We introduce a microscopic model for collinear multiferroics capable to reproduce, as a consequence of magnetic frustration and easy-axis anisotropy, the so-called "uudd" (or antiphase) magnetic ordering observed in several type II multiferroic materials. The crucial role of lattice distortions in the multiferroic character of these materials is entered into the model via an indirect magnetoelectric coupling, mediated by elastic degrees of freedom through a pantograph mechanism. Long range dipolar interactions set electric dipoles in the antiferroelectric order. We investigate this model by means of extensive DMRG computations and complementary analytical methods. We show that a lattice dimerization induces a spontaneous Z2 ferrielectric bulk polarization, with a sharp switch off produced by a magnetic field above a critical value. The topological character of the magnetic excitations makes this mechanism robust.
By studying the dielectric properties of the geometrically frustrated spinel CdV2O4, we observe ferroelectricity developing at the transition into the collinear antiferromagnetic ground state. In this multiferroic spinel, ferroelectricity is driven by local magnetostriction and not by the more common scenario of spiral magnetism. The experimental findings are corroborated by ab-initio calculations of the electric polarization and the underlying spin and orbital order. The results point towards a charge rearrangement due to dimerization, where electronic correlations and the proximity to the in…
In multiferroic BiFeO$_3$ a cycloidal antiferromagnetic structure is coupled to a large electric polarization at room temperature, giving rise to magnetoelectric functionality that may be exploited in novel multiferroic-based devices. In this paper, we demonstrate that by substituting samarium for 10% of the bismuth ions the periodicity of the room temperature cycloid is increased, and by cooling below $\sim15$ K the magnetic structure tends towards a simple G-type antiferromagnet, which is fully established at 1.5 K. We show that this transition results from $f-d$ exchange coupling, which ind…
Non-resonant X-ray magnetic scattering has been used to study the magnetic structure of multiferroic TbMnO3 in its ferroelectric phase. Circularly polarized X-rays were combined with a full polarization analysis of the scattered beam to reveal important new information on the magnetic structure of this canonical multiferroic. An applied electric field is shown to create a magnetic nearly mono-domain state in which the cylcoidal order on the Mn sublattice rotates either clockwise or counter-clockwise depending on the sign of the field. It is demonstrated how this technique provides sensitivity …
We discuss a model scenario for multiferroic systems of type II (collinear spins) where the electric dipolar order competes with a frustrated magnetic order in determining the elastic distortions of the lattice ion positions. High magnetic frustration due to second neighbors exchange and small spin easy-axis anisotropy lead to the appearance of the so called quantum magnetic plateau states. Increasing the magnetic field above the plateau border produces composite excitations, where fractionalized spin tertions arise together with spontaneous dipolar flips (in the form of domain walls) and enha…
Local multiferroic ordering at room temperature in collinear magnetoelectric antiferromagnets induced by flexo-Zeeman coupling
Helmholtz-Zentrum Dresden-Rossendorf e.V.（德累斯顿-罗森多夫亥姆霍兹中心）；Faculty of Physics of Dresden University of Technology（德累斯顿工业大学物理学院）；Helmholtz-Zentrum Berlin für Materialien und Energie（柏林亥姆霍兹材料与能源中心）；Department of Applied Physics, KTH Royal Institute of Technology（瑞典皇家理工学院应用物理系）
Despite remarkable progress in developing multifunctional materials, spin-driven ferroelectrics featuring both spontaneous magnetization and electric polarization are still rare. Among such ferromagnetic ferroelectrics are conical spin spiral magnets with a simultaneous reversal of magnetization and electric polarization that is still little understood. Such materials can feature various multiferroic domains that complicates their study. Here we study the multiferroic domains in ferromagnetic ferroelectric Mn$_{2}$GeO$_{4}$ using neutron diffraction, and show that it features a double-Q conica…
Magnetic structure of the multiferroic Ca$_{2}$CoSi$_{2}$O$_{7}$ was determined by neutron diffraction techniques. Combination of the polycrystalline and single-crystal samples experiments revealed a collinear antiferromagnetic structure with the easy axis along $<$100$>$ directions. The dielectric state was discussed in the framework of the spin-dependent $d$-$p$ hybridization mechanism, leading to the realization of the antiferroelectric structure. The origin of the magnetic anisotropy was discussed in comparison with the isostructural Ba$_{2}$CoGe$_{2}$O$_{7}$.
