling and simulations, we detect a highly anisotropic electronic state that simultaneously breaks three-fold rotational and inversion symmetry, and supports polar order. The evolution of the optical signatures as a function of temperature and layer number surprisingly reveals an ordered magnetic polar state that persists down to the ultrathin limit of monolayer NiI2. These observations establish NiI2 and transition metal dihalides as a new platform for studying emergent multiferroic phenomena, chiral magnetic textures and ferroelectricity in the two-dimensional limit.

Magnetoelectric Multiferroicity and Magnetic Anisotropy in Guanidinium Copper(II) Formate Crystal.

Hybrid metal-organic compounds as relatively new and prosperous magnetoelectric multiferroics provide opportunities to improve the polarization, magnetization and magneto-electric coupling at the same time, which usually have some limitations in the common type-I and type-II multiferroics. In this work we investigate the crystal of guanidinium copper (II) formate [C(NH)]Cu(HCOO) and give novel insights concerning the structure, magnetic, electric and magneto-electric behaviour of this interesting material. Detailed analysis of crystal structure at 100 K is given. Magnetization points to the copper (II) formate spin-chain phase that becomes ordered below 4.6 K into the canted antiferromagnetic (AFM) state, as a result of super-exchange interaction over different formate bridges. The performed ab-initio colinear density functional theory (DFT) calculations confirm the AFM-like ground state as a first approximation and explain the coupling of spin-chains into the AFM ordered lattice. In versatile measurements of magnetization of a crystal, including transverse component besides the longitudinal one, very large anisotropy is found that might originate from canting of the coordination octahedra around copper (II) in cooperation with the canted AFM order. With cooling down in zero fields the generation of spontaneous polarization is observed step-wise below 270 K and 210 K and the effect of magnetic field on its value is observed also in the paramagnetic phase. Measured polarization is somewhat smaller than the DFT value in the c-direction, possibly due to twin domains present in the crystal. The considerable magneto-electric coupling below the magnetic transition temperature is measured with different orientations of the crystal in magnetic field, giving altogether the new light onto the magneto-electric effect in this material.

Enrichment of magnetoelectric effect in the hexagonal BaTi1-xCoxO3 artificial type-II multiferroics by defects

Artificial magnetoelectric material with enrichment of magnetoelectric (ME) coupling coefficient was achieved via mixed-oxide route in cobalt substituted BaTiO3 multiferroics. The observed large ME coupling coefficient induced by spin–orbit interaction through the symmetry breaking due to the off-stoichiometry oxygen. Structural details extracted from the Rietveld refinement indicate the rapid arrival of a single hexagonal phase (P63/mmc) at the expense of the tetragonal phase (P4mm) above x = 0.03. SAED patterns evidence to the structural coexistence, morphotropic phase boundary (MPB), (P4mm + P63/mmc) in x = 0.01 and 0.03 while hexagonal phase alone in x ≥ 0.05. Core-level XPS spectrum of Ba(3d), Ti (2p), Co (2p), O (1s) evidences the occurrence of the single oxidation state of Ba ion (Ba2+) and aliovalent of Ti (Ti4+ and Ti3+), Co (Co3+ and Co2+) and O (O2− and O1−) ions respectively. The weakening of ferroelectric loops arises from the formation of the non-ferroelectric hexagonal phase by the non-stoichiometric oxygen. For the first time, a high value of energy efficiency of 54.7% was achieved in the BaTi0.99Co0.01O3 sample. The ferromagnetism originated from the contributions of the super-exchange interaction of Co3+(octahedral)-O2−-Co3+(pentahedral) and double-exchange interaction (Co2+-O2−-Co3+) Among all the samples, an excellent magnetoelectric coupling coefficient (αME) value of 29.6 mV/cm Oe is attained in the hexagonal BaTi0.93Co0.07O3 sample.

Crystal symmetry for incommensurate helical and cycloidal modulations.

A classification of magnetic superspace groups compatible with the helical and cycloidal magnetic modulations is presented. Helical modulations are compatible with groups from crystal classes 1, 2, 222, 4, 422, 3, 32, 6 and 622, while cycloidal modulations are compatible with groups from crystal classes 1, 2, m and mm2. For each magnetic crystal class, the directions of the symmetry-allowed (non-modulated) net ferromagnetic moment and electric polarization are given. The proposed classification of superspace groups is tested on experimental studies of type-II multiferroics published in the literature.

