Complex Magnetism and Magnetic Structures of the Metastable HoMnO3 Perovskite

Linear response theories for interatomic exchange interactions

The linear response is a perturbation theory establishing the relationship between given physical variable and the external field inducing this variable. A well-known example of the linear response theory in magnetism is the susceptibility relating the magnetization with the magnetic field. In 1987, Liechtensteinet alcame up with the idea to formulate the problem of interatomic exchange interactions, which would describe the energy change caused by the infinitesimal rotations of spins, in terms of this susceptibility. The formulation appears to be very generic and, for isotropic systems, expresses the energy change in the form of the Heisenberg model, irrespectively on which microscopic mechanism stands behind the interaction parameters. Moreover, this approach establishes the relationship between the exchange interactions and the electronic structure obtained, for instance, in the first-principles calculations based on the density functional theory. The purpose of this review is to elaborate basic ideas of the linear response theories for the exchange interactions as well as more recent developments. The special attention is paid to the approximations underlying the original method of Liechtensteinet alin comparison with its more recent and more rigorous extensions, the roles of the on-site Coulomb interactions and the ligand states, and calculations of antisymmetric Dzyaloshinskii-Moriya interactions, which can be performed alongside with the isotropic exchange, within one computational scheme. The abilities of the linear response theories as well as many theoretical nuances, which may arise in the analysis of interatomic exchange interactions, are illustrated on magnetic van der Walls materials CrX3(X=Cl, I), half-metallic ferromagnet CrO2, ferromagnetic Weyl semimetal Co3Sn2S2, and orthorhombic manganitesAMnO3(A=La, Ho), known for the peculiar interplay of the lattice distortion, spin, and orbital ordering.

Temperature evolution of 3d- and 4f-electron magnetic ordering in the ferrimagnetic Mn self-doped perovskite (Yb0.667Mn0.333)MnO3

A high-pressure synthesis method was employed to prepare Mn-self-doped perovskites (R_0.667Mn_0.333)MnO₃(R= Yb, Lu) at about 6 GPa and 1670 K. Crystal and magnetic structures of (Yb_0.667Mn_0.333)MnO₃have been studied by combining neutron powder diffraction, magnetic susceptibility and specific heat measurements. Within the orthorhombic space groupPnma, magnetic cations are located on site 4c(A site, occupied by two thirds of Yb³⁺and one third of Mn²⁺) and on site 4b(B site, occupied by two thirds of Mn³⁺and one third of Mn⁴⁺). The degree of structural distortion of the MnO₆octahedra follows the general trend of (R_1-xMn_x)MnO₃compounds which shows a decrease with increasing amount of Jahn-Teller inactive Mn⁴⁺cations. Mn-Mn interactions produce a collinear ferrimagnetic structure (T_C,Mn= 106 K) with ferromagnetically ordered Mn moments at the B site being coupled antiferromagnetically with ordered Mn moments at the A site. Mn-Yb interactions induce a small but non-zero ferromagnetic Yb³⁺moment which can explain a small decrease of the magnetic susceptibility at low temperature. Yb-Yb interactions create an antiferromagnetic structure atT_N,Yb≈ 40 K. Ordered moments of the ferrimagnetic and antiferromagnetic structures are oriented perpendicular to each other within theac-plane and Yb³⁺moments contribute to both structures. The appearance of ordered Yb³⁺moments induced by Mn-Yb interactions in perovskite (Yb_0.667Mn_0.333)MnO₃is a result of the Mn self-doping on the A site and has not been observed in the orthorhombic perovskite modification (space groupPnma) of the undoped parent compound YbMnO₃, but interestingly, it also appears in the hexagonal non-perovskite modification (space groupP6₃cm) of YbMnO₃.

Charge transfer enhanced magnetic correlations in type-II multiferroic Co3TeO6

Magnetic structure of the Co ions in monoclinic Co3TeO6 in the antiferroelectric state at 16 K has been determined by neutron powder together with single-crystal diffractions. The indices of the magnetic reflections that appear at the incommensurate positions were determined by diffractions from a single crystal, which allow to uniquely identify the magnetic modulation vector. There are two crystallographically distinct Co layers. Magnetic incommensurability appears in the Co spins in the layers comprising zig-zag chains, with a magnetic modulation vector of (0.357, 0.103, 0.121) at 3 K but changes to (0.4439, 0, 0.137) at 16 K, while the Co ions in the honeycomb webs form a collinear antiferromagnetic structure. Thermal reduction rate of the Co moments in the honeycomb webs was found to be much smaller than those in the zigzag chains. Shifting of large amounts of electronic charge into the Co─O bonds in the honeycomb webs on warming is used to understand the behavior.

