Within the Oseen-Frank theory we derive numerically exact solutions for axisymmetric localized states in chiral liquid crystal layers with homeotropic anchoring. These solutions describe recently observed two-dimensional skyrmions in confinement-frustrated chiral nematics [P. J. Acherman et al. Phys. Rev. E 90, 012505 (2014)]. We stress that these solitonic states arise due to a fundamental stabilization mechanism responsible for the formation of skyrmions in cubic helimagnets and other noncentrosymmetric condensed-matter systems.
Equilibrium states are calculated for a planar hexagonal antiferromagnet in a magnetic field oriented in the basal plane. As the field is rotated in the basal plane, a number of first-order phase transitions accompanied by magnetization jumps are observed in the range of metastable states in the system. The range and equilibrium parameters of the thermodynamically stable domain structure formed in the vicinity of such transitions are determined. Magnetization curves in RbMnCl3 are analyzed.
Antiferromagnetically coupled multilayers with perpendicular anisotropy, as [CoPt]/Ru, Co/Ir, Fe/Au, display ferromagnetic stripe phases as the ground states. It is theoretically shown that the antiferromagnetic interlayer exchange causes a relative shift of domains in adjacent layers. This "exchange shift" is responsible for several recently observed effects: an anomalous broadening of domain walls, the formation of so-called "tiger-tail" patterns, and a "mixed state" of antiferromagnetic and ferromagnetic domains in [CoPt]/Ru multilayers. The derived analitical relations between the values of the shift and the strength of antiferromagnetic coupling provide an effective method for a quantitative determination of the interlayer exchange interactions. [2,3,4,5]. Due to the strong competition between antiferromagnetic interlayer exchange and magnetostatic couplings [3,6], nanoscale superlattices with strong perpendicular anisotropy display specific multidomain states and unusual magnetization processes [2,3,5,7], which have no counterpart in other layered systems with perpendicular magnetization [8].So far, theoretical analysis of magnetization states and processes in antiferromagnetically coupled multilayers with out-of-plane magnetization has been based on micromagnetic models of stripe domains, where the domain walls throughout the whole stack of the ferromagnetic layers sit exactly on top of each other [3,6]. In our letter we show that this assumption is wrong. The antiferromagnetic interlayer coupling causes a lateral shift of the domain walls in the adjacent ferromagnetic layers. We develop a phenomenological theory of these complex stripe states. The analytical evaluation of a basic twolayer model shows that the formation and evolution of such "shifted" multidomain phases should appreciably influence the appearance and the magnetization processes of stripe states in perpendicular, antiferromagnetically coupled multilayers.As a model we consider stripe domains in a superlattice composed of N identical layers of thickness h antiferromagnetically coupled via a spacer of thickness s. The stripe domain phase consists of domains with alternate magnetization M along the z-axis perpendicular to the multilayer plane. The domains are separated by thin domain walls with a finite area energy density σ. The magnetic energy density of the model (Fig. 1 (a) ) can be written as a function of the stripe period D and the shift aThe first term in (1) describes the domain wall energy, w m is the stray field energy, J > 0 is the antiferromagnetic exchange interaction. The upper (lower) sign corresponds to an (anti)parallel arrangement of the magnetization in the adjacent layers. We call these modes ferro and antiferro stripe phases. We introduce a set of reduced geometrical parametersand two characteristic lengthsdescribing the relative energy contributions of the domain walls (l) and the interlayer coupling (δ) in comparison to the stray field energy. Then, the reduced energy w = W/(2πM 2 N ) can be writtenThe stray field ene...
Recently synthesized magnetic multilayers with strong perpendicular anisotropy exhibit unique magnetic properties including the formation of specific multidomain states. In particular, antiferromagnetically coupled multilayers own rich phase diagrams that include various multidomain ground states. Analytical equations have been derived for the stray-field components of these multidomain states in perpendicular multilayer systems. In particular, closed expressions for stray fields in the case of ferromagnetic and antiferromagnetic stripes are presented. The theoretical approach provides a basis for the analysis of magnetic force microscopy (MFM) images from this novel class of nanomagnetic systems. Peculiarities of the MFM contrast have been calculated for realistic tip models. [2,3,4,5]. These nanoscale synthetic antiferromagnets are characterized by new types of multidomain states, unusual demagnetization processes and other specific phenomena [2,3,5]. In contrast to other bulk and nanomagnetic systems, the multidomain states in perpendicular antiferromagnetic multilayers are determined by a strong competition between the antiferromagnetic interlayer exchange and magnetostatic couplings [3,6,7]. The remarkable role of stray-field effects in synthetic antiferromagnets and the peculiarities of their multidomain states are currently investigated by high resolution magnetic force microscopy (MFM)(for recent examples of successful experimental tests on domain theory by MFM see, e.g. Refs. [3,8]). From the theoretical side, only few results have been obtained on MFM images in antiferromagnetically coupled multilayers, mostly by numerical methods [2,5,9]. Here we present an analytical approach that provides a comprehensive description of stray-field distributions and MFM images in multidomain states of these nanostructures. We show that the stray-field components and their spatial derivatives, that are crucial for an analysis of MFM contrast, own distinctive features for different multidomain states. These features allow to recognize the particular distribution of the magnetization at the surfaces of domains and in the depth of the multilayers. The quantitative relations from theory for the MFM contrast can also serve to determine the values of magnetic interactions, i.e. materials parameters of an antiferromagnetic multilayer. We apply our results for an analysis of multidomain states observed in [Co/Pt]Ru As a model we consider strong stripes, i.e. so-called band domains in a superlattice composed of N identical layers of thickness h separated by spacers of thickness s, (see, Fig. 1). Note, that the term "stripe domains" is also commonly used to denote multidomain patterns consisting of stripes with weakly undulating magnetization which, however, stays predominantly in the layer plane [10]. On the other hand, the term band domains is used to describe structures of homogeneous domains with perpendicular magnetization that alternates between up and down direction. These two types of stripe domains should
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