Second-order nonlinear optical and linear ultraviolet-visible absorption properties of the type-II multiferroic candidates RbFe(AO4)2 ( A=Mo,Se,S )

Motivated by the search for type-II multiferroics, we present a comprehensive optical study of a complex oxide family of type-II multiferroic candidates: RbFe(MoO4)2, RbFe(SeO4)2, and RbFe(SO4)2. We employ rotational-anisotropy second harmonic generation spectroscopy (RA SHG), a technique sensitive to point symmetries, to address discrepancies in literature-assigned point/space groups and to identify the correct crystal structures. At room temperature we find that our RA SHG patterns rotate away from the crystal axes in RbFe(AO4)2 (A = Se, S), which identifies the lack of mirror symmetry and in-plane two-fold rotational symmetry. Also, the SHG efficiency of RbFe(SeO4)2 is two orders of magnitude stronger than RbFe(AO4)2 (A = Mo, S), which suggests broken inversion symmetry. Additionally, we present temperature-dependent linear optical characterizations near the band edge of this family of materials using ultraviolet-visible (UV-VIS) absorption spectroscopy. Included is experimental evidence of the band gap energy and band gap transition type for this family. Previously unreported sub-band gap absorption is also presented, which reveals prominent optical transitions, some with an unusual central energy temperature dependence. Furthermore, we find that by substituting the A-site in RbFe(AO4)2 (A = Mo, Se, S), the aforementioned transitions are spectrally tunable. Finally, we discuss the potential origin and impact of these tunable transitions.

Improper ferroelectricity in 134-type AA3′B4O12 perovskites

The 134-type $A$-site ordered ${\mathrm{LaMn}}_{3}{\mathrm{Cr}}_{4}{\mathrm{O}}_{12}$, that belongs to the family of $A{A}_{3}^{\ensuremath{'}}{B}_{4}{\mathrm{O}}_{12}$ perovskites, with cubic structure and magnetically driven improper polarization is puzzling because the conventional mechanisms leading to the creation of polarization in type-II multiferroics do not apply. By symmetry analysis and first-principles simulations, we discover an original and previously overlooked energetic term that naturally explains the origin of improper polarization in ${\mathrm{LaMn}}_{3}{\mathrm{Cr}}_{4}{\mathrm{O}}_{12}$. In addition, we demonstrate the existence of three other energetic invariants in $A{A}_{3}^{\ensuremath{'}}{B}_{4}{\mathrm{O}}_{12}$ perovskites, for which other physical quantities (such as oxygen tiltings or shear strain) mediate the interaction between $G$-type antiferromagnetic vectors to create and even enhance improper polarization.

Nanoengineering room temperature ferroelectricity into orthorhombic SmMnO3 films

Orthorhombic RMnO3 (R = rare-earth cation) compounds are type-II multiferroics induced by inversion-symmetry-breaking of spin order. They hold promise for magneto-electric devices. However, no spontaneous room-temperature ferroic property has been observed to date in orthorhombic RMnO3. Here, using 3D straining in nanocomposite films of (SmMnO3)0.5((Bi,Sm)2O3)0.5, we demonstrate room temperature ferroelectricity and ferromagnetism with TC,FM ~ 90 K, matching exactly with theoretical predictions for the induced strain levels. Large in-plane compressive and out-of-plane tensile strains (−3.6% and +4.9%, respectively) were induced by the stiff (Bi,Sm)2O3 nanopillars embedded. The room temperature electric polarization is comparable to other spin-driven ferroelectric RMnO3 films. Also, while bulk SmMnO3 is antiferromagnetic, ferromagnetism was induced in the composite films. The Mn-O bond angles and lengths determined from density functional theory explain the origin of the ferroelectricity, i.e. modification of the exchange coupling. Our structural tuning method gives a route to designing multiferroics.

First-principles study on structural, electronic, and ferroelectric properties of high-temperature RMn2O5 (R = Sm, Gd, Dy)

As a class of type-II multiferroics, RMn2O5 compounds show intriguing magnetoelectric coupling behaviors. However, the crystallographic characteristics of the high-temperature paramagnetic phase remain controversial. In present work, by employing PBEsol and SCAN exchange-correlation functionals, we have performed first-principles calculations to study the structural, electronic, and ferroelectric properties of the high-temperature RMn2O5 (R = Sm, Gd, Dy) compounds. According to our calculations, it is revealed that the high-temperature phase of RMn2O5 should be viewed as a super-paraelectric state due to the degeneracy of total energy for the centrosymmetric Pbam and polar Pm/P2 structures. Due to its unique structural and electronic properties, under certain external stimuli, the high-temperature RMn2O5 can develops the so-called electronic ferroelectricity through charge transition/transfer between Mn4+ and Mn3+ sites. In addition, the predicted ferroelectric polarization in the monoclinic Pm/P2 structures is no more than 1 μC/cm2. Our results may offer an alternative understanding for the complicated magnetoelectric behaviors occurred in the RMn2O5 family.