Non-collinear magnetism & multiferroicity: the perovskite case

The most important types of non-collinear magnetic orders that are realized in simple perovskite oxides are outlined in relation to multiferroicity. These orders are classified and rationalized in terms of a mimimal spin Hamiltonian, based on which the notion of spin-driven ferroelectricity is illustrated. These concepts find direct application in reference materials such as BiFeO3, GdFeO3 and TbMnO3 whose multiferroic properties are briefly reviewed.

Strategy for achieving multiferroic E-type magnetic order in orthorhombic manganites RMnO3 (R = La-Lu)

Based on first-principles calculations, multiferroic properties of orthorhombic manganites (RMnO₃, R = La-Lu) with E-type ground state have been achieved by lanthanide contraction (chemical pressure) and/or external strain. Our research demonstrates that a smaller R radius within the octahedral voids in RMnO₃ results in the increase in the tilts of the octahedra but only a gentle change in the Jahn-Teller (JT) distortion. The reduction of the intraplane octahedral rotation angle and the narrowed e_g states and lifting t_2g band edge are mainly responsible for the intraplane magnetic transition from ferromagnetic (La-Gd) to zigzag-like spin arrangement (Ho-Lu). In turn, the center-broken E-type RMnO₃ bulk characterizes the dominated electronic polarization behavior, benefiting from their distortion response to small R substitution, which gives rise to the strong magnetoelectricity. Subsequently, we have figured out the strain strategy for obtaining an E-type transition in light rare-earth manganites (La-Gd) by imposing a series of hypothetical strains, where the small intraplane rotation angle (Θ) and large JT distortion favor the small aspect ratios of a/b and c/b, respectively. The strained LaMnO₃ and GdMnO₃ achieve E-type transitions successfully by imposing a modest compressive strain along the a- and c-axes and remaining free along the b-direction. Simultaneously, their polarization behaviors were comparatively studied. It was found that the size of the A-site rare-earth ions has a great influence on the external strain response, in addition to its effect on the magnetic phase transition.

Magneto-electric multiferroics: designing new materials from first-principles calculations

In parallel with the revival of interest for magneto-electric multiferroic materials in the beginning of the century, first-principles simulations have grown incredibly in efficiency during the last two decades. Density functional theory calculations, in particular, have so become a must-have tool for physicists and chemists in the multiferroic community. While these calculations were originally used to support and explain experimental behaviour, their interest has progressively moved to the design of novel magneto-electric multiferroic materials. In this article, we mainly focus on oxide perovskites, an important class of multifunctional material, and review some significant advances to which contributed first-principles calculations. We also briefly introduce the various theoretical developments that were at the core of all these advances.

Electronic Percolation Threshold of Self-Standing Ag-LaCoO3 Porous Electrodes for Practical Applications

Perovskite LaCoO3 materials have various applications, from selective permeable membranes and gas sensing devices to water splitting applications. However, the intrinsic electrical resistivity of the perovskite limits the applicative potential. To overcome that, Ag powder was used with LaCoO3 to obtain porous composite electrodes with enhanced conductivities. For that, a series of composite Ag-LaCoO3 powders were prepared into pellets and pre-sintered at various temperatures up to 1000 ∘C. Their structural properties and morphology were investigated by X-ray diffraction and scanning electron microscopy. The electronic transport of compacted specimens was studied by impedance spectroscopy. The results indicate that the presence of Ag acts as pre-sintering additive to obtain porous electrodes, with porosity values as high as 40% at 50 vol. % Ag. Moreover, the overall electrical resistivity of the composite electrodes varied well over four orders of magnitude. The results are discussed within the generalized Bruggeman theory for effective media comprising arbitrarily shaped metallic and semiconducting inclusions.

PolyDis: simple quantification tool for distortion of polyhedra in crystalline solids

A new simple approach to quantitative measures of coordination polyhedra distortions from ideal symmetry is provided with PolyDis. Within the mathematical basis, it minimizes the normalized displacements of given polyhedra to the ideal shape. Applications are discussed, where PolyDis was used to analyze the temperature dependent distortion of LaAlO3, rare earth metal radius dependent distortion of RMnO3 and the increasing structural distortion of (A 3N)As with varying alkaline earth metal, all being perovskites. Additionally, the more complex structures of SrCuRSe3 and CsCu3 R 2Se5 comprising trigonal prisms, octahedra and tetrahedra are treated with PolyDis.

