Complex topological configurations are fertile ground for exploring emergent phenomena and exotic phases in condensed-matter physics. For example, the recent discovery of polarization vortices and their associated complex-phase coexistence and response under applied electric fields in superlattices of (PbTiO3)n/(SrTiO3)n suggests the presence of a complex, multi-dimensional system capable of interesting physical responses, such as chirality, negative capacitance and large piezo-electric responses1-3. Here, by varying epitaxial constraints, we discover room-temperature polar-skyrmion bubbles in a lead titanate layer confined by strontium titanate layers, which are imaged by atomic-resolution scanning transmission electron microscopy. Phase-field modelling and second-principles calculations reveal that the polar-skyrmion bubbles have a skyrmion number of +1, and resonant soft-X-ray diffraction experiments show circular dichroism, confirming chirality. Such nanometre-scale polar-skyrmion bubbles are the electric analogues of magnetic skyrmions, and could contribute to the advancement of ferroelectrics towards functionalities incorporating emergent chirality and electrically controllable negative capacitance.

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Observation of room-temperature polar skyrmions

The generalization of the Local Density Approximation (LDA) method for the systems with strong Coulomb correlations is presented which gives a correct description of the Mott insulators. The LDA+U method is based on the model hamiltonian approach and allows to take into account the non-sphericity of the Coulomb and exchange interactions. parameters. Orbital-dependent LDA+U potential gives correct orbital polarization and corresponding Jahn-Teller distortion. To calculate the spectra of the strongly correlated systems the impurity Anderson model should be solved with a many-electron trial wave function. All parameters of the many-electron hamiltonian are taken from LDA+U calculations. The method was applied to NiO and has shown good agreement with experimental photoemission spectra and with the oxygen Kα X-ray emission spectrum.

http://absimage.aps.org/image/MAR06/MWS_MAR06-2005-007233.pdf

First-principles calculations of electronic structure and spectra of strongly correlated systems: the LDA+U method

The helicity-orbital coupling is an intriguing feature of magnetic skyrmions in frustrated magnets. Here we explore the skyrmion dynamics in a frustrated magnet based on the J
 1-J
 2-J
 3 classical Heisenberg model explicitly by including the dipole-dipole interaction. The skyrmion energy acquires a helicity dependence due to the dipole-dipole interaction, resulting in the current-induced translational motion with a fixed helicity. The lowest-energy states are the degenerate Bloch-type states, which can be used for building the binary memory. By increasing the driving current, the helicity locking-unlocking transition occurs, where the translational motion changes to the rotational motion. Furthermore, we demonstrate that two skyrmions can spontaneously form a bound state. The separation of the bound state forced by a driving current is also studied. In addition, we show the annihilation of a pair of skyrmion and antiskyrmion. Our results reveal the distinctive frustrated skyrmions may enable viable applications in topological magnetism. Exploring the helicity-orbital coupling induced skyrmion properties is essential for the spintronic applications. Here the authors report the current controlled skyrmions and antiskyrmions dynamics with locking-unlocking helicity in frustrated magnets by including the dipole-dipole interaction in their model.

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Skyrmion dynamics in a frustrated ferromagnetic film and current-induced helicity locking-unlocking transition.

A previous study of the growth conditions has shown that single-phase BiFeO3 thin films can only be obtained in a narrow pressure-temperature window and that these films display a weak magnetic moment. Here we study in more detail the structure and the magnetism of single-phase BiFeO3 films by means of reciprocal space mapping, Raman spectroscopy and neutron diffraction. X-ray and Raman data suggest that the BiFeO3 structure is tetragonal for 70 nm-thick films and changes to monoclinic for 240 nm-thick films, thus remaining different from that of the bulk (rhombohedral) structure. In the 240 nm monoclinically distorted film neutron diffraction experiments allow the observation of a G-type antiferromagnetic order as in bulk single crystals. However, the satellite peaks associated with the long-wavelength cycloid present in bulk BiFeO3 are not observed. The relevance of these findings for the exploitation of the magnetoelectric properties of BiFeO3 is discussed.

Structural distortion and magnetism of BiFeO3 epitaxial thin films: a Raman spectroscopy and neutron diffraction study

Systems that exhibit phase competition, order parameter coexistence, and emergent order parameter topologies constitute a major part of modern condensed-matter physics. Here, by applying a range of characterization techniques, and simulations, we observe that in PbTiO3/SrTiO3 superlattices all of these effects can be found. By exploring superlattice period-, temperature- and field-dependent evolution of these structures, we observe several new features. First, it is possible to engineer phase coexistence mediated by a first-order phase transition between an emergent, low-temperature vortex phase with electric toroidal order and a high-temperature ferroelectric a1/a2 phase. At room temperature, the coexisting vortex and ferroelectric phases form a mesoscale, fibre-textured hierarchical superstructure. The vortex phase possesses an axial polarization, set by the net polarization of the surrounding ferroelectric domains, such that it possesses a multi-order-parameter state and belongs to a class of gyrotropic electrotoroidal compounds. Finally, application of electric fields to this mixed-phase system permits interconversion between the vortex and the ferroelectric phases concomitant with order-of-magnitude changes in piezoelectric and nonlinear optical responses. Our findings suggest new cross-coupled functionalities.