Observation of a ferro-rotational order coupled with second-order nonlinear optical fields

Ferroic orders can be classified by the symmetry of their order parameters, and ferroelectric, ferromagnetic and ferro-toroidal orders have already been observed. The ferro-rotational order1–3, whose order parameter is an axial vector invariant under both time-reversal and spatial-inversion operations, is the final ferroic to be identified and has a vector order parameter. This order is closely related to a number of phenomena such as polar vortices4, giant magnetoelectric coupling5 and spin-helicity-driven ferroelectricity6, but it has received little attention so far. Here, using high-sensitivity rotational-anisotropy second-harmonic generation, we have exploited the electric quadrupole contribution to the second-harmonic generation to directly couple to this centrosymmetric ferro-rotational order in an archetype of type-II multiferroics, RbFe(MoO4)2. We found that two domain states with opposite ferro-rotational vectors emerge with distinct populations at the critical temperature Tc ≈ 195 K and gradually evolve to reach an even ratio at lower temperatures. Moreover, we have identified the ferro-rotational order phase transition as weakly first order and have revealed its coupling field as a unique combination of the induced electric quadrupole second-harmonic generation and the incident fundamental electric fields. The authors use optical spectroscopy to show that RbFe(MoO4)2 hosts a ferro-rotational phase. This is the final form of ferroic order to be observed.

Spiral spin structures and skyrmions in multiferroics

Abstract In this article, we focus on (1) type-II multiferroics driven by spiral spin orderings and (2) magnetoelectric couplings in multiferroic skyrmion-hosting materials. We present both phenomenological understanding and microscopic mechanisms for spiral spin state, which is one of the essential starting points for type-II multiferroics and magnetic skyrmions. Two distinct mechanisms of spiral spin states (frustration and Dzyaloshinskii–Moriya [DM] interaction) are discussed in the context of the lattice symmetry. We also discuss the spin-induced ferroelectricity on the basis of the symmetry and microscopic atomic configurations. We compare two well-known microscopic models: the generalized inverse DM mechanism and the metal-ligand d-p hybridization mechanism. As a test for these models, we summarize the multiferroic properties of a family of triangular-lattice antiferromagnets. We also give a brief review of the magnetic skyrmions. Three types of known skyrmion-hosting materials with multiferroicity are discussed from the view point of crystal structure, magnetism, and origins of the magnetoelectric couplings. For exploration of new skyrmion-hosting materials, we also discuss the theoretical models for stabilizing skyrmions by magnetic frustration in centrosymmetric system. Several basic ideas for material design are given, which are successfully demonstrated by the recent experimental evidences for the skyrmion formation in centrosymmetric frustrated magnets.

Two-dimensional ferromagnetic-ferroelectric multiferroics in violation of the d0 rule

Contribution of d-electron to ferroelectricity of type-II multiferroics causes strong magneto-electric coupling and distinguishes them from the conventional type-I multiferroics. However, their therein polarization is too small because the ferroelectricity is merely a derivative from the magnetic order. Here we report a new class of multiferroic materials, monolayer VOX2 (X = Cl, Br, and I), which combine the advantages of type-I and type-II multiferroics. Both ferroelectricity and magnetism arise from the same V cation, where the filled d-orbital is perpendicular to an a priori ferroelectric polarization and thus poses no hindrance to ferroelectricity, indicating a violation of the usual d0 rule. This makes the combination of large polarizations and strong magneto-electric coupling possible. Our findings not only add new ferromagnetic-ferroelectric multiferroics, but also point to a unique mechanism to engineer multiferroics.

Dielectric evidence for possible type-II multiferroicity in α-RuCl3

$\alpha$-RuCl$_3$ is a Mott insulator with a honeycomb lattice with strong spin-orbit coupling. We report dielectric measurements on $\alpha$-RuCl$_3$ single crystals under field. At zero field, the dielectric constant, $\epsilon$, drops rapidly when cooled through the magnetic transition temperature T$_N$. With increasing field, the onset of the drop in $\epsilon$ tracks the T$_N$. Such behavior is absent with field above a critical value H$_c$ ~ 7.5 T, indicating the onset of a quantum phase transition. Our data suggest that the dielectric constant can be used as a probe of magnetic ordering in $\alpha$-RuCl$_3$, and $\alpha$-RuCl$_3$ is a possible type-II multiferroics.