First-principles study of the electric, magnetic, and orbital structure in perovskite ScMnO3

Perovskite ScMnO₃ has been synthesized under high temperature and high pressure. The magnetic ordering of this compound was proposed to be in the E-AFM state in previous theoretical research. Such magnetic ordering would lead the Mn³⁺ ions to be off-centered in the MnO₆ octahedra; however, this is not detected experimentally. To address this issue, we systematically investigate the magnetic, orbital, and electric structures of perovskite ScMnO₃ with first-principles calculations. It is found that its magnetic ground state is G-AFM and the magnetic ordering can explain the puzzle very well. Moreover, there is an unreported three-dimensional alternating cooperative orbital ordering in perovskite ScMnO₃. The antiferromagnetic coupling between the nearest-neighbor Mn³⁺ ions is stabilized by the strong octahedral distortions that decrease the ferromagnetic interaction between the e_g orbitals of the Mn³⁺ ions. In addition, we find that perovskite ScMnO₃ is a bipolar antiferromagnetic semiconductor in which completely spin-polarized currents with reversible spin polarization can be tuned simply by applying a gate voltage. Such controllability of the spin polarization of the current opens up new avenues for future spintronic devices. Our results not only suggest that the G-AFM phase is the ground magnetic state for perovskite ScMnO₃, but also enrich research in orbital ordering in rare-earth manganites.

The crystal structure and three-dimensional alternating complementary orbital ordering of perovskite ScMnO₃.

Tetramer Compound of Manganese Ions with Mixed Valence [MnII MnIII MnIV] and Its Spatial, Electronic, Magnetic, and Theoretical Studies

Using different spectroscopic techniques and computational calculations, we describe the structural and electromagnetic relationship that causes many interesting phenomena within a novel coordination compound with mixed valence manganese (II, III and IV) in its crystal and powder state. The novel compound [MnII MnIII MnIV(HL)2(H2L)2(H2O)4](NO3)2(H2O) 1 was obtained with the Schiff base (E)-2-((2-hydroxybenzylidene)amine)-2-(hydroximethyl)propane-1,3-diol, (H4L), and Mn(NO3)2.4H2O. The coordination reaction was promoted by the deprotonation of the ligand by the soft base triethylamine. The paper’s main contribution is the integration of the experimental and computational studies to explain the interesting magnetic behavior that the mixed valence manganese multimetallic core shows. The results presented herein, which are rarely found for Mn(II), (III) and (IV) complexes, will contribute to the understanding of the magnetic communication generated by the valence electrons and its repercussion in the local geometry and in the overall crystalline structure.

Crystal and Magnetic Structures and Properties of (Lu1- xMn x)MnO3 Solid Solutions

(Lu_{1- x}Mn _x)MnO₃ solid solutions, having the perovskite-type structure and Pnma space group, with 0 ≤ x ≤ 0.4 were synthesized by a high-pressure, high-temperature method at 6 GPa and about 1670 K from Lu₂O₃ and Mn₂O₃. Their crystal and magnetic structures were studied by neutron powder diffraction. The degree of octahedral MnO₆ tilting decreases in (Lu_{1- x}Mn _x)MnO₃ with increasing x. Only the incommensurate (IC) spin structure with a propagation vector of k = ( k₀, 0, 0) and k₀ ≈ 0.44 remains in (Lu_0.9Mn_0.1)MnO₃ in the whole temperature range below the Neel temperature T_N = 36 K, and the commensurate noncollinear E-type structure that has been reported in the literature for undoped o-LuMnO₃ is not observed. (Lu_{1- x}Mn _x)MnO₃ samples with 0.2 ≤ x ≤ 0.4 have a ferrimagnetic structure with a propagation vector of k = (0, 0, 0) and ferromagnetic (FM) ordering of Mn³⁺ and Mn⁴⁺ cations at the B site, which are antiferromagnetically coupled to a noncollinear predominantly FM arrangement of Mn²⁺ at the A site. The ferrimagnetic Curie temperature, T_C, increases monotonically from 67 K for x = 0.2 to 118 K for x = 0.4. Magnetic and dielectric properties of (Lu_{1- x}Mn _x)MnO₃ and a composition-temperature phase diagram are also reported.

