Electric control of spin helicity in a magnetic ferroelectric

Magnetoelastic coupling and critical behavior of some strongly correlated magnetic systems

The strongly correlated magnetic systems are attracting continuous attention in current condensed matter research due to their very compelling physics and promising technological applications. Being a host to charge, spin, and lattice degrees of freedom, such materials exhibit a variety of phases, and investigation of their physical behavior near such a phase transition bears an immense possibility. This review summarizes the recent progress in elucidating the role of magnetoelastic coupling on the critical behavior of some technologically important class of strongly correlated magnetic systems such as perovskite magnetites, uranium ferromagnetic superconductors, and multiferroic hexagonal manganites. It begins with encapsulation of various experimental findings and then proceeds toward describing how such experiments motivate theories within the Ginzburg-Landau phenomenological picture in order to capture the physics near a magnetic phase transition of such systems. The theoretical results that are obtained by implementing Wilson's renormalization-group to nonlocal Ginzburg-Landau model Hamiltonians are also highlighted. A list of possible experimental realizations of the coupled model Hamiltonians elucidates the importance of spin-lattice coupling near a critical point of strongly correlated magnetic systems.

All-electrical reading and writing of spin chirality

Spintronics promises potential data encoding and computing technologies. Spin chirality plays a very important role in the properties of many topological and noncollinear magnetic materials. Here, we propose the all-electrical detection and manipulation of spin chirality in insulating chiral antiferromagnets. We demonstrate that the spin chirality in insulating epitaxial films of TbMnO₃ can be read electrically via the spin Seebeck effect and can be switched by electric fields via the multiferroic coupling of the spin chirality to the ferroelectric polarization. Moreover, multivalued states of the spin chirality can be realized by the combined application of electric and magnetic fields. Our results are a path toward next-generation, low-energy consumption memory and logic devices that rely on spin chirality.

Combined Arrhenius-Merz Law Describing Domain Relaxation in Type-II Multiferroics

Electric fields were applied to multiferroic TbMnO_{3} single crystals to control the chiral domains, and the domain relaxation was studied over 8 decades in time by means of polarized neutron scattering. A surprisingly simple combination of an activation law and the Merz law describes the relaxation times in a wide range of electric field and temperature with just two parameters, an activation-field constant and a characteristic time representing the fastest possible inversion. Over the large part of field and temperature values corresponding to almost 6 orders of magnitude in time, multiferroic domain inversion is thus dominated by a single process, the domain wall motion. Only when approaching the multiferroic transition other mechanisms yield an accelerated inversion.

Supercurrent Induced by Chiral Coupling in Multiferroic/Superconductor Nanostructures

We study the transport and the superconducting dynamics in a layer of type II superconductor (SC) with a normal top layer that hosts a helical magnetic ordering that gives rise to spin-current-driven ferroelectric polarization. Proximity effects akin to this heterostructure result in an anisotropic supercurrent transport and modify the dynamic properties of vortices in the SC. The vortices can be acted upon and controlled by electric gating or other means that couple to the spin ordering in the top layer, which, in turn, alter the superconducting/helical magnet coupling characteristics. We demonstrate, using the time dependent Ginzburg-Landau approach, how the spin helicity of the top layer can be utilized for pinning and guiding the vortices in the superconducting layer.

Spiral spin structures and skyrmions in multiferroics

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.

Magnetization-polarization cross-control near room temperature in hexaferrite single crystals

Mutual control of the electricity and magnetism in terms of magnetic (H) and electric (E) fields, the magnetoelectric (ME) effect, offers versatile low power consumption alternatives to current data storage, logic gate, and spintronic devices. Despite its importance, E-field control over magnetization (M) with significant magnitude was observed only at low temperatures. Here we have successfully stabilized a simultaneously ferrimagnetic and ferroelectric phase in a Y-type hexaferrite single crystal up to 450 K, and demonstrated the reversal of large non-volatile M by E field close to room temperature. Manipulation of the magnetic domains by E field is directly visualized at room temperature by using magnetic force microscopy. The present achievement provides an important step towards the application of ME multiferroics.

Mutual control of the electric polarization and magnetization promises for low power consumption spintronic devices but remains challenging. Here the authors show reversal of non-volatile magnetization by electric field as well as the polarization switching by magnetic field in a single-component material, close to room temperature.

Spherical neutron polarimetry under high pressure for a multiferroic delafossite ferrite

The analysis of three-dimensional neutron spin polarization vectors, using a technique referred to as spherical neutron polarimetry (SNP), is a very powerful means of determining complex magnetic structures in magnetic materials. However, the requirement to maintain neutrons in a highly polarized state has made it difficult to use this technique in conjunction with extreme experimental conditions. We have developed a high pressure cell made completely of nonmagnetic materials and having no effect on neutron polarizations. Herein, we report the first SNP analyses under high pressure up to 4.0 GPa in the magnetoelectric multiferroic delafossite CuFeO2. This study also determined the complex spiral magnetic structures in these pressure-induced phases, by measuring the full neutron polarization matrix. The results presented herein demonstrate that the SNP measurements are feasible under high pressure conditions, and that this method is a useful approach to study pressure-induced physical phenomena.

