Starting from the irreducible representations of the group of the wave vector we construct the spin wave functions consistent with inversion symmetry, neglected in the usual representation analysis. We obtain the relation between the basis functions of different members of the star of the wave vector. We introduce order parameters and determine their transformation properties under the operations of the space group of the paramagnetic crystal. The results are applied to construct terms in the magnetoelectric interaction which are quadratic and quartic in the magnetic order parameters. The higher order magnetoelectric interactions can in principle induce components of the spontaneous polarization which are not allowed by the lowest order magnetoelectric interaction. We also obtain the relation between the spin wave functions of the incommensurate phase and those of the commensurate phase which lead to analogous relations between the order parameters of these two phases.
We have determined the magnetic structure of the low-temperature incommensurate phase of multiferroic YMn2O5 using single-crystal neutron diffraction. By employing corepresentation analysis, we have ensured full compliance with both symmetry and physical constraints, so that the electrical polarization must lie along the b axis, as observed. The evolution of the spin components and propagation through the commensurate-incommensurate phase boundary points unambiguously at the exchange-striction mechanism as the primary driving force for ferroelectricity.
The specific properties of incommensurate multiferroic phases resulting from the coupling of order-parameter replicates are worked out using the illustrative example of iron vanadate. The dephasing between the order-parameter copies induces an additional broken symmetry phase corresponding to the lowest symmetry of the system and varies critically at the transition to the multiferroic phase. It reflects the temperature dependence of the angle between paired spins in the antiferromagnetic spiral structure. Expressing the transition order-parameters in terms of spin-density waves allows showing …
We present the results of a theoretical analysis of two-dimensionally modulated incommensurate phases in crystals and define the space distribution of magnetization and polarization vector in the incommensurate phase and demonstrate that their averaging in the incommensurate phase period equals zero. We apply symmetry arguments and show that despite the fact that the phase transition in the system is described by reducible representation of the space group high symmetry phase the superspace symmetry group of the in-commensurate phase contains all symmetry point groups of the high symmetry phas…
The incommensurate magnetic structures and phase diagrams of multiferroics has been explored on the basis of accurate micromagnetic analysis taking into account the spin flexoelecric interaction (Lifshitz invariant). The objects of the study are BiFeO_3-like single crystals and epitaxial films grown on the <111> substrates. The main control parameters are the magnetic field, the magnetic anisotropy, and the epitaxial strain in the case of films. We predict novel quasi-cycloidal structures induced by external magnetic field or by epitaxial strain in the BiFeO_3-films. Phase diagrams representin…
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 …
Neutron diffraction and 7Li-NMR have been applied to determine the multiferroic system LiCu2O2, which has four chains (ribbon chains) of edge-sharing CuO4 square planes in a unit cell. We have confirmed that there are successive magnetic transitions at TN1=24.5 K and TN2=22.8 K. In the T region between TN1 and TN2, the quasi one-dimensional spins (S=1/2) of Cu2+ ions within a chain have a collinear and sinusoidally modulated structure with Cu-moments parallel to the c-axis and with the modulation vector along the b-axis. At T < TN2, an ellipsoidal helical spin structure with the incommensurate…
The low-temperature ferroelectric polarization of multiferroic $YMn_2O_5$ is completely reversed at a critical pressure of 10 kbar and the phase transition from the incommensurate to the commensurate magnetic phase is induced by pressures above 14 kbar. The high-pressure data correlate with thermal expansion measurements indicating a significant lattice strain at the low-temperature transition into the incommensurate phase. The results support the exchange striction model for the ferroelectricity in multiferroic $RMn_2O_5$ compounds and they show the importance of magnetic frustration as well …
This paper represents a detailed instruction manual for constructing the Landau expansion for magnetoelectric coupling in incommensurate ferroelectric magnets. The first step is to describe the magnetic ordering in terms of symmetry adapted coordinates which serve as complex valued magnetic order parameters whose transformation properties are displayed. In so doing we use the previously proposed technique to exploit inversion symmetry, since this symmetry had been universally overlooked. Having order parameters of known symmetry which describe the magnetic ordering, we are able to construct th…
We present a first-principles scheme for computing the magnetoelectric response of multiferroics. We apply our method to BiFeO3 (BFO) and related compounds in which Fe is substituted by other magnetic species. We show that under certain relevant conditions -- i.e., in absence of incommensurate spin modulation, as in BFO thin films and some BFO-based solid solutions -- these materials display a large linear magnetoelectric response. Our calculations reveal the atomistic origin of the coupling and allow us to identify the most promising strategies to enhance it.