Intrinsic Triple Order in A-site Columnar-Ordered Quadruple Perovskites: Proof of Concept

There is an emerging topic in the science of perovskite materials: A-site columnar-ordered A₂ A'A''B₄ O₁₂ quadruple perovskites, which have an intrinsic triple order at the A sites. However, in many examples reported so far, A' and A'' cations are the same, and the intrinsic triple order is hidden. Here, we investigate structural properties of Dy₂ CuMnMn₄ O₁₂ (1) and Ho₂ MnGaMn₄ O₁₂ (2) by neutron and X-ray powder diffraction and prove the triple order at the A sites. The cation distributions determined are [Ho₂ ]_A [Mn]_A' [Ga_0.66 Mn_0.34 ]_A'' [Mn_3.66 Ga_0.34 ]_B O₁₂ and [Dy₂ ]_A [Cu_0.73 Mn_0.27 ]_A' [Mn_0.80 Dy_0.20 ]_A'' [Mn_1.89 Cu_0.11 ]_B1 [Mn₂ ]_B2 O₁₂ . There are clear signatures of Jahn-Teller distortions in 1 and 2, and the orbital pattern is combined with an original type of charge ordering in 1. Columnar-ordered quadruple perovskites represent a new playground to study complex interactions between different electronic degrees of freedom. No long-range magnetic order was found in 2 by neutron diffraction, and its magnetic properties in low fields are dominated by an impurity with negative magnetization or magnetization reversal. On the other hand, 1 shows three magnetic transitions at 21, 125, and 160 K.

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.

Complex magnetic incommensurability and electronic charge transfer through the ferroelectric transition in multiferroic Co3TeO6

Polarized and unpolarized neutron diffractions have been carried out to investigate the nature of the magnetic structures and transitions in monoclinic Co₃TeO₆. As the temperature is lowered below 26 K long range order develops, which is fully incommensurate (ICM) in all three crystallographic directions. Below 19.5 K additional commensurate magnetic peaks develop, consistent with the Γ₄ irreducible representation, along with a splitting of the ICM peaks along the h direction which indicates that there are two separate sets of magnetic modulation vectors. Below 18 K, this small additional magnetic incommensurability disappears, ferroelectricity develops, an additional commensurate magnetic structure consistent with Γ₃ irreducible representation appears, and the k component of the ICM wave vector disappears. Synchrotron x-ray diffraction measurements demonstrate that there is a significant shift of the electronic charge distribution from the Te ions at the crystallographic 8 f sites to the neighboring Co and O ions. These results, together with the unusually small electric polarization, its strong magnetic field dependence, and the negative thermal expansion in all three lattice parameters, suggest this material is an antiferroelectric. Below15 K the k component of the ICM structure reappears, along with second-order ICM Bragg peaks, which polarized neutron data demonstrate are magnetic in origin.

MAGNDATA: towards a database of magnetic structures. I. The commensurate case

A free web page under the name MAGNDATA, which provides detailed quantitative information on more than 400 published magnetic structures, has been developed and is available at the Bilbao Crystallographic Server (http://www.cryst.ehu.es). It includes both commensurate and incommensurate structures. This first article is devoted to explaining the information available on commensurate magnetic structures. Each magnetic structure is described using magnetic symmetry, i.e. a magnetic space group (or Shubnikov group). This ensures a robust and unambiguous description of both atomic positions and magnetic moments within a common unique formalism. A non-standard setting of the magnetic space group is often used in order to keep the origin and unit-cell orientation of the paramagnetic phase, but a description in any desired setting is possible. Domain-related equivalent structures can also be downloaded. For each structure its magnetic point group is given, and the resulting constraints on any macroscopic tensor property of interest can be consulted. Any entry can be retrieved as a magCIF file, a file format under development by the International Union of Crystallography. An online visualization tool using Jmol is available, and the latest versions of VESTA and Jmol support the magCIF format, such that these programs can be used locally for visualization and analysis of any of the entries in the collection. The fact that magnetic structures are often reported without identifying their symmetry and/or with ambiguous information has in many cases forced a reinterpretation and transformation of the published data. Most of the structures in the collection possess a maximal magnetic symmetry within the constraints imposed by the magnetic propagation vector(s). When a lower symmetry is realized, it usually corresponds to an epikernel (isotropy subgroup) of one irreducible representation of the space group of the parent phase. Various examples of the structures present in this collection are discussed.

Symmetry conditions for type II multiferroicity in commensurate magnetic structures

Type II multiferroics are magnetically ordered phases that exhibit ferroelectricity as a magnetic induced effect. We show that in single-k magnetic phases the presence in the paramagnetic phase of non-symmorphic symmetry combined with some specific type of magnetic propagation vector can be sufficient for the occurrence of this type of multiferroic behaviour. Other symmetry scenarios especially favourable for spin driven multiferroicity are also presented. We review and classify known type II multiferroics under this viewpoint. In addition, some other magnetic phases which due to their symmetry properties can exhibit type II multiferroicity are pointed out.