Switching of the Chiral Magnetic Domains in the Hybrid Molecular/Inorganic Multiferroic (ND4)2[FeCl5(D2O)]

(ND₄)₂[FeCl₅(D₂O)] represents a promising example of the hybrid molecular/inorganic approach to create materials with strong magneto-electric coupling. Neutron spherical polarimetry, which is directly sensitive to the absolute magnetic configuration and domain population, has been used in this work to unambiguously prove the multiferroicity of this material. We demonstrate that the application of an electric field upon cooling results in the stabilization of a single-cycloidal magnetic domain below 6.9 K, while poling in the opposite electric field direction produces the full population of the domain with opposite magnetic chirality. We prove the complete switchability of the magnetic domains at low temperature by the applied electric field, which constitutes a direct proof of the strong magnetoelectric coupling. Additionally, we refine the magnetic structure of the ordered ground state, deducing the underlying magnetic space group consistent with the direction of the ferroelectric polarization, and we provide evidence of a collinear amplitude-modulated state with magnetic moments along the a-axis in the temperature region between 6.9 and 7.2 K.

Switching of Magnons by Electric and Magnetic Fields in Multiferroic Borates

Electric manipulation of magnetic properties is a key problem of materials research. To fulfill the requirements of modern electronics, these processes must be shifted to high frequencies. In multiferroic materials, this may be achieved by electric and magnetic control of their fundamental excitations. Here we identify magnetic vibrations in multiferroic iron borates that are simultaneously sensitive to external electric and magnetic fields. Nearly 100% modulation of the terahertz radiation in an external field is demonstrated for SmFe_{3}(BO_{3})_{4}. High sensitivity can be explained by a modification of the spin orientation that controls the excitation conditions in multiferroic borates. These experiments demonstrate the possibility to alter terahertz magnetic properties of materials independently by external electric and magnetic fields.

Multiferroic Hysteresis Loop

Multiferroics, showing both ferroelectric and magnetic order, are promising candidates for future electronic devices. Especially, the fundamental understanding of ferroelectric switching is of key relevance for further improvements, which however is rarely reported in literature. On a prime example for a spin-driven multiferroic, LiCuVO₄, we present an extensive study of the ferroelectric order and the switching behavior as functions of external electric and magnetic fields. From frequency-dependent polarization switching and using the Ishibashi-Orihara theory, we deduce the existence of ferroelectric domains and domain-walls. These have to be related to counterclockwise and clockwise spin-spirals leading to the formation of multiferroic domains. A novel measurement—multiferroic hysteresis loop—is established to analyze the electrical polarization simultaneously as a function of electrical and magnetic fields. This technique allows characterizing the complex coupling between ferroelectric and magnetic order in multiferroic LiCuVO₄.

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}.

Enhancement of Ferroelectricity for Orthorhombic (Tb0.861Mn0.121)MnO3-δ by Copper Doping

Copper-doped (Tb_0.861Mn_0.121)MnO_3-δ has been synthesized by the conventional solid state reaction method. X-ray, neutron, and electron diffraction data indicate that they crystallize in Pnma space group at room temperature. Two magnetic orderings are found for this series by neutron diffraction. One is the ICAM (incommensurate canted antiferromagnetic) ordering of Mn with a wave vector q_Mn = (∼0.283, 0, 0) with a ≈ 5.73 Å, b ≈ 5.31 Å, and c ≈ 7.41 Å, and the other is the CAM (canted antiferromagnetic) ordering of both Tb and Mn in the magnetic space group Pn'a2₁' with a ≈ 5.73 Å, b ≈ 5.31 Å, and c ≈ 7.41 Å. A dielectric peak around 40 K is found for the samples doped with Cu, which is higher than that for orthorhombic TbMnO₃.

Magnetic Reversal of Electric Polarization with Fixed Chirality of Magnetic Structure in a Chiral-Lattice Helimagnet MnSb_{2}O_{6}

The correlation between magnetic and dielectric properties has been investigated for the single crystal of the chiral triangular-lattice helimagnet MnSb_{2}O_{6}. We found that the spin-spiral plane in the ground state has a considerable tilting from the (110) plane and that the sign of the spin-spiral tilting angle is coupled to the clockwise or counterclockwise manner of spin rotation and accordingly to the sign of magnetically induced electric polarization. This leads to unique magnetoelectric responses such as the magnetic-field-induced selection of a single ferroelectric domain as well as the reversal of electric polarization just by a slight tilting of the magnetic field direction, where the chiral nature of the crystal structure plays a crucial role through the coupling of the chirality between the crystal and magnetic structures. Our results demonstrate that crystallographic chirality can be an abundant source of novel magnetoelectric functions with coupled internal degrees of freedom.

