Bound States of Skyrmions and Merons near the Lifshitz Point.

We study topological defects in anisotropic ferromagnets with competing interactions near the Lifshitz point. We show that Skyrmions and bimerons are stable in a large part of the phase diagram. We calculate Skyrmion-Skyrmion and meron-meron interactions and show that Skyrmions attract each other and form ring-shaped bound states in a zero magnetic field. At the Lifshitz point merons carrying a fractional topological charge become deconfined. These results imply that unusual topological excitations may exist in weakly frustrated magnets with conventional crystal lattices.

Edge states and skyrmion dynamics in nanostripes of frustrated magnets.

Magnetic skyrmions are particle-like topological excitations recently discovered in chiral magnets. Their small size, topological protection and the ease with which they can be manipulated by electric currents generated much interest in using skyrmions for information storage and processing. Recently, it was suggested that skyrmions with additional degrees of freedom can exist in magnetically frustrated materials. Here, we show that dynamics of skyrmions and antiskyrmions in nanostripes of frustrated magnets is strongly affected by complex spin states formed at the stripe edges. These states create multiple edge channels which guide the skyrmion motion. Non-trivial topology of edge states gives rise to complex current-induced dynamics, such as emission of skyrmion-antiskyrmion pairs. The edge-state topology can be controlled with an electric current through the exchange of skyrmions and antiskyrmions between the edges of a magnetic nanostructure.

Multiply periodic states and isolated skyrmions in an anisotropic frustrated magnet.

Multiply periodic states appear in a wide variety of physical contexts, such as the Rayleigh-Bénard convection, Faraday waves, liquid crystals and skyrmion crystals recently observed in chiral magnets. Here we study the phase diagram of an anisotropic frustrated magnet which contains five different multiply periodic states including the skyrmion crystal. We clarify the mechanism for stabilization of these states and discuss how they can be observed in magnetic resonance and electric polarization measurements. We also find stable isolated skyrmions with topological charge 1 and 2. Their spin structure, interactions and dynamics are more complex than those in chiral magnets. In particular, magnetic resonance in the skyrmion crystal should be accompanied by oscillations of the electric polarization with a frequency depending on the amplitude of the a.c. magnetic field. These results show that skyrmion materials with rich physical properties can be found among frustrated magnets. We formulate rules to help the search.

Artificial chemical and magnetic structure at the domain walls of an epitaxial oxide.

Progress in nanotechnology requires new approaches to materials synthesis that make it possible to control material functionality down to the smallest scales. An objective of materials research is to achieve enhanced control over the physical properties of materials such as ferromagnets, ferroelectrics and superconductors. In this context, complex oxides and inorganic perovskites are attractive because slight adjustments of their atomic structures can produce large physical responses and result in multiple functionalities. In addition, these materials often contain ferroelastic domains. The intrinsic symmetry breaking that takes place at the domain walls can induce properties absent from the domains themselves, such as magnetic or ferroelectric order and other functionalities, as well as coupling between them. Moreover, large domain wall densities create intense strain gradients, which can also affect the material's properties. Here we show that, owing to large local stresses, domain walls can promote the formation of unusual phases. In this sense, the domain walls can function as nanoscale chemical reactors. We synthesize a two-dimensional ferromagnetic phase at the domain walls of the orthorhombic perovskite terbium manganite (TbMnO3), which was grown in thin layers under epitaxial strain on strontium titanate (SrTiO3) substrates. This phase is yet to be created by standard chemical routes. The density of the two-dimensional sheets can be tuned by changing the film thickness or the substrate lattice parameter (that is, the epitaxial strain), and the distance between sheets can be made as small as 5 nanometres in ultrathin films, such that the new phase at domain walls represents up to 25 per cent of the film volume. The general concept of using domain walls of epitaxial oxides to promote the formation of unusual phases may be applicable to other materials systems, thus giving access to new classes of nanoscale materials for applications in nanoelectronics and spintronics.

Unfolding of vortices into topological stripes in a multiferroic material.

Multiferroic hexagonal RMnO(3) (R=rare earths) crystals exhibit dense networks of vortex lines at which six domain walls merge. While the domain walls can be readily moved with an applied electric field, the vortex cores so far have been impossible to control. Our experiments demonstrate that shear strain induces a Magnus-type force pulling vortices and antivortices in opposite directions and unfolding them into a topological stripe domain state. We discuss the analogy between this effect and the current-driven dynamics of vortices in superconductors and superfluids.