Non-collinear magnetism in multiferroic perovskites

We present an overview of the current interest in non-collinear magnetism in multiferroic perovskite crystals. We first describe the different microscopic mechanisms giving rise to the non-collinearity of spins in this class of materials. We discuss, in particular, the interplay between non-collinear magnetism and ferroelectric and antiferrodistortive distortions of the perovskite structure, and how this can promote magnetoelectric responses. We then provide a literature survey on non-collinear multiferroic perovskites. We discuss numerous examples of spin cantings driving weak ferromagnetism in transition metal perovskites, and of spin-induced ferroelectricity as observed in the rare-earth based perovskites. These examples are chosen to best illustrate the fundamental role of non-collinear magnetism in the design of multiferroicity.

Flexoelectricity, incommensurate phases and the Lifshitz point

The solutions for the minimizers of the energy density f (q, p)  =  Aq² + Bq⁴ + p² + gA,B + β(q'p - p'q)+ |q'|² +κ|p'|²] describe the flexoelectric effect with a flexoelectric coupling coefficient β. The order parameters q and p can be visualized as strain and polarisation, respectively. The parameter κ denotes the ratio of intrinsic length scales for q and p. We show that the structural ground-states include 3 phases, namely the paraelastic state q  =  p  =  0, the ferroelastic state where polarization exists inside and near twin boundaries, and the incommensurate (modulated) phases with a very rich array of structural modulations ranging from nearly pure sine waves to kink arrays and ripple states. The phases coincide in the multicritical Lifshitz point. Linear flexoelectricity p~q' is encountered only approximately inside the ferroelastic phase and near the phase boundary between the paraelastic phase and the incommensurate phase. The relationship between the polarisation and the strain gradient is highly non-linear in all other states. The spatial profiles and energy distributions are discussed in detail.

Pressure dependent structural changes and predicted electrical polarization in perovskite RMnO₃

High pressure x-ray diffraction measurements on perovskite RMnO3 (R  =  Dy, Ho and Lu) reveal that varying structural changes occur for different R ions. Large lattice changes (orthorhombic strain) occur in DyMnO3 and HoMnO3 while the Jahn-Teller (JT) distortion remains stable. Conversely, in the small R-ion system LuMnO3, Mn-O bond distortions are observed between 4 and 8 GPa with a broad minimum in the JT distortion. High pressure infrared measurements indicate that a phonon near 390 cm(-1) corresponding to the complex motion of the Mn and O ions changes anomalously for LuMnO3. It softens in the 4-8 GPa region, which is consistent with the structural change in Mn-O bonds and then hardens at higher pressures. By contrast, the phonons continuously harden with increasing pressure for DyMnO3 and HoMnO3. Density functional theory methods show that E-phase LuMnO3 is the most stable phase up to the 10 GPa pressure examined. Simulations indicate that the distinct structural change under pressure in LuMnO3 can possibly be used to optimize the electric polarization by pressure/strain.

Pressure effect on the properties of magnetic moments and phase transitions in YMnO3 from first principles

We report the properties of magnetic, electronic, phonon frequencies and magnetic phase transitions in orthorhombic perovskite YMnO₃ by means of first-principles calculations.

Modulated minerals as potential ferroic materials

A list of potential (multi-) ferroic systems is derived based on the idea that structure gradients can generate ferroic distortions. Structure gradients are restricted here to structural modulations, which are commonly observed in natural minerals. These minerals contain transition metals and are prone to Jahn-Teller distortions and magnetic instabilities. The list contains mineral groups, which are often available in mineralogical collections.

An organic approach for nanostructured multiferroics

Multiferroics are materials that simultaneously exhibit more than one ferroic order parameters, such as ferroelectricity, ferroelasticity and ferromagnetism. Recently, multiferroicity has received a significant revival of interest due to the colossal magnetoelectric coupling effect for the development of nano-ferronics. In this mini-review, we focus on a recent study of ferroelectricity, magnetism and magnetoelectric coupling within the newly discovered organic charge-transfer complexes. A systemic understanding of the origin of organic ferroelectricity and magnetism is provided. Furthermore, based on the recent mechanism of the magnetoelectric coupling effect: spin-ordering-induced electric polarization and ferroelectricity-induced spin alignment, we further present the recent progress in organic charge-transfer multiferroics and metal-organic framework multiferroics. The coexistence of polarization and magnetism at room temperature of organic charge-transfer complexes will be critical for the development of all-organic multiferroics.