Pressure and strain effects of hexagonal rare-earth manganites: a first-principles study

We have investigated the structural, electrical and magnetic properties as well as the phonon modes of hexagonal rare-earth manganites (RMnO3, R  =  Pr, Nd, Pm, Sm, Gd, Tb, Dy, Ho, Er, Tm and Lu) under chemical pressure, hydrostatic pressure and epitaxial strain by first-principles calculations. The magnetic ground state of RMnO3 is found to have Γ4 magnetic configuration and to be stable under all considered external conditions. In contrast, the K3 phonon mode, which is the primary order parameter and responsible for the 'improper ferroelectricity', is greatly influenced by pressure and epitaxial strain. Consequently, the electric polarization is enhanced by 56.7% when the chemical pressure increases from R  =  Pr to R  =  Lu. The hydrostatic pressure can also improve the polarization to a certain degree, e.g. by 14.7% from 0 GPa to 40 GPa in LuMnO3. Finally, the dependence of polarization on the epitaxial strain is also given, revealing that the compressive strain could promote the ferroelectricity while tensile strain will suppress it.

All-Electrical Measurement of Interfacial Dzyaloshinskii-Moriya Interaction Using Collective Spin-Wave Dynamics

Dzyaloshinskii-Moriya interaction (DMI), which arises from the broken inversion symmetry and spin-orbit coupling, is of prime interest as it leads to a stabilization of chiral magnetic order and provides an efficient manipulation of magnetic nanostructures. Here, we report all-electrical measurement of DMI using propagating spin wave spectroscopy based on the collective spin wave with a well-defined wave vector. We observe a substantial frequency shift of spin waves depending on the spin chirality in Pt/Co/MgO structures. After subtracting the contribution from other sources to the frequency shift, it is possible to quantify the DMI energy in Pt/Co/MgO systems. The result reveals that the DMI in Pt/Co/MgO originates from the interfaces, and the sign of DMI corresponds to the inversion asymmetry of the film structures. The electrical excitation and detection of spin waves and the influence of interfacial DMI on the collective spin-wave dynamics will pave the way to the emerging field of spin-wave logic devices.

Dynamical magnetoelectric phenomena of multiferroic skyrmions

Magnetic skyrmions, vortex-like swirling spin textures characterized by a quantized topological invariant, realized in chiral-lattice magnets are currently attracting intense research interest. In particular, their dynamics under external fields is an issue of vital importance both for fundamental science and for technical application. Whereas observations of magnetic skyrmions has been limited to metallic magnets so far, their realization was also discovered in a chiral-lattice insulating magnet Cu2OSeO3 in 2012. Skyrmions in the insulator turned out to exhibit multiferroic nature with spin-induced ferroelectricity. Strong magnetoelectric coupling between noncollinear skyrmion spins and electric polarizations mediated by relativistic spin-orbit interaction enables us to drive motion and oscillation of magnetic skyrmions by application of electric fields instead of injection of electric currents. Insulating materials also provide an environment suitable for detection of pure spin dynamics through spectroscopic measurements owing to the absence of appreciable charge excitations. In this article, we review recent theoretical and experimental studies on multiferroic properties and dynamical magnetoelectric phenomena of magnetic skyrmions in insulators. We argue that multiferroic skyrmions show unique coupled oscillation modes of magnetizations and polarizations, so-called electromagnon excitations, which are both magnetically and electrically active, and interference between the electric and magnetic activation processes leads to peculiar magnetoelectric effects in a microwave frequency regime.

Control of multiferroic domains by external electric fields in TbMnO₃

The control of multiferroic domains through external electric fields has been studied by dielectric measurements and by polarized neutron diffraction on single-crystalline TbMnO3. Full hysteresis cycles were recorded by varying an external field of the order of several kV mm(-1) and by recording the chiral magnetic scattering as well as the charge in a sample capacitor. Both methods yield comparable coercive fields that increase upon cooling.

Magnetoelectric effects in the skyrmion host material Cu2OSeO3

Insulating helimagnetic Cu₂OSeO₃ shows sizeable magnetoelectric effects in its skyrmion phase. Using magnetization measurements, magneto-current analysis and dielectric spectroscopy, we provide a thorough investigation of magnetoelectric coupling, polarization and dielectric constants of the ordered magnetic and polar phases of single-crystalline Cu₂OSeO₃ in external magnetic fields up to 150 mT and at temperatures below 60 K. From these measurements we construct a detailed phase diagram. Especially, the skyrmion phase and the metamagnetic transition of helical to conical spin order are characterized in detail. Finally we address the question if there is any signature of polar order that can be switched by an external electric field, which would imply multiferroic behaviour of Cu₂OSeO₃.