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Phase coexistence and electric-field control of toroidal order in oxide superlattices.

Non-coplanar swirling field textures, or skyrmions, are now widely recognized as objects of both fundamental interest and technological relevance. So far, skyrmions were amply investigated in magnets, where due to the presence of chiral interactions, these topological objects were found to be intrinsically stabilized. Ferroelectrics on the other hand, lacking such chiral interactions, were somewhat left aside in this quest. Here we demonstrate, via the use of a first-principles-based framework, that skyrmionic configuration of polarization can be extrinsically stabilized in ferroelectric nanocomposites. The interplay between the considered confined geometry and the dipolar interaction underlying the ferroelectric phase instability induces skyrmionic configurations. The topological structure of the obtained electrical skyrmion can be mapped onto the topology of domain-wall junctions. Furthermore, the stabilized electrical skyrmion can be as small as a few nanometers, thus revealing prospective skyrmion-based applications of ferroelectric nanocomposites.

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Discovery of stable skyrmionic state in ferroelectric nanocomposites

An energetic expression containing four different macroscopic terms is proposed to explain and understand coupled magnetic orders (and the directions of the simultaneously occurring ferromagnetic and/or antiferromagnetic vectors) in terms of anti-phase and/or in-phase tilting of oxygen octahedra in magnetic and multiferroic perovskites. This expression is derived from a suggested simple microscopic formula, and has its roots in the Dzyaloshinsky–Moriya interaction. Comparison with data available in the literature and with first-principles calculations we conduct here confirms the validity of such a simple and general law for any tested structural paraelectric and even ferroelectric phase, and for any chosen direction of any selected primary magnetic vector.

http://iopscience.iop.org/article/10.1088/0953-8984/24/31/312201/pdf

A simple law governing coupled magnetic orders in perovskites

This work is financially supported by ONR Grants No. N00014-11-1-0384, No. 00014-12-1-1034, and No. N00014-08-1-0915 (S.P. and L.B., for contributing to analytical derivations and phenomenology), ARO Grant No. W911NF-12-1- 0085 (Z.G. and L.B. for atomistic simulations under ac fields), and NSF Grant No. DMR-1066158 (L.L., R.W., and L.B for some effective Hamiltonian computations). I.S. acknowledges support from Grant No. MAT2012-33720 from the Spanish Ministerio de Economia y Competitividad. S.P. appreciates Grant No. 12-08-00887-a from the Russian Foundation for Basic Research. L.B. also acknowledges discussions with scientists sponsored by the Department of Energy, Office of
Basic Energy Sciences, under Contract No. ER-46612, Javier Junquera, Pablo Aguado-Puente, and Surendra Singh.

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Natural optical activity and its control by electric field in electrotoroidic systems

Combining temperature-dependent x-ray diffraction, Raman spectroscopy and first-principles-based effective Hamiltonian calculations, we show that varying the thickness of (Ba0.8Sr0.2)TiO3 (BST) thin films deposited on the same single substrate (namely, MgO) enables us to change not only the magnitude but also the sign of the misfit strain. Such previously overlooked control of the strain allows several properties of these films (e.g. Curie temperature, symmetry of ferroelectric phases, dielectric response) to be tuned and even optimized. Surprisingly, such desired control of the strain (and of the resulting properties) originates from an effect that is commonly believed to be detrimental to functionalities of films, namely the existence of misfit dislocations. The present study therefore provides a novel route to strain engineering, as well as leading us to revisit common beliefs.

https://iopscience.iop.org/article/10.1088/0953-8984/26/29/292201/pdf

Strain engineering of perovskite thin films using a single substrate.

A first-principles-based effective Hamiltonian approach is used to simulate the temperature-versus-misfit strain phase diagram of epitaxial (110) BaTiO${}_{3}$ (BTO) thin films. Unusual features are discovered that significantly differ from those found in BTO films grown along the ``usual'' [001] direction. Examples include the independency of the Curie temperature with compressive strain and the existence of specific monoclinic and triclinic phases near room temperature. These low-symmetry phases are associated with a rapid strain-induced rotation of the polarization and possess large piezoelectric and dielectric responses. Our atomistic technique provides an insight into these novel features, as well as other predicted phenomena.

/pdf/properties-of-epitaxial-110-batio-3-films-from-first-2f78zzsb6h.pdf

Zhigang Gui

Papers

Discovery of stable skyrmionic state in ferroelectric nanocomposites

A simple law governing coupled magnetic orders in perovskites

Natural optical activity and its control by electric field in electrotoroidic systems

Strain engineering of perovskite thin films using a single substrate.

Properties of epitaxial (110) BaTiO 3 films from first principles