CuFeO_2 is one of the multiferroic materials and is the first case that the electric polarization is not explained by the magnetostriction model or the spin-current model. We have studied this material using soft x-ray resonant diffraction and found that superlattice reflection 0, 1 - 2q, 0 appears in the ferroelectric and incommensurate magnetic ordered phase at the Fe L2,3 absorption edges and moreover that the rotation of the x-ray polarization such as from σ to π or from π to σ is allowed at this reflection. These findings definitely provide direct evidence that the 3d orbital state of Fe ions has a long range order in the ferroelectric state and support the spin-dependent d-p hybridization mechanism.
A comprehensive analysis of optical second harmonic generation (SHG) on an incommensurate (IC) magnetically ordered state is presented using multiferroic MnWO4 as model compound. Two fundamentally different SHG contributions coupling to the primary IC magnetic order or to secondary commensurate projections of the IC state, respectively, are distinguished. Whereas the latter can be described within the formalism of the 122 commensurate magnetic point groups the former involves a breakdown of the conventional macroscopic symmetry analysis because of its sensitivity to the lower symmetry of the l…
We report inelastic light scattering measurements of lattice dynamics related to the incommensurate orbital order in $\mathrm{CaMn_7O_{12}}$. Below the ordering temperature $T_\mathrm{o} \approx 250 \,\mathrm{K}$, we observe extra phonon peaks as a result of Brillouin-zone folding, as well as a soft vibrational mode with a power-law $T$-dependent energy, $Ω= Ω_{0}(1 - T/T_{\mathrm{o}})^{1/2}$. This temperature dependence demonstrates the second-order nature of the transition at $T_\mathrm{o}$, and it indicates that the soft mode can be regarded as the amplitude excitation of the composite orde…
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 …
The pressure ($p$) -- temperature ($T$) phase diagram for microscopic magnetism in the multiferroic compound HoMn$_{2}$O$_{5}$ was established using neutron diffraction measurements under a hydrostatic pressure up to 1.25 GPa. At ambient pressure, incommensurate--commensurate--incommensurate magnetic phase transitions occur successively with decreasing temperature. Upon applying pressure, the incommensurate phase at the lowest temperature almost decreases and the commensurate phase appears. The $p$ -- $T$ phase diagram established shows excellent agreement with the recently reported $p$ -- $T$…
Neutron diffraction, magnetic susceptibility, specific heat, and dielectric constant measurements of single crystal Co3TeO6 have been measured to study the interplay between the ferroelectricity and magnetic order. Long range incommensurate magnetic order develops below TM1=26 K, which is followed by three additional zero-field phase transitions at TM2=19.5 K, TM3=18 K, and TM4=16 K where the incommensurate order changes and commensurate order develops. In magnetic fields up to 14 T we find that the magnetic intensities and incommensurate wave vector are dramatically altered as ferroelectricit…
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…
The magnetic structure and the multiferroic relaxation dynamics of NaFeGe$_2$O$_6$ were studied by neutron scattering on single crystals partially utilizing polarization analysis. In addition to the previously reported transitions, the incommensurate spiral ordering of Fe$^{3+}$ moments in the $ac$ plane develops an additional component along the crystallographic $b$ direction below $T\approx 5\text{ K}$, which coincides with a lock-in of the incommensurate modulation. The quasistatic control of the spin-spiral handedness, respectively of the vector chirality, by external electric fields prove…
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 …
We have studied the crystal and magnetic structures of the magnetoelectric materials RMn2O5 (R = Tb, Ho, Dy) using neutron diffraction as a function of temperature. All three materials display incommensurate antiferromagnetic ordering below 40 K, becoming commensurate on further cooling. For R = Tb, Ho, a commensurate-incommensurate transition takes place at low temperatures. The commensurate magnetic structures have been solved and are discussed in terms of competing exchange interactions. The spin configuration within the ab plane is essentially the same for each system, and the radius of R …
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 …
Neutron powder diffraction and single crystal x-ray resonant magnetic scattering measurements suggest that Dy plays an active role in enhancing the ferroelectric polarization in multiferroic DyMnO3 above TNDy = 6.5 K. We observe the evolution of an incommensurate ordering of Dy moments with the same periodicity as the Mn spiral ordering. It closely tracks the evolution of the ferroelectric polarization which reaches a maximum value of 0.2 muC/m^2. Below TNDy, where Dy spins order commensurately, the polarization decreases to values similar for those of TbMnO3.