Multiferroic properties of o-LuMnO3 controlled by b-axis strain

Strain is a leading candidate for controlling magnetoelectric coupling in multiferroics. Here, we use x-ray diffraction to study the coupling between magnetic order and structural distortion in epitaxial films of the orthorhombic (o-) perovskite LuMnO(3). An antiferromagnetic spin canting in the E-type magnetic structure is shown to be related to the ferroelectrically induced structural distortion and to a change in the magnetic propagation vector. By comparing films of different orientations and thicknesses, these quantities are found to be controlled by b-axis strain. It is shown that compressive strain destabilizes the commensurate E-type structure and reduces its accompanying ferroelectric distortion.

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.

Influence of lone pair doping on the multiferroic property of orthorhombic HoMnO3: ab initio prediction

Using first principles density functional theory, we predict new multiferroic compounds Ho1/2A1/2MnO3 (A = As, Sb, Bi) with enhanced polarization. We find that doping of lone pair cations with different ionic radii, at the A-site of orthorhombic HoMnO3, results in a marked increase of the electronic polarization and its development along the b-axis. This development of electronic polarization along the b-axis is attributed to the breaking of the two-fold rotational symmetry which leads to the emergence of a polar b-axis. Furthermore, this symmetry breaking leads to the emergence of two inequivalent Mn ions (Mn(0) and Mn(1)) and the variance in their octahedral (Mn(0)O6 and Mn(1)O6) distortions. We rationalize the observed trends in the total polarization in terms of disparate eg electron hopping along the two different Mn(0) and Mn(1) chains. We expect large ionic polarization in the doped compounds due to the presence of 4s(2) As, 5s(2) Sb and 6s(2) Bi lone pairs, but surprisingly the effect of the lone pairs seems to be inactive. This is attributed to the strong GdFeO3 distortions exhibited by the MnO6 octahedron which hinders polar displacement of the lone pair cations.

Structural and magnetic properties of spontaneously phase-separated Eu0.5Sm0.5MnO3

We have studied structural and magnetic properties of Eu(0.5)Sm(0.5)MnO(3). The system shows strong orthorhombic distortion. The static Jahn-Teller effect modifies the low temperature magnetic properties, creating a complicated anisotropic magnetic ground state. A low temperature magnetic phase separation has also been realized that builds magnetic interfaces exhibiting strong exchange bias. Careful analysis of the magnetic behaviour indicates the origin of the exchange bias to be a phase separation between an A-type antiferromagnetic phase and a low temperature highly anisotropic phase originating from another ordering at the rare-earth sublattice.

Spin model of magnetostrictions in multiferroic Mn perovskites

We theoretically study origins of the ferroelectricity in the multiferroic phases of the rare-earth (R) Mn perovskites, RMnO(3), by constructing a realistic spin model including the spin-phonon coupling, which reproduces the entire experimental phase diagram in the plane of temperature and Mn-O-Mn bond angle for the first time. Surprisingly we reveal a significant contribution of the symmetric (S·S)-type magnetostriction to the ferroelectricity even in a spin-spiral-based multiferroic phase, which can be larger than the usually expected antisymmetric (S×S)-type contribution. This explains well the nontrivial behavior of the electric polarization. We also predict the noncollinear deformation of the E-type spin structure and a wide coexisting regime of the E and spiral states, which resolve several experimental puzzles.

First principles studies of multiferroic materials

Multiferroics, materials where spontaneous long-range magnetic and dipolar orders coexist, represent an attractive class of compounds, which combine rich and fascinating fundamental physics with a technologically appealing potential for applications in the general area of spintronics. Ab initio calculations have significantly contributed to recent progress in this area, by elucidating different mechanisms for multiferroicity and providing essential information on various compounds where these effects are manifestly at play. In particular, here we present examples of density-functional theory investigations for two main classes of materials: (a) multiferroics where ferroelectricity is driven by hybridization or purely structural effects, with BiFeO(3) as the prototype material, and (b) multiferroics where ferroelectricity is driven by correlation effects and is strongly linked to electronic degrees of freedom such as spin-, charge-, or orbital-ordering, with rare-earth manganites as prototypes. As for the first class of multiferroics, first principles calculations are shown to provide an accurate qualitative and quantitative description of the physics in BiFeO(3), ranging from the prediction of large ferroelectric polarization and weak ferromagnetism, over the effect of epitaxial strain, to the identification of possible scenarios for coupling between ferroelectric and magnetic order. For the second class of multiferroics, ab initio calculations have shown that, in those cases where spin-ordering breaks inversion symmetry (e.g. in antiferromagnetic E-type HoMnO(3)), the magnetically induced ferroelectric polarization can be as large as a few µC cm(-2). The examples presented point the way to several possible avenues for future research: on the technological side, first principles simulations can contribute to a rational materials design, aimed at identifying spintronic materials that exhibit ferromagnetism and ferroelectricity at or above room temperature. On the fundamental side, ab initio approaches can be used to explore new mechanisms for ferroelectricity by exploiting electronic correlations that are at play in transition metal oxides, and by suggesting ways to maximize the strength of these effects as well as the corresponding ordering temperatures.