Controlling and probing non-abelian emergent gauge potentials in spinor Bose-Fermi mixtures

Gauge fields, typified by the electromagnetic field, often appear as emergent phenomena due to geometrical properties of a curved Hilbert subspace, and provide a key mechanism for understanding such exotic phenomena as the anomalous and topological Hall effects. Non-abelian gauge potentials serve as a source of non-singular magnetic monopoles. Here we show that unlike conventional solid materials, the non-abelianness of emergent gauge potentials in spinor Bose-Fermi atomic mixtures can be continuously varied by changing the relative particle-number densities of bosons and fermions. The non-abelian feature is captured by an explicit dependence of the measurable spin current density of fermions in the mixture on the variable coupling constant. Spinor mixtures also provide us with a method to coherently and spontaneously generate a pure spin current without relying on the spin Hall effect. Such a spin current is expected to have potential applications in the new generation of atomtronic devices.

Abelian and non-abelian emergent gauge fields govern the physics of many topological phenomena, such as Hall effects. Here the authors show theoretically that in a spinor Bose-Fermi mixture the non-abelianness of the gauge potential can be tuned, offering the chance to study the abelian-non-abelian crossover.

Control of magnetism by electric fields

The electrical manipulation of magnetism and magnetic properties has been achieved across a number of different material systems. For example, applying an electric field to a ferromagnetic material through an insulator alters its charge-carrier population. In the case of thin films of ferromagnetic semiconductors, this change in carrier density in turn affects the magnetic exchange interaction and magnetic anisotropy; in ferromagnetic metals, it instead changes the Fermi level position at the interface that governs the magnetic anisotropy of the metal. In multiferroics, an applied electric field couples with the magnetization through electrical polarization. This Review summarizes the experimental progress made in the electrical manipulation of magnetization in such materials, discusses our current understanding of the mechanisms, and finally presents the future prospects of the field.

Uniaxial-stress control of spin-driven ferroelectricity in multiferroic Ba(2)CoGe(2)O(7)

We have demonstrated that spin-driven ferroelectricity in a tetragonal multiferroic Ba(2)CoGe(2)O(7) is controlled by applying uniaxial stress. We found that the application of compressive stress along the [110] direction leads to a 45° or 135° rotation of the sublattice magnetization of the staggered antiferromagnetic order in this system. This allows the spontaneous electric polarization to appear along the c axis. The present study suggests that an application of anisotropic stress, which is the simplest way to control symmetry of matter, can induce a variety of cross-correlated phenomena in spin-driven multiferroics.

Dielectric properties and electrical switching behaviour of the spin-driven multiferroic LiCuVO4

The simultaneous existence and coupling of ferroelectric and magnetic ordering in a material, so-called multiferroicity, is of great scientific interest due to the underlying complex physical mechanisms and its possible applications. Here we present the multiferroic properties of a prototypical spin-driven ferroelectric material, the spin-1/2 chain cuprate LiCuVO4. In this system, spiral spin order, with propagation in the b direction and a spin helix in the ab plane, induces ferroelectric polarization in the a direction when no magnetic field is applied. In an external magnetic field, the direction of the spin spiral and thus the direction of the electrical polarization can be switched. Broadband dielectric spectroscopy on a single crystalline sample oriented in two different directions was performed in applied external magnetic fields up to 9 T, demonstrating this switching behaviour of the ferroelectric polarization. Furthermore, detailed magnetic-field and temperature-dependent ferroelectric hysteresis-loop measurements reveal the switching of polarization by an electrical field, which implies the electric control of the spin helicity of LiCuVO4.

Spin and orbital orderings behind multiferroicity in delafossite and related compounds

Coupling between noncollinear magnetic ordering and ferroelectricicty in magnetoelectric multiferroics has been extensively studied in the last decade. Delafossite family compounds with triangular lattice structure provide a great opportunity to study the coupling between spin and electric dipole in multiferroics due to the variety of magnetic phases with different symmetry. This review introduces the magnetic and ferroelectric phase transitions in delafossite ferrites, CuFe(1-x)X(x)O(2) (X = Al, Ga), AgFeO(2) and the related compound α-NaFeO(2). In CuFeO(2), the ferroelectric phase appears under a magnetic field or chemical substitution. The proper screw magnetic ordering with the magnetic point group 21', which has been determined by detailed analysis in neutron diffraction experiments, induces the ferroelectric polarization along the monoclinic b axis in CuFeO2. The cycloidal magnetic orderings are realized in AgFeO(2) and α-NaFeO(2), which are of the point group m1' allowing polarization in the ac plane. The emergence of ferroelectric polarization can be explained by both the extended inverse Dzyaloshinsky-Moriya effect and the d − p hybridization mechanism. These mechanisms are supported by experimental evidence in CuFe(1-x)Ga(x)O2. The polarized neutron diffraction experiment demonstrated one-to-one correspondence between ferroelectric polarization and spin helicity, S(i) × S(j). The incommensurate orbital ordering with 2 Q wave vector, observed by the soft x-ray resonant diffraction experiment, proved that the spin-orbit interaction ties spin and orbital orders to each other, playing a crucial role for the emergence of ferroelectricity in CuFe(1-x)Ga(x)O2.