Thermally driven ratchet motion of a skyrmion microcrystal and topological magnon Hall effect.

Spontaneously emergent chirality is an issue of fundamental importance across the natural sciences. It has been argued that a unidirectional (chiral) rotation of a mechanical ratchet is forbidden in thermal equilibrium, but becomes possible in systems out of equilibrium. Here we report our finding that a topologically nontrivial spin texture known as a skyrmion--a particle-like object in which spins point in all directions to wrap a sphere--constitutes such a ratchet. By means of Lorentz transmission electron microscopy we show that micrometre-sized crystals of skyrmions in thin films of Cu2OSeO3 and MnSi exhibit a unidirectional rotation motion. Our numerical simulations based on a stochastic Landau-Lifshitz-Gilbert equation suggest that this rotation is driven solely by thermal fluctuations in the presence of a temperature gradient, whereas in thermal equilibrium it is forbidden by the Bohr-van Leeuwen theorem. We show that the rotational flow of magnons driven by the effective magnetic field of skyrmions gives rise to the skyrmion rotation, therefore suggesting that magnons can be used to control the motion of these spin textures.

Direct visualization of magnetoelectric domains.

The coupling between the magnetic and electric dipoles in multiferroic and magnetoelectric materials holds promise for conceptually novel electronic devices. This calls for the development of local probes of the magnetoelectric response, which is strongly affected by defects in magnetic and ferroelectric ground states. For example, multiferroic hexagonal rare earth manganites exhibit a dense network of boundaries between six degenerate states of their crystal lattice, which are locked to both ferroelectric and magnetic domain walls. Here we present the application of a magnetoelectric force microscopy technique that combines magnetic force microscopy with in situ modulating high electric fields. This method allows us to image the magnetoelectric response of the domain patterns in hexagonal manganites directly. We find that this response changes sign at each structural domain wall, a result that is corroborated by symmetry analysis and phenomenological modelling, and provides compelling evidence for a lattice-mediated magnetoelectric coupling. The direct visualization of magnetoelectric domains at mesoscopic scales opens up explorations of emergent phenomena in multifunctional materials with multiple coupled orders.

Linear magnetoelectric effect by orbital magnetism.

We use symmetry analysis and first-principles calculations to show that the linear magnetoelectric effect can originate from the response of orbital magnetic moments to the polar distortions induced by an applied electric field. Using LiFePO(4) as a model compound we show that spin-orbit coupling partially lifts the quenching of the 3d orbitals and causes small orbital magnetic moments (µ((L)) ≈ 0.3 µ(B)) parallel to the spins of the Fe(2+) ions. An applied electric field E modifies the size of these orbital magnetic moments inducing a net magnetization linear in E.

Anisotropic conductance at improper ferroelectric domain walls.

Transition metal oxides hold great potential for the development of new device paradigms because of the field-tunable functionalities driven by their strong electronic correlations, combined with their earth abundance and environmental friendliness. Recently, the interfaces between transition-metal oxides have revealed striking phenomena, such as insulator-metal transitions, magnetism, magnetoresistance and superconductivity. Such oxide interfaces are usually produced by sophisticated layer-by-layer growth techniques, which can yield high-quality, epitaxial interfaces with almost monolayer control of atomic positions. The resulting interfaces, however, are fixed in space by the arrangement of the atoms. Here we demonstrate a route to overcoming this geometric limitation. We show that the electrical conductance at the interfacial ferroelectric domain walls in hexagonal ErMnO(3) is a continuous function of the domain wall orientation, with a range of an order of magnitude. We explain the observed behaviour using first-principles density functional and phenomenological theories, and relate it to the unexpected stability of head-to-head and tail-to-tail domain walls in ErMnO(3) and related hexagonal manganites. As the domain wall orientation in ferroelectrics is tunable using modest external electric fields, our finding opens a degree of freedom that is not accessible to spatially fixed interfaces.

Magnetic excitations in the low-temperature ferroelectric phase of multiferroic YMn2O5 using inelastic neutron scattering.

We studied magnetic excitations in a low-temperature ferroelectric phase of the multiferroic YMn(2)O(5) using inelastic neutron scattering (INS). We identify low-energy magnon modes and establish a correspondence between the magnon peaks observed by INS and electromagnon peaks observed in optical absorption [A. B. Sushkov et al., Phys. Rev. Lett. 98, 027202 (2007).]. Furthermore, we explain the microscopic mechanism, which results in the lowest-energy electromagnon peak, by comparing the inelastic neutron spectral weight with the polarization in the commensurate ferroelectric phase.