Apart from being so far the only known binary multiferroic compound, CuO has a much higher transition temperature into the multiferroic state, 230 K, than any other known material in which the electric polarization is induced by spontaneous magnetic order, typically lower than 100 K. Although the magnetically induced ferroelectricity of CuO is firmly established, no magnetoelectric effect has been observed so far as direct crosstalk between bulk magnetization and electric polarization counterparts. Here we demonstrate that high magnetic fields of about 50 T are able to suppress the helical mod…
An effective model is developed to explain the phase diagram and the mechanism of magnetoelectric coupling in multiferroics, $RMn_2O_5$. We show that the nature of magnetoelectric coupling in $RMn_2O_5$ is a coupling between two Ising-type orders, namely, the ferroelectric order in the b axis, and the coupled magnetic order between two frustrated antiferromagnetic chains. The frustrated magnetic structure drives the system to a commensurate-incommensurate phase transition, which can be understood as a competition between a collinear or col-plane order stemming from the `order by disorder' mech…
Ferroelectricity in the incommensurate helical magnetic phase (below TN, 43K) of alpha CaCr2O4 has been confirmed by pyroelectric measurements. Magnetoelectric and magnetodielectric coupling exist below TN and are proportional to the square of magnetic field. From symmetry analysis, we suggest that the presence of an external electric field destabilizes the symmetrical 2221' phase and stabilizes 21' symmetry. This provides a unique system in which polarization varies as the fourth-degree of the order-parameter amplitude and exhibit a vanishingly small value below the first-order transition at …
We employ neutron spherical polarimetry to determine the nature and population of the coexisting antiferromagnetic domains in multiferroic YMn2O5. By applying an electric field, we prove that reversing the electrical polarization results in the population inversion of two types of in-plane domains, related to each other by inversion. Our results are completely consistent with the exchange striction mechanism of ferroelectricity, and support a unified model where cycloidal ordering is induced by coupling to the main magnetic order parameter.
A current challenge in the field of magnetoelectric multiferroics is to identify systems that allow a controlled tuning of states displaying distinct magnetoelectric responses. Here we show that the multiferroic ground state of the archetypal multiferroic TbMnO3 is dramatically modified by epitaxial strain. Neutron diffraction reveals that in highly strained films the magnetic order changes from the bulk-like incommensurate bc-cycloidal structure to commensurate magnetic order. Concomitant with the modification of the magnetic ground state, optical second-harmonic generation (SHG) and electric…
With the perovskite multiferroic RMnO3 (R = Gd, Tb, Dy) as guidance, we argue that the Dzyaloshinskii-Moriya interaction (DMI) provides the microscopic mechanism for the coexistence and strong coupling between ferroelectricity and incommensurate magnetism. We use Monte-Carlo simulations and zero temperature exact calculations to study a model incorporating the double-exchange, superexchange, Jahn-Teller and DMI terms. The phase diagram contains a multiferroic phase between A and E antiferromagnetic phases, in excellent agreement with experiments.