The minimal model to describe many spin chain materials with ferroelectric properties is the Heisenberg model with ferromagnetic nearest neighbor coupling J1 and antiferromagnetic next-nearest neighbor coupling J2. Here we study the thermodynamics of this model using a density-matrix algorithm applied to transfer matrices. We find that the incommensurate spin-spin correlations - crucial for the ferroelectric properties and the analogue of the classical spiral pitch angle - depend not only on the ratio J2/|J1| but also strongly on temperature. We study small easy-plane anisotropies which can st…
Neutron diffraction has been used to determine the magnetic structure of Na$_8$Cu$_5$O$_{10}$, a stoichiometric compound containing chains based on edge-sharing CuO$_4$ plaquettes. The chains are doped with 2/5 hole per Cu site and exhibit long-range commensurate charge order with an onset well above room temperature. Below $T_N = 23$ K, the neutron data indicate long-range collinear magnetic order with a spin density modulation whose propagation vector is commensurate along and incommensurate perpendicular to the chains. Competing interchain exchange interactions are discussed as a possible o…
The magnetic properties of a trigonal prism unit of the spin-2 frustrated compound Ca3Co2O6 are studied by means of the density-matrix renormalization group method. A magnetization plateau at $ms/3$ ($ms$ is the saturation magnetization) with ferrimagnetic structure is observed. By fitting the experimental data of magnetic curve, an estimation of the couplings gives J1=-26.84K, J_{2}=0.39K, and J_{3}=0.52K. The local magnetic moments are unveiled to exhibit an incommensurate sinusoidally modulation along the three chains of the trigonal prism, which gives a strong theoretical support to the ex…
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 handedness that can be reversed by E. We further show close association between cycloidal and ferroelectric domains through E-driven spin and electric polarization hysteresis. We suggest that definite cycloidal handedness is ac…
Ferroelectric spiral magnets DyMnO3 and TbMnO3 show similar behavior of electric polarization in applied magnetic fields. Studies of the field dependence of lattice modulations on the contrary show a completely different picture. Whereas in TbMnO3 the polarization flop from P||c to P||a is accompanied by a sudden change from incommensurate to commensurate wave vector modulation, in DyMnO3 the wave vector varies continuously through the flop transition. This smooth behavior may be related to the giant magnetocapacitive effect observed in DyMnO3.
A combination of density functional theory calculations, many-body model considerations, magnetization and electron spin resonance measurements shows that the multiferroic FeTe$_2$O$_5$Br should be described as a system of alternating antiferromagnetic $S=5/2$ chains with strong Fe-O-Te-O-Fe bridges weakly coupled by two-dimensional frustrated interactions, rather than the previously reported tetramer models. The peculiar temperature dependence of the incommensurate magnetic vector can be explained in terms of interchain exchange striction being responsible for the emergent net electric polari…
Results of high resolution x-ray diffraction experiments are presented for single crystals of the spin gap compound BaCuSi$_2$O$_6$ in the temperature range from 16 to 300 K. The data show clear evidence of a transition from the room temperature tetragonal phase into an incommensurately modulated orthorhombic structure below $\sim$100 K. This lattice modulation is characterized by a resolution limited wave vector {\bf q}$_{IC}$=(0,$\sim$0.13,0) and its 2$^{nd}$ and 3$^{rd}$ harmonics. The phase transition is first order and exhibits considerable hysteresis. This observation implies that the sp…
The magnetic excitations in multiferroic TbMnO3 have been studied by inelastic neutron scattering in the spiral and sinusoidally ordered phases. At the incommensurate magnetic zone center of the spiral phase, we find three low-lying magnons whose character has been fully determined using neutron-polarization analysis. The excitation at the lowest energy is the sliding mode of the spiral, and two modes at 1.1 and 2.5meV correspond to rotations of the spiral rotation plane. These latter modes are expected to couple to the electric polarization. The 2.5meV-mode is in perfect agreement with recent…
X-ray resonant scattering has been used to measure the magnetic order of the Dy ions below 40K in multiferroic DyMn$_{2}$O$_{5}$. The magnetic order has a complex behaviour. There are several different ordering wavevectors, both incommensurate and commensurate, as the temperature is varied. In addition a non-magnetic signal at twice the wavevector of one of the commensurate signals is observed, the maximum intensity of which occurs at the same temperature as a local maximum in the ferroelectric polarisation. Some of the results, which bear resemblence to the behaviour of other members of the R…