Origin of electromagnon excitations in multiferroic RMnO3.

Electromagnon excitations in multiferroic orthorhombic RMnO3 are shown to result from the Heisenberg coupling between spins despite the fact that the static polarization arises from the much weaker Dzyaloshinskii-Moriya exchange interaction. We present a model incorporating the structural characteristics of this family of manganites that is confirmed by far infrared transmission data as a function of temperature and magnetic field and inelastic neutron scattering results. A deep connection is found between the magnetoelectric dynamics of the spiral phase and the static magnetoelectric coupling in the collinear E phase of this family of manganites.

Scaling behavior of the magnetocapacitance of YbMnO(3).

We observe a seemingly complex magnetic field dependence of the dielectric constant of hexagonal YbMnO(3) near the spin ordering temperature. After rescaling, the data taken at different temperatures and magnetic fields collapse on a single curve describing the sharp anomaly in nonlinear magnetoelectric response at the magnetic transition. We show that this anomaly is a result of the competition between two magnetic phases. The scaling and the shape of the anomaly are explained using the phenomenological Landau description of the competing phases in hexagonal manganites.

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

Mode softening, ferroelectric transition, and tunable photonic band structures in a point-dipole crystal.

We study the photonic band structure of cubic crystals of point dipoles. It is shown that in contrast to earlier claims these systems cannot have an omnidirectional photonic band gap. For sufficiently large plasma frequencies, however, they exhibit softening of photonic bands, leading to (anti)ferroelectric ordering of the dipoles and the possibility to open and tune directional band gaps by external electric fields. The model studied may be realized through lattices of quantum dots.

Orbital ordering in charge transfer insulators.

We discuss a new mechanism of orbital ordering, which in charge transfer insulators is more important than the usual exchange interactions and which can make the very type of the ground state of a charge transfer insulator, i.e., its orbital and magnetic ordering, different from that of a Mott-Hubbard insulator. This purely electronic mechanism allows us to explain why orbitals in Jahn-Teller materials typically order at higher temperatures than spins, and to understand the type of orbital ordering in a number of materials, e.g., K2CuF4, without invoking the electron-lattice interaction.

Frustrated spin model as a hard-sphere liquid.

We show that one-dimensional topological objects (kinks) are natural degrees of freedom for an antiferromagnetic Ising model on a triangular lattice. Its ground states and the coexistence of spin ordering with an extensive zero-temperature entropy can easily be understood in terms of kinks forming a hard-sphere liquid. Using this picture we explain effects of quantum spin dynamics on that frustrated model, which we also study numerically.

Charge-ordering signatures in the optical properties of beta-Na0.33V2O5.

Temperature dependent optical spectra are reported for beta-Na0.33V2O5. The sodium ordering transition at T(Na)=240 K and, in particular, the charge ordering transition at T(MI)=136 K strongly influence the optical spectra. The metal-insulator transition at T(MI) leads to the opening of a pseudogap ( variant Planck's over 2pi omega=1700 cm(-1)) and to the appearance of a large number of optical phonons. These observations and the presence of a midinfrared band (typical for low dimensional metals) strongly suggest that the charge carriers in beta-Na0.33V2O5 are small polarons.

Orbital ordering in frustrated Jahn-Teller systems with 90 degrees exchange.

We show that superexchange interactions in frustrated Jahn-Teller systems with transition metal ions connected by the 90 degrees metal-oxygen-metal bonds (e.g., NaNiO2, LiNiO2, and ZnMn2O4) are much different from those in materials with the 180 degrees bonds. In the 90 degrees -exchange systems spins and orbitals are decoupled: the spin exchange is much weaker than the orbital one and it is ferromagnetic for all orbital states. Though the mean-field orbital ground state is strongly degenerate, quantum orbital fluctuations select particular ferro-orbital states. We explain the orbital and magnetic ordering observed in NaNiO2 and show that LiNiO2 is not a spin-orbital liquid.

Peierls transition with acoustic phonons and solitwistons in carbon nanotubes.

We show that the Peierls instability can result in softening of acoustic phonons with small wave vectors and suggest that this unusual transition takes place in carbon nanotubes, resulting in a static twist deformation of the nanotube lattice. The topological excitations in the ordered phase are immobile and propagate only in pairs.