We present a theoretical examination of the magneto-electric response in the recently discovered multiferroic insulator Cu$_2$OSeO$_3$. Combining Monte Carlo simulation and Ginzburg-Landau analysis we predict the response in each of the magnetic phases, including helical, conical, ferromagnetic and Skyrmion crystal phases, both for thin film and bulk systems. A common feature for all non-collinear phases is that the magneto-electric susceptibility increases linearly with the applied magnetic field. Being both calculable and measurable, the magneto-electric susceptibility can serve as a new pow…
We have directly imaged reversible electrical switching of the cycloidal rotation direction (magnetic polarity) in a (111)-BiFeO3 epitaxial-film device at room temperature by non-resonant x-ray magnetic scattering. Consistent with previous reports, fully relaxed (111)-BiFeO3 epitaxial films consisting of a single ferroelectric domain were found to comprise a sub-micron-scale mosaic of magneto-elastic domains, all sharing a common direction of the magnetic polarity, which was found to switch reversibly upon reversal of the ferroelectric polarization without any measurable change of the magneto-…
Quantum Dynamics of Multiferroic Helimagnets: a Schwinger-Boson Approach
我们研究的量子动力学/波动的摆线螺旋磁铁的Schwinger玻色子方法。与经典涨落形成鲜明对比的是，量子涨落本质上是共线的，这使得随着温度的降低，共线自旋密度波态略高于螺旋摆线态。从这个角度讨论了螺旋线的约化椭圆比、中子散射和红外吸收光谱等物理性质，并讨论了它们与准一维LiCu $_2$ O $_2$和LiCuVO $_4$的可能关系.
In contrast to well studied multiferroic manganites with a spiral structure, the electric polarization in multiferroic borates is induced within collinear antiferromagnetic structure and can easily be switched by small static fields. Because of specific symmetry conditions, static and dynamic properties in borates are directly connected, which leads to giant magnetoelectric and magnetodielectric effects. Here we prove experimentally that the giant magnetodielectric effect in samarium ferroborate SmFe3(BO3)4 is of intrinsic origin and is caused by an unusually large electromagnon situated in th…
The electric field effect on magnetism was examined in the multiferroic conical magnet Mn$_2$GeO$_4$, which shows a strong coupling between ferromagnetic and ferroelectric order parameters. The systematic evaluation of the electric polarization in the multiferroic phase below 5.5 K under various field cooling conditions reveals that small magnetic fields of 0.1 T significantly reduce the required electric fields needed to reach saturation. By applying electric fields during magnetic field dependent hysteresis measurements of magnetization M and polarization P an electrically controllable excha…
Soft x-ray absorption experiments on the transition metal L2,3 edge of multiferroic MnWO4 and antiferromagnetic CoWO4 are presented. The observed linear polarization dependence, analyzed by full-multiplet calculations, is used to determine the ground state wave function of the magnetic Mn2+ and Co2+ ions. The impact of the local structure and the spin-orbit coupling on the orbital moment is discussed in terms of the single-ion anisotropy. It is shown that the orbital moment in CoWO4 is responsible for the collinear antiferromagnetism, while the small size of spin-orbit coupling effects make sp…
The time dependence of switching multiferroic domains in MnWO$_4$ has been studied by time-resolved polarized neutron diffraction. Inverting an external electric field inverts the chiral magnetic component within rise times ranging between a few and some tens of milliseconds in perfect agreement with macroscopic techniques. There is no evidence for any faster process in the inversion of the chiral magnetic structure. The time dependence is well described by a temperature-dependent rise time suggesting a well-defined process of domain reversion. As expected, the rise times decrease when heating…
Experimental techniques using Bragg diffraction may elucidate electronic and magnetic properties of ferric ions in multiferroic ScFeO3 that are puzzling. A collinear magnetic motif of dipole moments is not expected for s-state ions with an acentric parent (paramagnetic) structure, because single-site anisotropy is negligible and antisymmetric exchange interactions promote an inhomogeneous magnetic motif. However, current indications are that ScFeO3 supports G-type antiferromagnetism, with an unknown moment direction, which implies that ferric ions are not in the high-spin 6S state. It is argue…
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 (ND4)2[FeCl5(D2O)]. 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 fi…
The chiral components in the magnetic order in multiferroic MnWO4 have been studied by neutron diffraction using spherical polarization analysis as a function of temperature and of external electric field. We show that sufficiently close to the ferroelectric transition it is possible to switch the chiral component by applying moderate electric fields at constant temperature. Full hysteresis cycles can be observed which indicate strong pinning of the magnetic order. MnWO4, furthermore, exhibits a magnetoelectric memory effect across heating into the paramagnetic and paraelectric phase.