Structure and spin dynamics of multiferroic BiFeO3

Multiferroic materials have attracted much interest due to the unusual coexistence of ferroelectric and (anti-)ferromagnetic ground states in a single compound. They offer an exciting platform for new physics and potentially novel devices. BiFeO3 is one of the most celebrated multiferroic materials and has highly desirable properties. It is the only known room-temperature multiferroic with TC ≈ 1100 K and TN ≈ 650 K, and exhibits one of the largest spontaneous electric polarisations, P ≈ 80 µC cm(-2). At the same time, it has a magnetic cycloid structure with an extremely long period of 620 Å, which arises from competition between the usual symmetric exchange interaction and the antisymmetric Dzyaloshinskii-Moriya (DM) interaction. There is also an intriguing interplay between the DM interaction and single ion anisotropy K. In this review, we have attempted to paint a complete picture of bulk BiFeO3 by summarising the structural and dynamic properties of both the spin and lattice parts and their magneto-electric coupling.

Phase transition and phase separation in multiferroic orthorhombic Dy(1-x)Ho(x)MnO3 (0 ≤ x ≤ 1)

We report on structural, magnetic, ferroelectric, and thermodynamic properties of polycrystalline orthorhombic manganites Dy_1−xHo_xMnO₃ for Ho substitution levels 0 ≤ x ≤ 1. This system offers a possibility to systemically modulate the multiferroicity of RMnO₃ via tuning the A-site ionic radii as well as the A-site magnetism. The successive transition of the multiferroic ground state is traced from the bc-cycloidal (DyMnO₃) to the E-type antiferromagnetic phase (HoMnO₃). In the middle substitution range 0.4 < x < 0.5, the phase separation is prominent, which's residual may survive in an even wider range. Accompanied with the phase transition and phase separation, obvious enhancement of both the polarization and magnetoelectric response is observed. Our experimental study also confirmed that the rare earth (Dy/Ho)-Mn exchange striction is a crucial role in deciding the multiferroicity of manganites.

Electric field control of ferroelectric domain structures in MnWO4

Competing interactions make the magnetic structure of MnWO4 highly frustrated, and only the AF2 phase of the three magnetically ordered phases (AF1, AF2, AF3) is ferroelectric. The high frustration may thus allow a possibility to tune the magnetic structure by means of an electric field via magnetoelectric coupling. By using the pyroelectric current method, we measure the remnant ferroelectric polarization in MnWO4 upon application of a poling electric field via two different roadmaps. It is demonstrated that an electric field as low as 10 kV cm(-1) is sufficient to enhance the stability of a ferroelectric AF2 phase at the expense of a non-ferroelectric AF1 phase. This work suggests that electric field induced electrostatic energy, although small due to weak magnetically induced electric polarization, may effectively tune ferroelectric domain structures, and thus the magnetic structure of highly frustrated multiferroic materials.

Multiferroics of spin origin

Multiferroics, compounds with both magnetic and ferroelectric orders, are believed to be a key material system to achieve cross-control between magnetism and electricity in a solid with minute energy dissipation. Such a colossal magnetoelectric (ME) effect has been an issue of keen interest for a long time in condensed matter physics as well as a most desired function in the emerging spin-related electronics. Here we begin with the basic mechanisms to realize multiferroicity or spin-driven ferroelectricity in magnetic materials, which have recently been clarified and proved both theoretically and experimentally. According to the proposed mechanisms, many families of multiferroics have been explored, found (re-discovered), and newly developed, realizing a variety of colossal ME controls. We overview versatile multiferroics from the viewpoints of their multiferroicity mechanisms and their fundamental ME characteristics on the basis of the recent advances in exploratory materials. One of the new directions in multiferroic science is the dynamical ME effect, namely the dynamical and/or fast cross-control between electric and magnetic dipoles in a solid. We argue here that the dynamics of multiferroic domain walls significantly contributes to the amplification of ME response, which has been revealed through the dielectric spectroscopy. Another related issue is the electric-dipole-active magnetic resonance, called electromagnons. The electromagnons can provide a new stage of ME optics via resonant coupling with the external electromagnetic wave (light). Finally, we give concluding remarks on multiferroics physics in the light of a broader perspective from the emergent electromagnetism in a solid as well as from the possible application toward future dissipationless electronics.

