Fig.1. Skyrmion lattices in chiral helimagnets: (a) π − ; (b) 2 / π Skyrmionic textures in chiral magnets A. A. Leonov, U. K. Röβler, A. N. Bogdanov IFW Dresden, P.O. Box 270116, D-01171 Dresden, Germany In noncentrosymmetric magnetic systems, chiral Dzyaloshinskii-Moriya (DM) interactions provide a unique mechanism for the stabilization of localized noncollinear states in two dimensions (baby-Skyrmions) and in three dimensions (Skyrmion-strings or Hopfions ) with fixed sense of rotation. Multi-Skyrmionic states built from these objects can form multiply modulated magnetic phases that may underlie the exotic magnetic phenomena of “partial order” or the field-driven “A-phase” observed in MnSi and other cubic helimagnets [1]. Based on the standard phenomenological (Dzyaloshinskii [2]) model, we obtain new numerically exact solutions for 2D Skyrmion lattices (Fig.1), formulate their basic properties, and elucidate physical mechanisms of their formation and stability [3]. In particular, these models are relevant for magnetic textures that may occur in thin magnetic films with induced chiral DM couplings due to the broken inversion symmetry at the surface. Our detailed numerical studies show that the bound Skyrmion states in two dimensions arise as hexagonal lattices of π ± - Skyrmions (with the magnetization in the center along or opposite to the magnetic field, Fig.1a) or square staggered lattices of 2 / π - Skyrmions (Fig.1b). In the simplest case of a Skyrmionic texture, the structure is homogeneous in the third dimension. The Skyrmions preserve ideal axisymmetric “double twist” core in condensed phases, while a continuation into a space-filling texture is frustrated. The 2 / π -lattices contain defect lines with zero modulus value. Thus, they may form thermodynamically stable states only near the ordering temperature [3]. The evolution of Skyrmion lattices in an increasing magnetic field leads to a succession of phase transitions of first or second kind between diverse textures and finally ends by the formation of isolated Skyrmion-filaments with fixed radius and shape embedded in a homogeneously magnetized matrix. Dense packing of these elastically interacting tubes with repulsive cores may result in partially ordered mesophases, e.g., hexatic arrangements of Skyrmions with a six-fold ordering of the nearest-neighbour bond orientation at higher temperature or completely amorphous liquid-like textures. In the framework of the phenomenological model including only isotropic interactions (exchange, Zeeman, DM energy contributions), the considered Skyrmion lattices are only metastable states as the competing conical one-dimensional spiral forms the equilibrium state. But owing to the weak couplings between Skyrmions, secondary effects like anisotropies and/or fluctuations can stabilize Skyrmionic textures as compared to simple helices. Also the topological nature of Skyrmion condensates makes the magnetization processes in chiral magnets history-dependent and hysteretic. [1] C. Pfleiderer et al., Nature 427, 6971 (2004); C. Pappas et al., Phys. Rev. Lett. 102, 197202 (2009); S. Mühlbauer et al. Science 323, 915 (2009); [2] I. E. Dzyaloshinskii, Sov. Phys. JETP 19, 960 (1964); [3] U. K. Röβler, A. A. Leonov, A. N. Bogdanov, J. Phys., in press; arXiv: 0907.3651v2 (2009); arXiv: 0904.4842v1 (2009); U. K. Rößler, A. N. Bogdanov, C. Pfleiderer, Nature 442, 797 (2006).

A. A. Leonov, U. K. Röβler and A. N. Bogdanov- Skyrmionic textures in chiral magnets

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Fig.1. Skyrmion lattices in chiral helimagnets: (a) π− ; (b) 2/π

Skyrmionic textures in chiral magnets

A. A. Leonov, U. K. Röβler, A. N. Bogdanov

IFW Dresden, P.O. Box 270116, D-01171 Dresden, Germany

In noncentrosymmetric magnetic systems, chiral Dzyaloshinskii-Moriya (DM) interactions provide a unique mechanism for the stabilization of localized noncollinear states in two dimensions (baby-Skyrmions) and in three dimensions (Skyrmion-strings or Hopfions ) with fixed sense of rotation. Multi-Skyrmionic states built from these objects can form multiply modulated magnetic phases that may underlie the exotic magnetic phenomena of “partial order” or the field-driven “A-phase” observed in MnSi and other cubic helimagnets [1]. Based on the standard phenomenological (Dzyaloshinskii [2]) model, we obtain new numerically exact

solutions for 2D Skyrmion lattices (Fig.1), formulate their basic properties, and elucidate physical mechanisms of their formation and stability [3]. In particular, these models are relevant for magnetic textures that may occur in thin magnetic films with induced chiral DM couplings due to the broken inversion symmetry at the surface. Our detailed numerical studies show that the bound Skyrmion states in two dimensions arise as hexagonal lattices of π± -Skyrmions (with the magnetization in the center along or opposite to the magnetic field, Fig.1a) or square staggered lattices of 2/π -Skyrmions (Fig.1b). In the simplest case of a Skyrmionic texture, the structure is homogeneous in the third dimension. The Skyrmions preserve ideal axisymmetric “double twist” core in condensed phases, while a continuation into a space-filling texture is frustrated. The 2/π -lattices contain defect lines with zero modulus value. Thus, they may form thermodynamically stable states only near the ordering temperature [3]. The evolution of Skyrmion lattices in an increasing magnetic field leads to a succession of phase transitions of first or second kind between diverse textures and finally ends by the formation of isolated Skyrmion-filaments with fixed radius and shape embedded in a homogeneously magnetized matrix. Dense packing of these elastically interacting tubes with repulsive cores may result in partially ordered mesophases, e.g., hexatic arrangements of Skyrmions with a six-fold ordering of the nearest-neighbour

bond orientation at higher temperature or completely amorphous liquid-like textures. In the framework of the phenomenological model including only isotropic interactions (exchange, Zeeman, DM energy contributions), the considered Skyrmion lattices are only metastable states as the competing conical one-dimensional spiral forms the equilibrium state. But owing to the weak couplings between Skyrmions, secondary effects like anisotropies and/or fluctuations can stabilize Skyrmionic textures as compared to simple helices. Also the topological nature of Skyrmion condensates makes the magnetization processes in chiral magnets history-dependent and hysteretic. [1] C. Pfleiderer et al., Nature 427, 6971 (2004); C. Pappas et al., Phys. Rev. Lett. 102, 197202 (2009); S. Mühlbauer et al. Science 323, 915 (2009); [2] I. E. Dzyaloshinskii, Sov. Phys. JETP 19, 960 (1964); [3] U. K. Röβler, A. A. Leonov, A. N. Bogdanov, J. Phys., in press; arXiv: 0907.3651v2 (2009); arXiv: 0904.4842v1 (2009); U. K. Rößler, A. N. Bogdanov, C. Pfleiderer, Nature 442, 797 (2006).