Non-reciprocal directional dichroism, also called the optical-diode effect, is an appealing functional property inherent to the large class of non-centrosymmetric magnets. However, the in-situ electric control of this phenomenon is challenging as it requires a set of conditions to be fulfilled: Special symmetries of the magnetic ground state, spin-excitations with comparable magnetic- and electric-dipole activity and switchable electric polarization. We demonstrate the isothermal electric switch between domains of Ba$_2$CoGe$_2$O$_7$ possessing opposite magnetoelectric susceptibilities. Combin…
All-electrical control of a dynamic magnetoelectric effect is demonstrated in a classical multiferroic manganite DyMnO3, a material containing coupled antiferromagnetic and ferroelectric orders. Due to intrinsic magnetoelectric coupling with electromagnons a linearly polarized terahertz light rotates upon passing through the sample. The amplitude and the direction of the polarization rotation are defined by the orientation of ferroelectric domains and can be switched by static voltage. These experiments allow the terahertz polarization to be tuned using the dynamic magnetoelectric effect.
We present a neutron diffraction study of FeV2O4, which is rare in exhibiting spin and orbital degrees of freedom on both cation sublattices of the spinel structure. Our data confirm the existence of three structural phase transitions previously identified with x-ray powder diffraction, and reveal that the lower two transitions are associated with sequential collinear and canted ferrimagnetic transitions involving both cation sites. Through consideration of local crystal and spin symmetry, we further conclude that Fe2+ cations are ferro-orbitally ordered below 135K and V3+ orbitals order at 60…
Motivated by the recent observations of incommensurate magnetic order and electric polarization in YBaCuFeO5 up to temperatures TN2 as high as 230K [1,2] we report here for the first time a model for the incommensurate magnetic structure of this material that we complement with ab-initio calculations of the magnetic exchange parameters. Using neutron powder diffraction we show that the appearance of polarization below TN2 is accompanied by the replacement of the high temperature collinear magnetic order by a circular inclined spiral with propagation vector ki=(1/2, 1/2, 1/2+-q). Moreover, we f…
We have investigated electrically-active magnetic excitations (electromagnons) in perovskite manganites with the $E$-type (up-up-down-down) spin structure by terahertz spectroscopy. Eu$_{1-x}$Y$_x$MnO$_3$ (0.1$\le x\le$1) and Y$_{1-y}$Lu$_y$MnO$_3$ (0$\le y\le$1) without magnetic $f$-moments, which host collinear sinusoidal, $A$-type, cycloidal, and $E$-type spin orders, are used to examine the systematics of possible electromagnons. Three-peak structures (23, 35, 45 cm$^{-1}$) of magnetic origin show up in the $E$-type phase with little composition ($y$) dependence of frequencies, making a co…
The complete magnetic and multiferroic phase diagram of Mn$_{1-x}$Co$_{x}$WO$_4$ single crystals is investigated by means of magnetic, heat capacity, and polarization experiments. We show that the ferroelectric polarization $\overrightarrow{P}$ in the multiferroic state abruptly changes its direction twice upon increasing Co content, x. At x$_{c1}$=0.075, $\overrightarrow{P}$ rotates from the $b-$axis into the $a-c$ plane and at x$_{c2}$=0.15 it flips back to the $b-$axis. The origin of the multiple polarization flops is identified as an effect of the Co anisotropy on the orientation and shape…