Phase transitions and rare-earth magnetism in hexagonal and orthorhombic DyMnO(3) single crystals

The floating-zone method with different growth ambiences has been used to selectively obtain hexagonal or orthorhombic DyMnO(3) single crystals. The crystals were characterized by x-ray powder diffraction of ground specimens and a structure refinement as well as electron diffraction. We report magnetic susceptibility, magnetization and specific heat studies of this multiferroic compound in both the hexagonal and the orthorhombic structure. The hexagonal DyMnO(3) shows magnetic ordering of Mn(3+) (S = 2) spins on a triangular Mn lattice at T(N)(Mn) = 57 K characterized by a cusp in the specific heat. This transition is not apparent in the magnetic susceptibility due to the frustration on the Mn triangular lattice and the dominating paramagnetic susceptibility of the Dy(3+) (S = 9/2) spins. At T(N)(Dy) = 3 K, a partial antiferromagnetic order of Dy moments has been observed. In comparison, the magnetic data for orthorhombic DyMnO(3) display three transitions. The data broadly agree with results from earlier neutron diffraction experiments, which allows for the following assignment: a transition from an incommensurate antiferromagnetic ordering of Mn(3+) spins at T(N)(Mn) = 39 K, a lock-in transition at T(lock-in) = 16 K and a second antiferromagnetic transition at T(N)(Dy) = 5 K due to the ordering of Dy moments. Both the hexagonal and the orthorhombic crystals show magnetic anisotropy and complex magnetic properties due to 4f-4f and 4f-3d couplings.

Strain-induced effects on antiferromagnetic ordering and magnetocapacitance in orthorhombic HoMnO(3) thin films

We investigated the magnetic and ferroelectric properties of c-axis oriented orthorhombic phase HoMnO(3) (o-HMO in Pbnm symmetry setting) thin films grown on Nb-doped SrTiO(3)(001) substrates. The o-HMO films exhibit an antiferromagnetic ordering near 42 K, irrespective of the orientation of the applied field. However, an additional magnetic ordering occurring around 35 K was observed when the field was applied along the c-axis of o-HMO, which was absent when the field was applied in the ab-plane. The magnetocapacitance measured along the c-axis showed that although there is evidence of dielectric constant enhancement when the temperature is below 35 K the expected abrupt change in dielectric constant appears at a much lower temperature and reaches maximum around 13.5 K, indicating that the low-temperature c-axis polarization might be related to the ordering of the Ho(3+) moment. The lattice constant analyses using x-ray diffraction and the observation of a slight magnetization hysteresis suggest that the weak second magnetic transition along the c-axis at 35 K might be more relevant to the strain-induced effect on antiferromagnetism.

First principles study of improper ferroelectricity in TbMnO3

We carry out a first-principles theoretical study of the magnetically induced polarization in orthorhombic TbMnO3, a prototypical material in which a cycloidal-spin structure generates an electric polarization via the spin-orbit interaction. We compute both the electronic and the lattice-mediated contributions to the polarization and find that the latter is strongly dominant. We analyze the spin-orbit induced forces and lattice displacements from both atomic and mode-decomposition viewpoints, and show that a simple model based on nearest Mn-Mn neighbor Dzyaloshinskii-Moriya interactions is not able to account fully for the results. The direction and magnitude of our computed polarization are in good agreement with experiment.

Dual nature of improper ferroelectricity in a magnetoelectric multiferroic

Using first-principles calculations, we study the microscopic origin of ferroelectricity (FE) induced by magnetic order in the orthorhombic HoMnO3. We obtain the largest ferroelectric polarization observed in the whole class of improper magnetic ferroelectrics to date. We find that the two proposed mechanisms for FE in multiferroics, lattice and electronic based, are simultaneously active in this compound: a large portion of the ferroelectric polarization arises due to quantum-mechanical effects of electron orbital polarization, in addition to the conventional polar atomic displacements. An interesting mechanism for switching the magnetoelectric domains by an electric field via a 180 degrees coherent rotation of Mn spins is also proposed.