Multiferroic properties of exotic double perovskite A2BB' O6

Multiferroic material in which there co-exist at least two of the ferro-phases,namely ferroelectricity,(anti-) ferromagnetism,and ferroelasticity,has attracted considerable attention in recent years due to its intriguing physics and potential applications for advanced multifunctional devices.However,multiferroic materials are rare due to the contradictory requirements between electrical polarization and magnetism.So far,only several compounds have been reported to show above-room temperature multiferroics.Thus,it is essential to search for new materials.The two most significant strategies to obtain multiferroics are 1) to incorporate magnetic transition-metal ions into polar structures to obtain polar magnets,and 2) to introduce special magnetic structure to drive ferroelectricity (the so-called type-Ⅱ multiferroics).Exotic double perovskite-related oxide A2BB'O6 with small A-site cations is one of the most extensively studied multiferroic families in recent years. The small A-site cations give small perovskite tolerance factor (t),and mostly high-pressure synthesis is required to stabilize the exotic perovskite structure.The crystal structure of exotic A2BB' O6 oxides can crystallize into either the centrosymmetric alumina corundum (AL),ilmenite (IL),or distorted GdFeO3-type perovskite structure,or the polar LiNbO3(LN),Ni3TeO6(NTO),or ordered ilmenite (OIL) structure.The polar LN,NTO,and OIL structures can accommodate magnetic transition-metal ions at both the A and B/B'sites in octahedral coordination,giving enhanced magnetic interactions and thus robust magneto-electric effect and high spontaneous polarization as well (usually above 50 C/cm-2,more than twice that in the renown BaTiO3),examples include the LN-type Mn2FeNbO6,and Mn2FeTaO6,OIL-type Mn2FeMoO6,and NTO-type Mn2FeMoO6,Mn2FeWO6,and Mn2MnWO6.These polar magnets show potential multiferroic responses even above room temperature (e.g.,ferromagnetic ordering temperature up to 340 K in NTO-type Mn2FeMoO6) and magnetoelectric coupling effect as in Mn2MnWO6.Magnetoelectric coupling can also arise in centrosymmetric IL structure in the absence of helical spin structure,such as those that are observed in Mn2FeSbO6,which exhibits colinear ferrimagnetic spin arrangement but magnetostriction induced antiferroelectricity.The corundum derivatives (AL,LN,IL,OIL,and NTO) and perovskite phases are competitive,depending on the electron configuration and synthesis pressure,and usually higher pressure favors the formation of perovskite structure.Compared with polar magnets in the corundum family,the exotic double perovskite adopts distorted GdFeO3-type structure (P21/n) with eight-coordination of the A-sites.In some double perovskite materials,the electric polarization can be induced by the special magnetic order,such as the ⇈⇊ magnetic structure induced type-Ⅱ multiferroics exemplified by A2CoMnO6(A=Lu,Y,Yb,Lu).In this review paper,we first compare the structure features of conventional and exotic double perovskite A2BB'O6 derived from the simple ABO3 analog,then summarize the recent progress of multiferroics in exotic double perovskite family,such as the polar magnets with transition-metal (Mn and Ni) cations at the A sites,type-Ⅱ multiferroic Mn2FeSbO6,and A2CoMnO6(A=Lu,Y,Yb,Lu). Finally,the problems and prospection of multiferroics in exotic double perovskite A2BB'O6 are also discussed to give a reference for the future research.

Proton transfer ferroelectricity/multiferroicity in rutile oxyhydroxides.

Oxyhydroxide minerals such as FeOOH have been a research focus in geology for studying the Earth's interior, and also in chemistry for studying their oxygen electrocatalysis activity. In this paper the first-principle evidence of a new class of ferroelectrics/multiferroics is given. In this class are: β-CrOOH (guyanaite), ε-FeOOH, β-GaOOH, and InOOH, which are earth-abundant minerals which have been experimentally verified to possess distorted rutile structures, are ferroelectric with considerable polarizations (up to 24 μC cm-2) and piezoelectric coefficients. Their atomic-thick layer may possess vertical polarization will not be diminished by depolarizing field because of the formation of O-HO bonds that can be hardly symmetrized. Furthermore, β-CrOOH is revealed to be a combination of a high Curie temperature (TC) in-plane type-I multiferroics and vertical type-II multiferroics, which is strain tunable and may give a desirable coupling between magnetism and ferroelectricity. Supported by experimental evidence on reversible conversion between metal oxyhydroxides and dioxides and their good lattice match that gives convenient epitaxial growth, a heterostructure composed of oxyhydroxides and common metal dioxides (e.g., TiO2, SnO2 and CrO2) may be constructed for various applications such as ferroelectric field-effect transistors and multiferroic tunneling junctions.

Control of Chiral Magnetism Through Electric Fields in Multiferroic Compounds above the Long-Range Multiferroic Transition.

Polarized neutron scattering experiments reveal that type-II multiferroics allow for controlling the spin chirality by external electric fields even in the absence of long-range multiferroic order. In the two prototype compounds TbMnO_{3} and MnWO_{4}, chiral magnetism associated with soft overdamped electromagnons can be observed above the long-range multiferroic transition temperature T_{MF}, and it is possible to control it through an electric field. While MnWO_{4} exhibits chiral correlations only in a tiny temperature interval above T_{MF}, in TbMnO_{3} chiral magnetism can be observed over several kelvin up to the lock-in transition, which is well separated from T_{MF}.