Polarization enhancement and ferroelectric switching enabled by interacting magnetic structures in DyMnO₃ thin films

The mutual controls of ferroelectricity and magnetism are stepping towards practical applications proposed for quite a few promising devices in which multiferroic thin films are involved. Although ferroelectricity stemming from specific spiral spin ordering has been reported in highly distorted bulk perovskite manganites, the existence of magnetically induced ferroelectricity in the corresponding thin films remains an unresolved issue, which unfortunately halts this step. In this work, we report magnetically induced electric polarization and its remarkable response to magnetic field (an enhancement of ~800% upon a field of 2 Tesla at 2 K) in DyMnO₃ thin films grown on Nb-SrTiO₃ substrates. Accompanying with the large polarization enhancement, the ferroelectric coercivity corresponding to the magnetic chirality switching field is significantly increased. A picture based on coupled multicomponent magnetic structures is proposed to understand these features. Moreover, different magnetic anisotropy related to strain-suppressed GdFeO₃-type distortion and Jahn-Teller effect is identified in the films.

Charge carriers and small-polaron migration as the origin of intrinsic dielectric anomalies in multiferroic TbMnO3 polycrystals

Temperature-dependent and frequency-dependent dielectric investigations have been performed in TbMnO3 polycrystals sintered in either oxidative or reductive atmospheres. The results revealed the occurrence of two dielectric anomalies above 100 K, which are caused by the thermal activation of charge carriers and their motion in grain cores and grain boundaries. The temperature dependence of the bulk dc conductivity was also analysed and indicates that charge carriers move between inequivalent sites according to a variable-range-hopping mechanism. Also, a strong correlation between dielectric properties and crystalline structure was observed. Furthermore, a low-temperature dielectric relaxation, commonly reported in rare-earth manganite crystals, was observed in both samples. This relaxation follows the empirical Cole-Cole model and was attributed to small-polaron tunnelling. Polaron motion was observed to be affected by the magnetic transitions, structural properties and intrinsic anisotropies in TbMnO3. It is also worth mentioning that the dielectric anomaly due to motion of charge carriers in grain boundaries is the only one of extrinsic origin, while the anomalies related to carrier motion in grain cores and small-polaron tunnelling are intrinsic to TbMnO3.

Bond distortion effects and electric orders in spiral multiferroic magnets

In this paper we study the bond distortion effect on the electric polarization in spiral multiferroic magnets based on cluster and chain models. The bond distortion breaks the inversion symmetry and modifies the d-p hybridization. Consequently, it will affect the electric polarization, which can be divided into the spin-current part and the lattice-mediated part. The spin-current polarization can be written in terms of [Formula: see text] with anisotropic amplitude, and the lattice-mediated polarization exists only when the M-O-M bond is distorted. The electric polarization for three-atom M-O-M and four-atom M-O2-M clusters is calculated. We also study possible electric ordering in three kinds of chains made of different clusters. We apply our theory to multiferroic cuprates and find that the results are qualitatively in agreement with experimental observations.

Competing exchanges and spin-phonon coupling in Eu(1-x)R(x)MnO3 (R=Y, Lu)

This work is focused on the phase diagrams and physical properties of Y-doped and Lu-doped EuMnO3. The differences in the corresponding phase boundaries in the (x,T) phase diagram could be overcome by considering a scaling of the Y(3+) and Lu(3+) concentrations to the tolerance factor. This outcome evidences that the tolerance factor is in fact a more reliable representative of the lattice deformation induced by doping. The normalization of the phase boundaries using the tolerance factor corroborates previous theoretical outcomes regarding the key role of competitive FM and AFM exchanges in determining the phase diagrams of manganite perovskites. However, significant differences in the nature and number of phases at low temperatures and concentrations could not be explained by just considering the normalization to the tolerance factor. The vertical phase boundary observed just for Lu-doped EuMnO3, close to 10% Lu, is understood by considering a low temperature Peierls-type spin-phonon coupling, which stabilizes the AFM-4 phase in Lu-doped EuMnO3.

Anomalous exchange bias at collinear/noncollinear spin interface

We report on the interfacial magnetic coupling in manganite bilayers of collinear ferromagnetic La_0.7Sr_0.3MnO₃ and noncollinear multiferroic TbMnO₃. Exchange bias is observed at the Néel temperature of TbMnO₃ (~41 K) due to the onset of long-range antiferromagnetic ordering in the Mn spin sublattice. Interestingly, an anomalous plateau of exchange bias emerges at the ordering temperature of Tb spins (~10 K), and we ascribe this unique feature to the strong coupling between Tb and Mn spin sublattices in TbMnO₃, which in turn influences the magnetic coupling across the interface. On the other hand, the enhancement of coercivity in La_0.7Sr_0.3MnO₃/TbMnO₃ shows monotonous temperature dependence. Our results illustrate a strong interfacial magnetic interaction at the La_0.7Sr_0.3MnO₃/TbMnO₃ interface, highlighting the roles of competing spin orders, magnetic frustration, and coupling between multiple spin sublattices in artificial collinear/noncollinear spin heterostructures.