Magnetic order and the underlying magnetic model of the multiferroic pyroxene NaFeGe2O6 are systematically investigated by neutron powder diffraction, thermodynamic measurements, density-functional bandstructure calculations, and Monte-Carlo simulations. Upon cooling, NaFeGe2O6 first reveals one-dimensional spin-spin correlations in the paramagnetic state below about 50 K, revealed by magnetic diffuse scattering. The sinusoidal spin-density wave with spins along the a-direction sets in at 13 K, followed by the cycloidal configuration with spins lying in the (ac) plane below 11.6 K. Microscopic…
Neutron diffraction and nuclear quadrupole resonance (NQR) measurements were employed to investigate magnetic order in the non-ferroelectric phase preceding the low-temperature multiferroic state in FeTe2O5Br. Refnement of the neutron diffraction data and simulations of 79,81Br NQR spectra reveal that the incommensurate magnetic ordering in the non-ferroelectric state comprises amplitude-modulated magnetic moments, similarly as in the multiferroic state. The two ordered states differ in the orientation of the magnetic moments and phase shifts between modulation waves. Surprisingly, all symmetr…
The magnetic and multiferroic phase diagram of Mn$_{0.85}$Co$_{0.15}$WO$_4$ single crystals is investigated by means of magnetic, heat capacity, dielectric, polarization, and neutron scattering experiments. Three magnetic phase transitions are detected through distinct anomalies in all physical quantities. The ferroelectric polarization is observed only along the b-axis below 10 K but not along the a-axis as recently suggested. The magnetic phases studied by neutron scattering are very complex. Up to four different magnetic structures, partially coexisting at certain temperature ranges, have b…
We argue for a recently observed puzzling multiferroic behavior in s=1/2 1D chain cuprate LiCu2O2 with edge-shared arrangement of CuO4 plaquettes and incommensurate spiral spin ordering can be consistently explained if one takes into account the nonrelativistic exchange-induced electric polarization on the Cu2+ centers substituting for the positions native for the Cu1+ ions. These substituent centers are proved to be an effective probe of the spin incommensurability and magnetic field effects.
Terahertz (THz) radiation has been observed from multiferroic BiFeO$_3$ thin films via ultrafast modulation of spontaneous polarization upon carrier excitation with illumination of femtosecond laser pulses. The radiated THz pulses from BiFeO$_3$ thin films were clarified to directly reflect the spontaneous polarization state, giving rise to a memory effect in a unique style and enabling THz radiation even at zero-bias electric field. On the basis of our findings, we demonstrate potential approaches to ferroelectric nonvolatile random access memory with nondestructive readability and ferroelect…
We present macroscopic and neutron diffraction data on multiferroic lightly Co-doped Ni$_3$V$_2$O$_8$. Doping Co into the parent compound suppresses the sequence of four magnetic phase transitions and only two magnetically ordered phases, the paraelectric high temperature incommensurate (HTI) and ferroelectric low temperature incommensurate (LTI), can be observed. Interestingly, the LTI multiferroic phase with a spiral (cycloidal) magnetic structure is stabilized down to at least 1.8 K, which could be revealed by measurements of the electric polarization and confirmed by neutron diffraction on…
We have performed synchrotron radiation X-ray and neutron diffraction measurements on magnetoelectric multiferroic CuFe1-xAlxO2 (x=0.0155), which has a proper helical magnetic structure with incommensurate propagation wave vector in the ferroelectric phase. The present measurements revealed that the ferroelectric phase is accompanied by lattice modulation with a wave number 2q, where q is the magnetic modulation wave number. We have calculated the Fourier spectrum of the spatial modulations in the local electric polarization using a microscopic model proposed by Arima [T. Arima, J. Phys. Soc. …
Elastic neutron scattering is used to study the spin correlations in the multiferroic $\rm Mn_{1-x}Fe_{x}WO_4$ with $x=0.035, 0.05$ and 0.10. The noncollinear, incommensurate (ICM) magnetic structure associated with the ferroelectric (FE) phase in pure $\rm MnWO_4$ is suppressed at $x=0.035$ and completely absent at $x=0.10$. The ICM spin order and FE phase can be restored by applying a magnetic field along the spin easy-axis. The low-$T$ commensurate magnetic structure extends in both H/T with increasing Fe concentration. The systematic evolution of the magnetic and electric properties indica…
The present paper studies, using ab-initio calculations, the influence of the incommensurate structural modulations on the low energy physics of the $Sr\_{14-x}Ca\_xCu\_{24}O\_{41}$ oxides. On-site, nearest-neighbor and next-nearest-neighbor effective parameters were computed within a $t-J+V$ model based on the copper magnetic orbitals. The structural modulations appear to be the key degree of freedom, responsible for the low energy properties such as the electron localization, the formation of dimers in the $x=0$ compound or the anti-ferromagnetic order in the $x=13.6$ compound.