Although superspace formalism has become the standard approach for the analysis of structurally modulated crystals, it has remained during the last thirty years almost unexplored as a practical tool to deal with magnetic incommensurate structures. This situation has recently changed with the development of new computer tools for magnetic phases based on this formalism. In this context we show here that, as in the case of nonmagnetic incommensurate systems, the concept of superspace symmetry provides a simple, efficient and systematic way to characterize the symmetry and rationalize the structu…
We have performed a systematic study of the electronic structures of BiMeO3 (Me = Sc, Cr, Mn, Fe, Co, Ni) series by soft X-ray emission (XES) and absorption (XAS) spectroscopy. The band gap values were estimated for all compounds in the series. For BiFeO3 a band gap of ~0.9 eV was obtained from the alignment of the O Ka XES and O 1s XAS. The O 1s XAS spectrum of BiNiO3 indicates that the formation of holes is due to a Ni2+ valency rather than a Ni3+ valency. We have found that the O Ka XES and O 1s XAS of BiMeO3 probing partially occupied and vacant O 2p states, respectively, are in agreement …
Symmetry Analysis of Magnetoelectric Coupling Effect in All Point Groups
National Laboratory of Solid State Microstructures and School of Physics, Nanjing University（南京大学固体微结构物理国家重点实验室和物理学院）；Collaborative Innovation Center of Advanced Microstructures, Nanjing University（南京大学先进微结构协同创新中心）；Key Laboratory of Computational Physical Sciences (Ministry of Education), Institute of Computational Physical Sciences, and Department of Physics, Fudan University（复旦大学计算物理教育部重点实验室、计算物理科学研究所和物理系）
The coexistence and coupling of magnetic and ferroelectric orderings in single phase multiferroics has evinced enormous scientific interest as it involves breaking of time reversal and space inversion symmetries in the same material. The mutual controllability of the two diverse orderings in multiferroics has potential for developing new generation multifunctional sensor, actuator and data storage devices. We present here evidence for a new exotic facet of multiferroicity, whereby one can raise the strength of antiferromagnetic (AFM) superexchange interaction and hence tune the Néel temperatur…
We uncover a new pathway towards multiferroicity, showing how magnetism can drive ferroelectricity without relying on inversion symmetry breaking of the magnetic ordering. Our free-energy analysis demonstrates that any commensurate spin-density-wave ordering with a phase dislocation, even if it is collinear, gives rise to an electric polarization. Due to the dislocation the electronic and magnetic and inversion centers do not coincide, which turns out to be a sufficient condition for multiferroic coupling. The novel mechanism explains the formation of multiferroic phases at the magnetic commen…
Hexagonal LuFe2O4 is a promising charge-order (CO) driven multiferroic material with high charge and spin ordering temperatures. The coexisting charge and spin orders on Fe3+/Fe2+ sites result in novel magnetoelectric behaviors, but the coupling mechanism between the charge and spin orders remains elusive. Here, by tuning external pressure, we reveal three correlated spin-charge ordered phases in LuFe2O4: i) a centrosymmetric incommensurate three-dimensional CO with ferrimagnetism, ii) a non-centrosymmetric incommensurate quasi-two-dimensional CO with ferrimagnetism, and iii) a centrosymmetric…
TbMnO3 is an orthorhombic insulator where incommensurate spin order for temperature T_N < 41K is accompanied by ferroelectric order for T < 28K. To understand this, we establish the magnetic structure above and below the ferroelectric transition using neutron diffraction. In the paraelectric phase, the spin structure is incommensurate and longitudinally-modulated. In the ferroelectric phase, however, there is a transverse incommensurate spiral. We show that the spiral breaks spatial inversion symmetry and can account for magnetoelectricity in TbMnO3.