Imprinting magnetic information in manganites with x rays

The effect of x rays on an orbital and charge ordered epitaxial film of a Pr0.5Ca0.5MnO3 is presented. As the film is exposed to x rays, the antiferromagnetic response increases and concomitantly the conductivity of the film improve. These results are discussed in terms of a persistent x-ray induced doping, leading to a modification of the magnetic structure. This effect allows writing electronic and magnetic information in the film and represents a novel way of manipulating magnetism.

Helical screw type magnetic structure of the multiferroic CaMn7O12 with low Cu-doping

The modulated crystal structure and modulated magnetic ordering of the multiferroic CaCu(x)Mn(7-x)O(12) is studied by analysing neutron and synchrotron-radiation (SR) powder diffraction data with a model based on the magnetic superspace group R31'(00γ)ts. Both atomic position modulations and magnetic modulations are described with the modulation vector (0, 0, q). The magnetic ordering is a screw-type circular helix where the magnetic moments are perpendicular to the c direction. The temperature dependence of the modulation vector length and the ordered magnetic moments of Mn(3+) and Mn(4+) ions is given between T = 50 K and the Néel temperature T(N) is approximately equal to 90 K. The atomic position modulation length L(p) and the magnetic modulation length L(m) fulfil the relation L(m) = 2L(p) at all temperatures between 50 K and T(N).

Dynamical magnetoelectric effects in multiferroic oxides

Multiferroics with coexistent ferroelectric and magnetic orders can provide an interesting laboratory to test unprecedented magnetoelectric (ME) responses and their possible applications. One such example is the dynamical and/or resonant coupling between magnetic and electric dipoles in a solid. As examples of such dynamical ME effects, (i) the multiferroic domain wall dynamics and (ii) the electric dipole active magnetic responses are discussed with an overview of recent experimental observations.

Femtoscale Magnetically Induced Lattice Distortions in Multiferroic TbMnO3

Magneto-electric multiferroics exemplified by TbMnO3 possess both magnetic and ferroelectric long-range order. The magnetic order is mostly understood, whereas the nature of the ferroelectricity has remained more elusive. Competing models proposed to explain the ferroelectricity are associated respectively with charge transfer and ionic displacements. Exploiting the magneto-electric coupling, we used an electric field to produce a single magnetic domain state, and a magnetic field to induce ionic displacements. Under these conditions, interference between charge and magnetic x-ray scattering arose, encoding the amplitude and phase of the displacements. When combined with a theoretical analysis, our data allow us to resolve the ionic displacements at the femtoscale, and show that such displacements make a substantial contribution to the zero-field ferroelectric moment.

Supramolecular cations of the m-fluoroanilinium(dibenzo[18]crown-6) in ferromagnetic salt

A supramolecular cation of (m-FAni(+))(DB[18]crown-6), where m-FAni(+) and DB[18]crown-6 denote m-fluoroanilinium(+) and dibenzo[18]crown-6, respectively, which is the polar unit rotating in the ferroelectric crystal of (m-FAni(+))(DB[18]crown-6)[Ni(dmit)(2)](-), was introduced into a ferromagnetic [MnCr(oxalate)(3)](-) salt as the counter cation. The crystal structure of (m-FAni(+))(DB[18]crown-6)[MnCr(oxalate)(3)](-)(CH(3)OH)(CH(3)CN) (1) is constructed from alternating layers of a two-dimensional honeycomb layer of [MnCr(oxalate)(3)](-) and (m-FAni(+))(DB[18]crown-6) supramolecular cations. The anionic layer is composed of Mn(II) and Cr(III) ions with S = 5/2 and S = 3/2 spins, respectively, bridged by the oxalate anions, which show ferromagnetic ordering at 5.5 K. The supramolecular structure is formed through the formation of hydrogen bonds between the ammonium hydrogen atoms of the m-FAni(+) cations and the oxygen atoms of the DB[18]crown-6 cavity. No orientational disorder of the fluorine atoms was observed in our X-ray structural analysis, suggesting that a two-fold flip-flop motion of the m-FAni(+) cations does not occur in the salt. The rotational freedom of the m-FAni(+) cations in the salt is restricted by the steric hindrance from neighbouring DB[18]crown-6 molecules. A design strategy for the rotation in a salt is discussed, based on the volume that the supramolecular cations occupy in the unit cell.

Coupled magnetic cycloids in multiferroic TbMnO3 and Eu3/4Y1/4MnO3

Based on the detailed Mn L(2,3)-edge x-ray resonant scattering results, we report a new complexity in the magnetic order of multiferroic orthomangnites, which has been considered as the simple A-type cycloid order inducing ferroelectricity. The Dzyaloshinskii-Moriya interaction involved in the orthorhombic distortion brings on F-type canting from the A type, and the ordering type becomes the off-phase synchronized bc cycloid in TbMnO(3) or the tilted antiphase ab cycloid in Eu(3/4)Y(1/4)MnO(3). The F-type canting is responsible for the magnetic field-driven multiferroicity to weak ferromagnetism transition.