We have employed resonant x-ray magnetic scattering to specifically probe the magnetic order of the rare-earth ions in multiferroic $\mathrm{TbMn_2O_5}$. Two energy resonances were observed, one originated from the E1-E1 dipolar transition and the other from the E2-E2 quadrupolar transition. These resonances directly probe the valence 5d band and the partially occupied 4f band, respectively. First, full polarization analysis, which is a measurement of the scattered polarization as a function of incident polarization, confirmed a spin polarization of the terbium valence states (probed by the E1…
The precise crystal symmetry and hence the emergence of the electric polarization still remains an open question in the multiferroic materials $R$Mn$_2$O$_5$ ($R$ = rare-earth, Bi, Y). While previous diffraction studies have indicated that $R$Mn$_2$O$_5$ possesses the centro-symmetric space group P$bam$, an atomic displacement allowing for the electric polarization would require a non-centrosymmetric crystal symmetry. Our single crystal neutron diffraction experiments on TbMn$_2$O$_5$ provide direct evidence of a reduced crystallographic symmetry already above the magnetic and ferroelectric ph…
We report a magnetic x-ray scattering study of the field-induced multiferroic GdFe3(BO3)4. Resonant x-ray magnetic scattering at the Gd LII,III edges indicates that the Gd moments order at TN ~ 37 K. The magnetic structure is incommensurate below TN, with the incommensurability decreasing monotonically with decreasing temperature until a transition to a commensurate magnetic phase is observed at T ~ 10 K. Both the Gd and Fe moments undergo a spin reorientation transition at TSR ~ 9 K such that the moments are oriented along the crystallographic c axis at low temperatures. With magnetic field a…
The crystal and magnetic structure of multiferroic LiFe(WO$_4$)$_2$ were investigated by temperature and magnetic-field dependent specific heat, susceptibility and neutron diffraction experiments on single crystals. Considering only the two nearest-neighbour magnetic interactions, the system forms a $J_1$, $J_2$ magnetic chain but more extended interactions are sizeable. Two different magnetic phases exhibiting long-range incommensurate order evolve at $T_{\text{N}1}\approx 22.2 \text{ K}$ and $T_{\text{N}2}\approx 19 \text{ K}$. First, a spin-density wave develops with moments lying in the $a…
Through a combination of neutron diffraction and Landau theory we describe the spin ordering in the ground state of the quadruple perovskite manganite CaMn7O12 - a magnetic multiferroic supporting an incommensurate orbital density wave that onsets above the magnetic ordering temperature, TN1 = 90 K. The multi-k magnetic structure in the ground state was found to be a nearly-constant-moment helix with modulated spin helicity, which oscillates in phase with the orbital occupancies on the Mn3+ sites via trilinear magneto-orbital coupling. Our phenomenological model also shows that, above TN2 = 48…
Polarized neutron diffraction experiments have been performed on multiferroic materials $R$Mn$_{2}$O$_{5}$ ($R=$Ho, Er) under electric fields in the ferroelectric commensurate (CM) and the low-temperature incommensurate (LT-ICM) phases, where the former has the highest electric polarization and the latter has reduced polarization. It is found that, after cooling in electric fields down to the CM phase, the magnetic chirality is proportional to the electric polarization. Also we confirmed that the magnetic chirality can be switched by the polarity of the electric polarization in both the CM and…
Synchrotron x-ray diffraction and resonant magnetic scattering experiments on single crystal DyMnO3 have been carried out between 4 and 40 K. Below TN(Dy) = 5K, the Dy magnetic moments order in a commensurate structure with propagation vector 0.5 b*. Simultaneous with the Dy magnetic ordering, an incommensurate lattice modulation with propagation vector 0.905 b* evolves while the original Mn induced modulation is suppressed and shifts from 0.78 b* to 0.81 b*. This points to a strong interference of Mn and Dy induced structural distortions in DyMnO3 besides a magnetic coupling between the Mn an…
Comprehensive x-ray scattering studies, including resonant scattering at Mn L-edge, Tb L- and M-edges, were performed on single crystals of TbMn2O5. X-ray intensities were observed at a forbidden Bragg position in the ferroelectric phases, in addition to the lattice and the magnetic modulation peaks. Temperature dependences of their intensities and the relation between the modulation wave vectors provide direct evidences of exchange striction induced ferroelectricity. Resonant x-ray scattering results demonstrate the presence of multiple magnetic orders by exhibiting their different temperatur…