The magnon and optical phonon spectrum of an incommensurate multiferroic such as BiFeO3 is considered in the framework of a phenomenological Landau theory. The resulting spin wave spectrum is quite distinct from commensurate substances due to soft mode anisotropy and magnon zone folding. The former allows electrical control of spin wave propagation via reorientation of the spontaneous ferroelectric moment. The latter gives rise to multiple magneto-dielectric resonances due to the coupling of optical phonons at zero wavevector to magnons at integer multiples of the cycloid wavevector. These res…
A complex magnetic order of the multiferroic compound Co3TeO6 has been revealed by neutron powder diffraction studies on ceramics and crushed single crystals. The compound adopts a monoclinic structure (s.g. C2/c) in the studied temperature range 2 K - 300 K but exhibits successive antiferromagnetic transitions at low temperature. Incommensurate antiferromagnetic order with the propagation vector k1 = (0, 0.485, 0.055) sets in at 26 K. A transition to a second antiferromagnetic structure with k2 = (0, 0, 0) takes place at 21.1 K. Moreover, a transition to a commensurate antiferromagnetic struc…
We present a theoretical analysis of the temperature-magnetic field-concentration phase diagram of the multiferroic Mn$_{1-x}$M$_{x}$WO$_{4}$ (M=Fe, Zn, Mg), which exhibits three ordered phases, with collinear and non-collinear incommensurate and with a commensurate magnetic order. The middle phase is also ferroelectric. The analysis uses a semi-phenomenological Landau theory, based on a Heisenberg Hamiltonian with a single-ion anisotropy. With a small number of adjustable parameters, the Landau theory gives an excellent fit to all three transition lines, as well as the magnetic and the ferroe…
At ambient pressure (P) and below 5.5 K, olivine-type Mn2GeO4 hosts a multiferroic (MF) phase where a multicomponent, i.e., multi-k magnetic order generates spontaneous ferromagnetism and ferroelectricity (FE) along the c axis. Under high P the FE disappears above 6 GPa, yet the P evolution of the magnetic structure remained unclear based on available data. Here we report high P single crystal neutron diffraction experiments in theMF phase at T = 4.5 K.We observe clearly that the incommensurate spiral component of the magnetic order responsible for FE varies little with P up to 5.1 GPa. With s…
MnWO4 is regarded as a canonical example of multiferroic materials, where the multiferroic activity is caused by a spin-spiral alignment. We argue that, in reality, MnWO4 has two sources of the spin-spirality, which conflict with each other. One is the Dzyaloshinskii-Moriya (DM) interactions, reflecting the P2/c symmetry of the lattice. The P2/c structure of MnWO4 has an inversion center, that connects two Mn sublattices. Therefore, from the viewpoint of DM interactions, different Mn sublattices are expected to have opposite spin chirality. Another source is competing isotropic exchange intera…
Spin and lattice dynamics of CaMn7O12 ceramics were investigated using infrared, THz and inelastic neutron scattering (INS) spectroscopies in the temperature range 2 to 590 K, and, at low temperatures, in applied magnetic fields of up to 12 T. On cooling, we observed phonon splitting accompanying the structural phase transition at Tc = 450K as well as the onset of the incommensurately modulated structure at 250 K. In the two antiferromagnetic phases below T_N1 = 90K and T_N2 = 48 K, several infrared-active excitations emerge in the meV range; their frequencies correspond to the maxima in the m…
Magnetic and ferroelectric properties of layered geometrically frustrated cluster compound FeTe$_2$O$_5$Br were investigated with single-crystal neutron diffraction and dielectric measurements. Incommensurate amplitude modulated magnetic order with the wave vector $\bf{q}$=($\half$, 0.463, 0) develops below $T_N=10.6(2) {\rm K}$. Simultaneously, a ferroelectric order with the spontaneous polarization perpendicular to ${\bf q}$ and to Fe$^{3+}$ magnetic moments emerges. The observed ferroelectricity and extraordinary linear scaling of the ferroelectric and magnetic order parameter are provoked …
The layered perovskite YBaCuFeO5 (YBCFO) is considered one of the best candidates to high-temperature chiral multiferroics with strong magnetoelectric coupling. In RBaCuFeO5 perovskites (R: rare-earth or Y) A-site cations are fully ordered whereas their magnetic properties strongly depend on the preparation process. They exhibit partial cationic disorder at the B-site that generates a magnetic spiral stabilized through directionally assisted long range coupling between canted locally frustrated spins. Moreover the orientation of its magnetic spiral can be critical for the magnetoelectric respo…
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…
Multiferroic TbMnO3 is investigated using x-ray diffraction in high magnetic fields. Measurements on first and second harmonic structural reflections due to modulations induced by the Mn and Tb magnetic order are presented as function of temperature and field oriented along the a and b-directions of the crystal. The relation to changes in ordering of the rare earth moments in applied field is discussed. Observations below T_N(Tb) without and with applied magnetic field point to a strong interaction of the rare earth order, the Mn moments and the lattice. Also, the incommensurate to commensurat…
In this paper we investigate peculiarities of phase transition high-symmetry - incommensurate phase in inhomogeneous systems. We obtain the nonlinear dispersion law and then present a renormalization group analysis of phase transitions in multiferroics. We have determined the dependence of critical indices on the nonextensivity parameter of the system.