We report a comprehensive inelastic neutron scattering study of the hybrid molecule-based multiferroic compound (ND4)2FeCl5D2O in the zero-field incommensurate cycloidal phase and the high-field quasi-collinear phase. The spontaneous electric polarization changes its direction concurrently with the field-induced magnetic transition, from mostly aligned with the crystallographic a-axis to the c-axis. To account for such change of polarization direction, the underlying multiferroic mechanism was proposed to switch from the spin-current model induced via the inverse Dzyalloshinskii-Moriya interac…
Multiferroicity induced by dislocated spin-density waves
我们发现了一个新的途径走向多铁性，显示如何磁性可以驱动铁电性，而不依赖于反转对称性破缺的磁序。我们的自由能分析表明，任何相称的自旋密度波有序的相位位错，即使它是共线的，引起电极化的强度。由于位错的存在，电子中心、磁性中心和反转中心不重合，这是多铁性耦合的充分条件。新的机制解释了形成的多铁性相的磁性可磁化性转变，如观察到的YMn $_{2}$ O $_{5}$和相关化合物。我们预测，在这些多铁性材料中，振荡的电极化是伴随着均匀极化。在此基础上，我们提出了具有铁电性的新型磁性材料。
We study the nonlinear magnon spin current induced by an ac electric field under light irradiation in collinear antiferromagnets with broken inversion symmetry. For linearly polarized light, we find that a dc spin current appears through ``the magnon spin shift current" mechanism, which is driven by a spin polarization generation in the two magnon creation process and has a close relationship to the geometry of magnon bands through Berry connection. For circularly polarized light, a dc spin current appears through ``the spin injection current" mechanism, which is proportional to the relaxation…
Complete magnetoelectric (ME) phase diagrams of orthorhombic $R$MnO$_{3}$ with and without magnetic moments on the $R$ ions have been established. Three kinds of multiferroic ground states, the $ab$-cycloidal, the $bc$-cycloidal, and the collinear $E$-type phases, have been identified by the distinct ME responses. The electric polarization of the $E$-type phase dominated by the symmetric spin exchange ($bm{S}_{i} cdot bm{S}_{j}$) is more than 10 times as large as that of the $bc$-cycloidal phase dominated by the antisymmetric one ($bm{S}_{i} times bm{S}_{j}$), and the ME response is enhanced n…
We performed magnetic and ferroelectric measurements, associated with Landau theory and symmetry analysis, in order to clarify the situation of the YMnO3 system, a classical example of type I multiferroics. We found that the only magnetic group compatible with all experimental data (neutrons scattering, magnetization,polarization, dielectric constant, second harmonic generation) is the P6'3 group. In this group a small ferromagnetic component along c is induced by the Dzyaloshinskii-Moriya interaction, and observed here in SQUID magnetization measurements. We found that the ferromagnetic and a…
We present a 57Fe Mössbauer spectroscopy study of the two incommensurate magnetic phases in the multiferroic material FeVO4. We devise lineshapes appropriate for planar elliptical and collinear modulated magnetic structures and show that they reproduce very well the Mössbauer spectra in FeVO4, in full qualitative agreement with a previous neutron diffraction study. Quantitatively, our spectra provide precise determinations of the characteristics of the elliptical and modulated structures which are in good agreement with the neutron diffraction results. We find that the hyperfine field elliptic…
We present a theoretical study of the onset of electric polarization close to a surface in magnetic materials and in thin films and multilayers. We consider two different paths that lead to the onset of multiferroic behavior at the boundary in materials that are bulk collinear ferromagnets or antiferromagnets. These two paths are distinguished by the presence or absence of a surface induced Dzyaloshinskii-Moriya interaction which can be taken into account through Lifshitz invariants in the free energy of the system. Experimental consequences are discussed in the light of the developed theory.