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…
We report $^{51}$V nuclear magnetic resonance (NMR) studies on single crystals of the multiferroic material FeVO$_4$. The high-temperature Knight shift shows Curie-Weiss behavior, $^{51}K = a/(T + θ)$, with a large Weiss constant $θ\approx$ 116 K. However, the $^{51}$V spectrum shows no ordering near these temperatures, splitting instead into two peaks below 65 K, which suggests only short-ranged magnetic order on the NMR time scale. Two magnetic transitions are identified from peaks in the spin-lattice relaxation rate, $1/^{51}T_1$, at temperatures $T_{N1} \approx$ 19 K and $T_{N2} \approx$ 1…
Here we use low-temperature scanning tunneling microscopy and spectroscopy to study the polar surfaces of PdCoO2. On the CoO2-terminated polar surface, we detect the quasiparticle interference pattern originating from the Rashba spin-split surface states. On the well-ordered Pd-terminated polar surface, we observe a regular lattice which has larger lattice constant than the atomic lattice of PdCoO2. In comparison with the shape of the hexagonal bulk Fermi surface, we identify this regular lattice as a fully two-dimensional incommensurate charge modulation that is driven by the Fermi surface ne…
We have investigated the structural, magnetic and dielectric properties of Pb-based langasite compound Pb$_3$TeMn$_3$P$_2$O$_{14}$ both experimentally and theoretically in the light of metal-oxygen covalency, and the consequent generation of multiferroicity. It is known that large covalency between Pb 6$p$ and O 2$p$ plays instrumental role behind stereochemical lone pair activity of Pb. The same happens here but a subtle structural phase transition above room temperature changes the degree of such lone pair activity and the system becomes ferroelectric below 310 K. Interestingly, this structu…
We study the electronic and magnetic structures of multiferroic CaMn$_7$O$_{12}$ by first-principle calculations, based on the experimentally determined modulated crystal structure. We confirm the presence of a 3$d$ orbital modulation of the Mn2 (Mn$^{3+}$) sites, previously inferred from the Jahn-Teller crystal distortions. Our results indicate that in the multiferroic phase the magnetic structure of the Mn3 (Mn$^{4+}$) sites is anharmonically modulated via orbitally-mediated coupling with the structural modulation, and that the Dzyaloshinskii-Moriya and exchange striction mechanisms contribu…
From magnetic susceptibility, dielectric permittivity, electric polarization and specific heat measurements, we discover spin-induced ferroelectricity and magnetoelectric coupling in Mn3TeO6 and observe two successive magnetic transitions at low temperatures. A non-ferroelectric intermediate magnetic state occurs below 23 K and a multiferroic ground state emerges below 21 K. Moreover, Mn3TeO6 is a candidate for a multiferroic material where two types of incommensurate spin structures, cycloidal and helical, coexist. Theoretically, both spin substructures may contribute to the macro electric po…
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…
The spin dynamics of the geometrically frustrated triangular antiferromagnet multiferroic CuCrO2 have been mapped out using inelastic neutron scattering. The relevant spin Hamiltonian parameters modelling the incommensurate modulated helicoid have been determined, and correspond to antiferromagnetic nearest and next-nearest neighbour interactions in the ab plane, with a strong planar anisotropy. The weakly dispersive excitation along c reflects the essentially two-dimensional character of the magnetic interactions and according to classical energy calculations it is weakly ferromagnetic. Our r…
The effects of substituting nonmagnetic Mg2+ and Zn2+ ions for the Mn2+ (S = 5/2) ions on the structural, magnetic and dielectric properties of the multiferroic frustrated antiferromagnet MnWO4 were investigated. Polycrystalline samples of Mn1-xMgxWO4 and Mn1-xZnxWO4 (0<x<0.3) solid solutions were prepared by a solid-state route and characterized via X-ray and neutron diffraction, magnetization, and dielectric permittivity measurements. Mg and Zn substitutions give rise to very similar effects. The Neel temperature TN, the AF3-to-AF2 magnetic phase transition temperature T2, and the critical f…