Competing interactions and geometric frustration provide favourable conditions for exotic states of matter. Such competition often causes multiple phase transitions as a function of temperature and can lead to magnetic structures that break inversion symmetry, thereby inducing ferroelectricity [1-4]. Although this phenomenon is understood phenomenologically [3-4], it is of great interest to have a conceptually simpler system in which ferroelectricity appears coincident with a single magnetic phase transition. Here we report the first such direct transition from a paramagnetic and paraelectric …
Prediction of Magnetoelectric Multiferroic Janus Monolayers VOXY(X/Y = F, Cl, Br, or I, and X$\not=$Y) with in-plane ferroelectricity and out-of-plane piezoelectricity
Linearly polarized spectra of far-infrared (IR) transmission in HoMn2O5 multiferroic single crystals have been studied in the frequency range between 8.5 and 105 cm-1 and for temperatures between 5 K and 300 K. Polarization of IR-active excitations depends on the crystallographic directions in HoMn2O5 and is sensitive to the magnetic phase transitions. We attribute some of the infrared-active excitations to electric-dipole transitions between ligand-field split states of Ho3+ ions. For light polarization along crystalline b-axis, the oscillator strength of electric dipoles at low frequencies (…
Motivated by the discovery of multiferroicity in the geometrically frustrated triangular antiferromagnet CuCrO$_2$ below its Néel temperature $T_N$, we investigate its magnetic and ferroelectric properties using ab initio calculations and Monte Carlo simulations. Exchange interactions up to the third nearest neighbors in the $ab$ plane, inter-layer interaction and single ion anisotropy constants in CuCrO$_2$ are estimated by series of density functional theory calculations. In particular, our results evidence a hard axis along the [110] direction due to the lattice distortion that takes place …
We report a giant linear magnetoelectric coupling in strained BiMnO3 thin films in which the disorder associated with an islanded morphology gives rise to extrinsic relaxor ferroelectricity that is not present in bulk centrosymmetric ferromagnetic crystalline BiMnO3. Strain associated with the disorder is treated as a local variable which couples to the two ferroic order parameters, magnetization M and polarization P. A straightforward "gas under a piston" thermodynamic treatment explains the observed correlated temperature dependencies of the product of susceptibilities and the magnetoelectri…
We have investigated magnetic field dependences of a ferroelectric incommensurate-helimagnetic order in a trigonal magneto-electric (ME) multiferroic CuFe1-xAlxO2 with x=0.015, which exhibits the ferroelectric phase as a ground state, by means of neutron diffraction, magnetization and dielectric polarization measurements under magnetic fields applied along various directions. From the present results, we have established the H-T magnetic phase diagrams for the three principal directions of magnetic fields; (i) parallel to the c axis, (ii) parallel to the helical axis, and (iii) perpendicular t…
Multiferroism can originate from the breaking of inversion symmetry caused by magnetic-spiral order. The usual mechanism for stabilizing a magnetic spiral is competition between magnetic exchange interactions differing by their range and sign, such as nearest-neighbor and next-nearest- neighbor interactions. Since the latter are usually weak the onset temperatures for multiferroism via this mechanism are typically low. By considering a realistic model for YBaCuFeO$_5$ we propose an alternative mechanism for magnetic-spiral order, and hence for multiferroism, that occurs at much higher temperat…
(Ba/Sr)3NbFe3Si2O14 is a magnetoelectric multiferroic with an incommensurate antiferromagnetic spiral magnetic structure which induces electric polarization at 26 K. The structure, as revealed by x-rays and neutrons, as well as static and dynamic magnetic and dielectric properties of these compounds have been studied down to 6 K under different conditions. Both the compounds have similar crystal structure but with different lattice constants down to 6 K. The Ba-and Sr-compounds exhibit a transition at 26 K and 25 K respectively, as indicated by the specific heat capacity and dc specific magnet…