We propose a microscopic theory for magnetic switching of electric polarization (P) in the spin-spiral multiferroics by taking TbMnO3 and DyMnO3 as examples. We reproduce their phase diagrams under a magnetic field H_ex by Monte-Carlo simulation of an accurate spin model and reveal that competition among the Dzyaloshinskii-Moriya interaction, spin anisotropy, and spin exchange is controlled by the applied H_ex, resulting in magnetic transitions accompanied by reorientation or vanishing of P. We also discuss the relevance of the proposed mechanisms to many other multiferroics such as LiCu2O2, M…
Electromagnons in multiferroic RMn2O5 compounds and their microscopic origin
本文总结了多铁性RMn_2 O_5化合物中电磁振子的现有实验数据，其中R表示稀土离子Y或Bi，并讨论了一个现实的微观模型，这些材料的假设基础上，磁-感生铁电性和电磁振子吸收完全依赖于各向同性海森堡交换和自旋与极性晶格模式的磁致伸缩耦合，相对论效应该模型解释了许多磁性和光学性质的RMn 2 O 5锰氧化物，如自旋重取向过渡，磁致极化，外观的电磁振子峰在非共线自旋状态和光的偏振，该峰被观察到。我们比较了RMn 2 O 5和RMnO 3化合物的电磁振子的实验和理论结果。
We show that strong electromagnon peaks can be found in absorption spectra of non-collinear magnets exhibiting a linear magnetoelectric effect. The frequencies of these peaks coincide with the frequencies of antiferromagnetic resonances and the ratio of the spectral weights of the electromagnon and antiferromagnetic resonance is related to the ratio of the static magnetoelectric constant and magnetic susceptibility. Using a Kagome lattice antiferromagnet as an example, we show that frustration of spin ordering gives rise to magnetoelastic instabilities at strong spin-lattice coupling, which tr…
We report the remarkably robust ferroelectric state in the multiferroic compound Mn$_{1-x}$Zn$_x$WO$_4$. The substitution of the magnetic Mn$^{2+}$ with nonmagnetic Zn$^{2+}$ reduces the magnetic exchange and provides control of the various magnetic and multiferroic states of MnWO$_4$. Only 5 % of Zn substitution results in a complete suppression of the frustrated collinear (paraelectric) low temperature phase. The helical magnetic and ferroelectric phase develops as the ground state. The multiferroic state is stable up to a high level of substitution of more than 50 %. The magnetic, thermodyn…
We propose that concurrently magnetic and ferroelectric, i.e. multiferroic, compounds endowed with electrically-active magnetic excitations (electromagnons) provide a key to produce large directional dichroism for long wavelengths of light. By exploiting the control of ferroelectric polarization and magnetization in a multiferroic oxide Ba$_2$CoGe$_2$O$_7$, we demonstrate the realization of such a directional light-switch function at terahertz frequecies in resonance with the electromagnon absorption. Our results imply that this hidden potential is present in a broad variety of multiferroics.