Coupling of frustrated ising spins to the magnetic cycloid in multiferroic TbMnO(3)

We report on diffraction measurements on multiferroic TbMnO(3) which demonstrate that the Tb- and Mn-magnetic orders are coupled below the ferroelectric transition T(FE) = 28 K. For T<T(FE) the magnetic propagation vectors (tau) for Tb and Mn are locked so that tau(Tb) = tau(Mn), while below T(N)(Tb) = 7 K we find that tau(Tb) and tau(Mn) lock-in to rational values of 3/7b* and 2/7b*, respectively, and obey the relation 3tau(Tb)-tau(Mn)=1. We explain this novel matching of wave vectors within the frustrated anisotropic next-nearest-neighbor Ising model coupled to a periodic external field produced by the Mn-spin order. The tau(Tb)=tau(Mn) behavior is recovered when Tb magnetization is small, while the tau(Tb) = 3/7 regime is stabilized at low temperatures by a peculiar arrangement of domain walls in the ordered state of Ising-like Tb spins.

Chemical size effect on the magnetic and electrical properties in the (Tb(1-)(x)Eu(x))MnO(3) (0 < or = x < or = 1.0) system

The effect of isovalent chemical substitution of Eu3+ into the Tb3+ sites on the magnetic and electrical properties of (Tb1-xEux)MnO3 (0 </= x </= 1.0) system has been investigated. The orthorhombic structure with space group Pbnm is observed in this series of materials. An increase in Mn-O bond distance with increasing Eu content leads to improvement in the overlap between the Mn 3d and O 2p orbital thereby causing a decrease in activation energy and resistivity. Moreover, as the Eu content increases, the effective moments (mueff) are reduced linearly and an exchange coupling is observed in Tb-Tb, Tb-Eu, and Eu-Eu complexes for x = 0.1 and 0.3 samples. Both these features can be related to the substitution of bigger Eu3+ ions replacing the original Tb-Tb coupling.

Ferroelectricity in the magnetic E-phase of orthorhombic perovskites

We show that the symmetry of the spin zigzag chain E phase of the orthorhombic perovskite manganites and nickelates allows for the existence of a finite ferroelectric polarization. The proposed microscopic mechanism is independent of spin-orbit coupling. We predict that the polarization induced by the E-type magnetic order can potentially be enhanced by up to 2 orders of magnitude with respect to that in the spiral magnetic phases of TbMnO3 and similar multiferroic compounds.

Unusual evolution of the magnetic interactions versus structural distortions in RMnO3 perovskites

We report the refinement of x-ray powder diffraction together with magnetic and thermal conductivity measurements made on the entire family of RMnO3 perovskites prepared by melt growth or under high pressure. Analysis of the data has identified the origin of the transition from type-A to type-E magnetic order as a competition between t-orbital and e-orbital spin-spin interactions within each Mn-O-Mn bond in the (001) planes, the e-orbital interactions decreasing with decreasing R3+-ion size.

Ferroelectricity and giant magnetocapacitance in perovskite rare-earth manganites

The relationships among magnetism, lattice modulation, and dielectric properties have been investigated for RMnO3 (R=Eu, Gd, Tb, and Dy). These compounds show a transition to an incommensurate lattice structure below their Néel temperature, and subsequently undergo an incommensurate-commensurate (IC-C) phase transition. For TbMnO3 and DyMnO3 it was found that the IC-C transition is accompanied by a ferroelectric transition, associated with a lattice modulation in the C phase. DyMnO3 shows a gigantic magnetocapacitance with a change of dielectric constant up to Deltaepsilon/epsilon approximately 500%.

Unveiling new magnetic phases of undoped and doped manganites

Novel ground-state spin structures in undoped and lightly doped manganites are investigated based on the orbital-degenerate double-exchange model, via mean-field and numerical techniques. In undoped manganites, a new antiferromagnetic (AFM) state, called the E-type phase, is found adjacent in parameter space to the A-type AFM phase. Its structure is in agreement with recent experimental results. This insulating E-AFM state is also competing with a ferromagnetic metallic phase as well. For doped layered manganites, the phase diagram includes another new AFM phase of the CxE1-x type. Experimental signatures of the new phases are discussed.