We report a neutron diffraction study of the multiferroic mechanism in (ND4)2FeCl5D2O, a molecular compound that exhibits magnetically induced ferroelectricity. This material exhibits two successive magnetic transitions on cooling: a long-range order transition to an incommensurate (IC) collinear sinusoidal spin state at TN=7.3 K, followed by a second transition to an IC cycloidal spin state at TFE=6.8 K, the later of which is accompanied by spontaneous ferroelectric polarization. The cycloid structure is strongly distorted by spin-lattice coupling as evidenced by the observations of both odd …
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…
The symmetry conditions for the development of a macroscopic electrical polarization as a secondary order parameter to a magnetic ordering transition, and the constraints on the direction of the polarization vector, are determined by a non-conventional application of the theory of irreducible co-representations. In our approach, which is suitable for both magnetic and structural modulations, anti-unitary operators are employed to describe symmetry operations that exchange the propagation vector $\textbf{k}$ with $\textbf{-k}$, rather than operations combined with time-reversal as in classical …
In the vicinity of hole density, 1/8, La-based high-$T_{c}$ superconductors exhibit long-range order of incommensurate antiferromagnetism (IC-AF). Motivated by this observation, we explore the possible stabilization of IC-AF ordering due to the existence of static charge density modulation (CDM). We use Ginzburg-Landau free energy based on the mean field theory of the t-J model. It is shown numerically that three kinds of CDM including a stripe pattern can stabilize static IC-AF ordering. We also argue that such CDMs can cause the saturation of the degree of incommensurability ($η$) as a funct…
We investigated the magnetic structure of an orthorhombic YMnO3 thin film by resonant soft x-ray and hard x-ray diffraction. We observed a temperature-dependent incommensurate magnetic reflection below 45 K and a commensurate lattice-distortion reflection below 35 K. These results demonstrate that the ground state is composed of coexisting E-type and cycloidal states. Their different ordering temperatures clarify the origin of the large polarization to be caused by the E-type antiferromagnetic states in the orthorhombic YMnO3 thin film.
We have demonstrated that ferroelectric polarization in a spin-driven multiferroic CuFe1-xGaxO2 with x = 0.035 can be controlled by the application of uniaxial pressure. Our neutron diffraction and in-situ ferroelectric polarization measurements have revealed that the pressure dependence of the ferroelectric polarization is explained by repopulation of three types of magnetic domains originating from the trigonal symmetry of the crystal. We conclude that the spin-driven anisotropic lattice distortion and the fixed relationship between the directions of the magnetic modulation wave vector and t…
Neutron diffraction measurements under high magnetic fields have been performed for the multiferroic compound HoMn$_{2}$O$_{5}$. At zero field, high-temperature incommensurate magnetic (HT-ICM) -- commensurate magnetic (CM) -- low-temperature incommensurate magnetic (LT-ICM) orders occur with decreasing temperature, where ferroelectric polarization arises only in the CM phase. Upon applying a magnetic field, the LT-ICM phase completely disappears and the CM phase is induced at the lowest temperature. This field-induced CM state is completely associated with the field-induced electric polarizat…
Density-functional calculations are carried out to investigate incommensurate magnetic structures and ferroelectric polarization in newly discovered multiferroic material MnI$_2$. The exchange interactions among local moments on Mn are parameterized by mapping the mean-field Heisenberg model on to total energy difference of several magnetic ordering states. The experimentally observed noncollinear magnetic states are well reproduced by using this model and exchange interaction parameters. The direction of polarization experimentally measured is also consistent with the result derived from the …
We have performed dielectric measurements and neutron diffraction experiments on the double perovskite In2NiMnO6. A ferroelectric polarization, P ~ 30 μC/m2, is observed in a polycrystalline sample below TN = 26 K where a magnetic phase ransition occurs. The neutron diffraction experiment demonstrates that a complex noncollinear magnetic structure with "cycloidal" and "proper screw" components appears below TN, which has the incommensurate propagation vector k = (ka,0,ks; ka ~ 0.274, ks ~ -0.0893). The established magnetic point group 21' implies that the macroscopic ferroelectric polarization…