Multiferroics, defined for those multifunctional materials in which two or more kinds of fundamental ferroicities coexist, have become one of the hottest topics of condensed matter physics and materials science in recent years. The coexistence of several order parameters in multiferroics brings out novel physical phenomena and offers possibilities for new device functions. The revival of research activities on multiferroics is evidenced by some novel discoveries and concepts, both experimentally and theoretically. In this review article, we outline some of the progressive milestones in this st…
Strain-Induced Relaxor Multiferroicity at Room Temperature in Hexaferrite BaFe12O19 Thin Films
Cornell University（康奈尔大学）；The Pennsylvania State University（宾夕法尼亚州立大学）；Leibniz-Institut für Kristallzüchtung（莱布尼兹晶体生长研究所）；Oak Ridge National Laboratory（橡树岭国家实验室）；University of Tennessee（田纳西大学）；University of California, Berkeley（加州大学伯克利分校）；University of North Texas（北德克萨斯大学）；University of Southern California（南加州大学）；Kavli Institute at Cornell for Nanoscale Science（康奈尔纳米科学卡弗里研究所）
There is great interest in hybrid organic-inorganic materials such as metal-organic frameworks (MOFs). The compounds [C(NH$_{2}$)$_{3}$]M(HCOO)$_{3}$, where M=Cu$^{2+}$ or Cr$^{2+}$ are Jahn-Teller (JT) active ions, are MOF with perovskite topology which crystallizes in polar space group Pna2$_{1}$. In inorganic compounds, octahedral tilting and Jahn-Teller structural distortions are usually non-polar distortions. However, in this MOF cooperative interactions between the antiferro-distortive distortions of the framework and the C(NH2)$_{3}$ organic cation via hydrogen bonding breaks the invers…
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 i…
We study the dynamical interplay between ferroelectricity and magnetism in a multiferroic with a helical magnetic order. We show that the dynamical exchange-striction induces a biquadratic interaction between the spins and transverse phonons resulting in quantum fluctuations of the spontaneous ferroelectric polarization $\mathbf{P}$ in the ferroelectric phase. The hybridization between the spin wave and the fluctuation of the electric polarization leads to low-lying transverse phonon modes. Those are perpendicular to $\mathbf{P}$ and to the helical spins at small wave vector but then turn para…
Breaking of spatial inversion symmetry (SIS) induces unique phenomena in condensed matter. Besides the classic examples such as natural optical activity and piezoelectricity, the spin-orbit interaction further enriches the effect of SIS breaking, as exemplified by the Rashba effect. In particular, by combining this symmetry with magnetic fields or another type of time-reversal symmetry (TRS) breaking, noncentrosymmetric materials can be made to exhibit nonreciprocal responses, which are responses that differ for rightward and leftward stimuli. For example, resistivity becomes directionally dep…
We present a comprehensive single crystal neutron diffraction investigation of the $\rm Mn_{1-x}Co_{x}WO_4$ with $0.02\leq x \leq0.30$. At lower concentration $x \leq 0.05$, the system is quickly driven into the multiferroic phase with spin structure forming an elliptical spiral order similar to the parent compound. The reduction of electric polarization is ascribed to the tilting of the spiral plane. For $x\sim 0.075$, the magnetic structure undergoes a spin flop transition that is characterized by a sudden rotation of the spin helix envelope into the $ac$ plane. This spin structure persists …
Spin-dependent electric dipole operators are investigated group-theoretically for the emergence of an electric dipole induced by a single spin or by two spins, where the spin dependences are completely classified up to the quadratic order. For a single spin, a product of spin operators behaves as an even-parity electric quadrupole operator, which differs from an odd-parity electric dipole. The lack of the inversion symmetry allows the even- and odd-parity mixing, which leads to the electric dipole described by the electric quadruple operators. Point-group tables are given for classification of…
Contradictory results on the ferroelectric response of type II multiferroic YBaCuFeO$_{5}$, in its incommensurate phase, has of late, opened up a lively debate. There are ambiguous reports on the nature of the spiral magnetic state. Using first-principles DFT calculations for the parent compound within LSDA+U+SO approximation, the multiferroic response and the nature of spiral state is revealed. The helical spiral is found to be more stable below the transition temperature as spins prefer to lie in ab plane. The Dzyaloshinskii-Moriya (DM) interaction and the spin current mechanism were earlier…
