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1Since the 1950s Heisenberg and others have attempted to explain the appearance of countable particles in quantum field theory in terms of stable localized field configurations [1]. As an exception Skyrme's model succeeded to describe nuclear particles as localized states, so-called 'skyrmions', within a non-linear field theory [2]. Skyrmions are a characteristic of non-linear continuum models ranging from microscopic to cosmological scales [3,4,5,6]. Skyrmionic states have been found under non-equilibrium conditions, or when stabilised by external fields or the proliferation of topological defects. Examples are Turing patterns in classical liquids [7], spin textures in quantum Hall magnets [8], or the blue phases in liquid crystals [9], respectively. However, it is believed that skyrmions cannot form spontaneous ground states like ferromagnetic or antiferromagnetic order in magnetic materials. Here, we show theoretically that this assumption is wrong and that skyrmion textures may form spontaneously in condensed matter systems with chiral interactions without the assistance of external fields or the proliferation of defects. We show this within a phenomenological continuum model, that is based on a few material-specific parameters that may be determined from experiment. As a new condition not considered before, we allow for softened amplitude variations of the magnetisation -a key property of, for instance, metallic magnets. Our model implies that spontaneous skyrmion lattice ground states may exist quite generally in a large number of materials, notably at surfaces and in thin films as well as in bulk compounds, where a lack of space inversion symmetry leads to chiral interactions.The possibility that particle-like states may form spontaneously in continuous fields has motivated intense theoretical efforts in the past. Derrick and Hobart established by rather general arguments that particle-like configurations are not stable in the majority of nonlinear field models [10,11]. However, a few exceptions have been found. Skyrme showed that particle-like excitations of continuous fields exist in the presence of certain non-linear interactions [2]. As a drawback, the interactions considered by Skyrme are physically not transparent, because they involve higher order derivative terms that are technically intractable. Therefore, Skyrme's approach is not viable in the context of ordered states in condensed matter that are ruled by short range interactions. In contrast, a physically transparent exception to the Derrick-Hobart theorem has been recognized in systems with bro-2 ken inversion symmetry, where chiral interactions lead to skyrmion excitations in condensed matter systems [12,14,16]. Chiral interactions exist in many different systems, e.g., (i) spin-orbit interactions in non-centrosymmetric materials, also referred to as DzyaloshinskyMoriya (DM) interactions [13], (ii) in non-centrosymmetric ferroelectrics, (iii) for certain structural phase transitions, (iv) in chiral liquid crystals, and (v) in the form of Che...

Skyrmions are topologically stable vortex-like objects with a swirling spin configuration which

A phenomenological theory of chiral symmetry breaking in magnetic nanostructures is developed considering induced, inhomogeneous chiral interactions (Dzyaloshinsky-Moriya-type). Application of the theory to films and multilayers with in-plane and out-of-plane magnetization predicts modulated and two-dimensional localized patterns (vortices). These new classes of magnetic patterns are intrinsically stable and localized on nanometer scale. Various experimental observations agree qualitatively with structures derived from this theory.

Axisymmetric magnetic lines of nanometer sizes (chiral vortices or skyrmions) have been predicted to exist in a large group of noncentrosymmetric crystals more than two decades ago. Recently these magnetic textures have been directly observed in nanolayers of cubic helimagnets and monolayers of magnetic metals. We develop a micromagnetic theory of chiral skyrmions in thin magnetic layers for magnetic materials with intrinsic and induced chirality. Such particle-like and stable micromagnetic objects can exist in broad ranges of applied magnetic fields including zero field. Chiral skyrmions can be used as a new type of highly mobile nanoscale data carriers.

We report on detailed magnetic measurements on the cubic helimagnet FeGe in external magnetic fields and temperatures near the onset of long-range magnetic order at T(C)=278.2(3) K. Precursor phenomena display a complex succession of temperature-driven crossovers and phase transitions in the vicinity of T(C). The A-phase region, present below T(C) and fields H<0.5 kOe, is split in several pockets. The complexity of the magnetic phase diagram is theoretically explained by the confinement of solitonic kinklike or Skyrmionic units that develop an attractive and oscillatory intersoliton coupling owing to the longitudinal inhomogeneity of the magnetization.