Anisotropic multiferroic properties of SrMnGe2O6 pyroxene single crystals were systematically investigated by means of magnetization, heat capacity, pyroelectric current measurement and elastic and inelastic neutron scattering experiments. Single crystal neutron diffraction allows us to unambiguously reveal the presence of two incommensurate magnetic orderings: a non-polar amplitude-modulated collinear sinusoidal magnetic structure emerges at TN1=4.36(2)K followed by a polar elliptical cycloidal spin structure below TN2=4.05(2)K. Pyroelectric current measurements on single crystal confirm the …
The magnetic, dielectric and structural properties of type-I multiferroic KNiPO$_4$ have been investigated by neutron powder diffraction, magnetization, dielectric and high temperature synchrotron-XRD measurements. Below the Néel transition of $T_\mathrm{N}$ = 25 K, KNiPO$_4$ displays a weakly non-collinear antiferromagnetic (AFM) structure with the orientation of the Ni$^{2+}$ magnetic moments mainly along $a$ axis. The compound crystallizes in the polar orthorhombic $Pna2_1$ space group at room temperature. A second-order structural phase transition corresponding to the onset ferroelectricit…
High resolution inelastic neutron scattering reveals that the elementary magnetic excitations in multiferroic MnWO4 consist of low energy dispersive electromagnons in addition to the well-known spin-wave excitations. The latter can well be modeled by a Heisenberg Hamiltonian with magnetic exchange coupling extending to the 12th nearest neighbor. They exhibit a spin-wave gap of 0.61(1) meV. Two electromagnon branches appear at lower energies of 0.07(1) meV and 0.45(1) meV at the zone center. They reflect the dynamic magnetoelectric coupling and persist in both, the collinear magnetic and parael…
We present a simple two-dimensional model in which the lattice degrees of freedom mediate the interactions between magnetic moments and electric dipoles. This model reproduces basic features, such as a sudden electric polarization switch-off when a magnetic field is applied and the ubiquitous dimerized distortion patterns and magnetic $\uparrow \uparrow \downarrow \downarrow$ ordering, observed in several multiferroic materials of different composition. The list includes E-type manganites, RMnO$_3$, nickelates such as in YNiO$_3$ and other materials under strain, such as TbMnO$_3$. In spite of…
To understand the collinear-magnetism-driven ferroelectricity in multiferroic Ca3CoMnO6 compound, we have established an elastic diatomic Ising spin-chain model with axial-next-nearest-neighbor interaction to describe its magnetoelectric properties. By employing magneto-phonon decoupling and transfer-matrix method, the possible ground-state configurations and thermodynamic behaviors of the system have been exactly determined. From the perspective of the ground-state configuration, we analyze the computational results and make a detail comparison with experimental data. The parameter relation f…
The spin-wave excitations of the multiferroic $\rm MnWO_4$ have been measured in its low-temperature collinear commensurate phase using high-resolution inelastic neutron scattering. These excitations can be well described by a Heisenberg model with competing long-range exchange interactions and a single-ion anisotropy term. The magnetic interactions are strongly frustrated within the zigzag spin chain along c axis and between chains along the a axis, while the coupling between spin along the b axis is much weaker. The balance of these interactions results in the noncollinear incommensurate spi…
The discovery of multiferroic behavior in monolayer NiI$_2$ provides a new symmetry-broken state in van der Waals monolayers, featuring the simultaneous emergence of helimagnetic order and ferroelectric order at a critical temperature of $T=21$ K. However, the microscopic origin of multiferroic order in NiI$_2$ monolayer has not been established, and in particular, the role of non-colinear magnetism and spin-orbit coupling in this compound remains an open problem. Here we reveal the origin of the two-dimensional multiferroicity in NiI$_2$ using first-principles electronic structure methods. We…
LiCu2O2 is the first multiferroic cuprate to be reported and its ferroelectricity is induced by complex magnetic ordering in ground state, which is still in controversy today. Herein, we have grown nearly untwinned LiCu2O2 single crystals of high quality and systematically investigated their dielectric and ferroelectric behaviours in external magnetic fields. The highly anisotropic response observed in different magnetic fields apparently contradicts the prevalent bc- or ab- plane cycloidal spin model. Our observations give strong evidence supporting a new helimagnetic picture in which the nor…
Our results describe an unprecedented example of change in the mechanism of magnetically-induced electric polarization from spin current to spin-dependent p-d hybridization model. We have followed the evolution of the magnetic structures of (ND4)2[FeCl5 D2O] compound using single crystal neutron diffraction under external magnetic field. The spin arrangements change from incommensurate cycloidal to commensurate distorted-cycloidal and finally to quasi-collinear. The determination of the magnetic structures allows us to explain the observed electric polarization in the different ferroelectric p…