Multiferroic M-type hexaferrites with a room-temperature conical state and magnetically controllable spin helicity

Magnetic and magnetoelectric (ME) properties have been studied for single crystals of Sc-doped M-type barium hexaferrites. Magnetization (M) and neutron diffraction measurements revealed that by tuning Sc concentration a longitudinal conical state is stabilized up to above room temperatures. ME measurements have shown that a transverse magnetic field (H) can induce electric polarization (P) at lower temperatures and that the spin helicity is nonvolatile and endurable up to near the conical magnetic transition temperature. It was also revealed that the response (reversal or retention) of the P vector upon the reversal of M varies with temperature. In turn, this feature allows us to control the relation between the spin helicity and the M vectors with H and temperature.

Theoretically predicted picosecond optical switching of spin chirality in multiferroics

We show theoretically with an accurate spin Hamiltonian describing the multiferroic Mn perovskites that the application of the picosecond optical pulse with a terahertz frequency can switch the spin chirality through intensely exciting the electromagnons. There are four states with different spin chiralities, i.e., clockwise and counterclockwise ab/bc-plane spin spirals, and by tuning the strength, shape and length of the pulse, the switching among these states can be controlled at will. Dynamical pattern formation during the switching is also discussed.

A phenomenological Landau theory for electromagnons in cubic spinel multiferroic CoCr₂O₄

Non-anisotropic free energy is considered which under minimization yields two magnetic phases: a conical spin density wave and a low temperature conical cycloid. Using equations of motion, the excitation spectrum is studied. Knowing the nature of these excitations, the dielectric function as well as the fluctuation specific heat is computed and compared with the experimental spectrum. Due to the electromagnon going soft, the dielectric function (imaginary part) as well as the specific heat capacity show peaks at the temperature where ferroelectricity appears in the system.

Multiferroics with spiral spin orders

Cross correlation between magnetism and electricity in a solid can host magnetoelectric effects, such as magnetic (electric) induction of polarization (magnetization). A key to attain the gigantic magnetoelectric response is to find the efficient magnetism-electricity coupling mechanisms. Among those, recently the emergence of spontaneous (ferroelectric) polarization in the insulating helimagnet or spiral-spin structure was unraveled, as mediated by the spin-exchange and spin-orbit interactions. The sign of the polarization depends on the helicity (spin rotation sense), while the polarization direction itself depends on further details of the mechanism and the underlying lattice symmetry. Here, we describe some prototypical examples of the spiral-spin multiferroics, which enable some unconventional magnetoelectric control such as the magnetic-field-induced change of the polarization direction and magnitude as well as the electric-field-induced change of the spin helicity and magnetic domain.

Magnetic digital flop of ferroelectric domain with fixed spin chirality in a triangular lattice helimagnet

The ferroelectric properties in a magnetic field (H) of varying magnitude and direction have been investigated for the triangular-lattice helimagnet CuFe(1-x)Ga(x)O(2) (x = 0.035). The in-plane H was found to induce the rearrangement of six possible multiferroic domains. Upon every 60 degrees rotation of in-plane H around the c axis, a unique 120 degrees flop of electric polarization occurs as a result of the switch of the helical magnetic q vector. The chirality of the spin helix is always conserved upon the q flop. The possible origin is discussed in light of the stable structure of the multiferroic domain wall.

Coupled magnetic and ferroelectric domains in multiferroic Ni3V2O8

Electric control of multiferroic domains is demonstrated through polarized magnetic neutron diffraction. Cooling to the cycloidal multiferroic phase of Ni3V2O8 in an electric field E causes the incommensurate Bragg reflections to become neutron spin polarizing, the sense of neutron polarization reversing with E. Quantitative analysis indicates the E-treated sample has a handedness that can be reversed by E. We further show a close association between cycloidal and ferroelectric domains through E-driven spin and electric polarization hysteresis. We suggest that a definite cycloidal handedness is achieved through magnetoelastically induced Dzyaloshinskii-Moriya interactions.

Magnetic-field-induced polarization flop in multiferroic TmMn2O5

We discovered a reversible electric polarization flop from the a axis (P(a)) to the b axis (P(b)) in multiferroic TmMn2O5 below 5 K by applying a magnetic field of approximately 0.5 T along the c axis. This phenomenon is the first example of the rare-earth (R) compound RMn2O5. This magnetic-field-induced polarization flop corresponds to a magnetic phase transition from one incommensurate magnetic (ICM) P(a) phase to another ICM P(b) phase, which is equivalent to an ICM P(b) phase above 5 K under no magnetic field. The spin chirality in the bc plane, which was observed in the P(b) phase by polarized neutron diffraction, disappeared in the ICM P(a) phase. This indicates that the polarization in the ICM phases of TmMn2O5 was induced by an S(i) x S(j)-type interaction.