In cubic noncentrosymmetric ferromagnets uniaxial distortions suppress the helical states and stabilize Skyrmion lattices in a broad range of thermodynamical parameters. Using a phenomenological theory for modulated and localized states in chiral magnets, the equilibrium parameters of the Skyrmion and helical states are derived as functions of the applied magnetic field and induced uniaxial anisotropy.These results show that due to a combined effect of induced uniaxial anisotropy and an applied magnetic field Skyrmion lattices can be formed as thermodynamically stable states in large intervals of magnetic field and temperatures in cubic helimagnets, e.g., in intermetallic compounds MnSi, FeGe, (Fe,Co) where L is a vector order parameter (e.g. the magnetization vector M in magnetic materials or the director n in chiral liquid crystals), ∂ k L i ≡ ∂L i /∂x k are spatial derivatives of the order parameter. In condensed matter physics there are no physical interactions underlying energy contributions with higherorder spatial derivatives. [7] On the contrary, the invariants of type (1) arise in systems with intrinsic [9, 10] and induced chirality.[6] Particularly, in noncentrosymmetric magnetic materials such interactions stem from the chiral part of spin-orbit couplings (Dzyaloshinskii-Moriya interactions).[9] Chiral interactions of type (1) stabilize helical [9,11] and Skyrmionic structures [5,12] with fixed rotation sense (Fig. 1) [15]. Therefore, additional effects are necessary to stabilize Skyrmionic states in these systems. [2,13] In this paper we demonstrate that uniaxial distortions suppress the helical phases and enable the thermodynamic stability of the Skyrmion lattice in a broad range of applied magnetic fields. The calculated magnetic phase diagram allows to formulate practical recommendations on the possibility to stabilize Skyrmion states at low temperatures in MnSi, FeGe, (Fe,Co)Si and similar intermetallic compounds with B20-structure.Following the phenomenological theory developed in Refs. [9,11] we write the magnetic energy density for a cubic helimagnet with uniaxial distortions along z-axis aswhere A is the exchange stiffness, the second term is the Zeeman energy,zy ) =D M·rotM is the chiral energy with the Dzyaloshinskii constant D,i ] includes exchange (B) and cubic (K c ) anistropies [11]. The last term in (2) is uniaxial anisotropy induced by distortions.The Dzyaloshinskii-Moriya energy w D (2) favours spatially modulated chiral states where the magnetization rotates with a fixed turning sense in the plane perpendicular to the propagation direction (Fig. 1). The sign and magnitude of the Dzyaloshinskii constant D determine the modulation period and the sense of rotation, respectively. Thus, in zero magnetic field, H = 0, and for zero anisotropies, B = K c = K = 0, a flat helix forms the magnetic ground state as a single harmonic mode with wave number q 0 = D/(2A), where the phase angle φ of the magnetization varies linearly along the

A phenomenological theory of magnetic states in noncentrosymmetric tetragonal antiferromagnets is developed, which has to include homogeneous and inhomogeneous terms (Lifshitz-invariants) derived from Dzyaloshinskii-Moriya couplings. Magnetic properties of this class of antiferromagnets with low crystal symmetry are discussed in relation to its first known members, the recently detected compounds Ba2CuGe2O7 and K2V3O8. Crystallographic symmetry and magnetic ordering in these systems allow the simultaneous occurrence of chiral inhomogeneous magnetic structures and weak ferromagnetism. New types of incommensurate magnetic structures are possible, namely, chiral helices with rotation of staggered magnetization and oscillations of the total magnetization. Fieldinduced reorientation transitions into modulated states have been studied and corresponding phase diagrams are constructed. Structures of magnetic defects (domain-walls and vortices) are discussed. In particular, vortices, i.e. localized non-singular line defects, are stabilized by the inhomogeneous Dzyaloshinskii-Moriya interactions in uniaxial noncentrosymmetric antiferromagnets.

Modulated phases occur in numerous functional materials like giant ferroelectrics and magnetic shape memory alloys. To understand the origin of these phases, we review and generalize the concept of adaptive martensite. As a starting point, we investigate the coexistence of austenite, adaptive 14M phase and tetragonal martensite in Ni-Mn-Ga magnetic shape memory alloy epitaxial films. The modulated martensite can be constructed from nanotwinned variants of a tetragonal martensite phase. By combining the concept of adaptive martensite with branching of twin variants, we can explain key features of modulated phases from a microscopic view. This includes phase stability, the sequence of 6M-10M-NM intermartensitic transitions, and magnetocrystalline anisotropy.DOI:

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