Cylindrical Domain Wall Research Articles

Magnetic stripes and skyrmions with helicity reversals

It was recently realized that topological spin textures do not merely have mathematical beauty but can also give rise to unique functionalities of magnetic materials. An example is the skyrmion--a nano-sized bundle of noncoplanar spins--that by virtue of its nontrivial topology acts as a flux of magnetic field on spin-polarized electrons. Lorentz transmission electron microscopy recently emerged as a powerful tool for direct visualization of skyrmions in noncentrosymmetric helimagnets. Topologically, skyrmions are equivalent to magnetic bubbles (cylindrical domains) in ferromagnetic thin films, which were extensively explored in the 1970s for data storage applications. In this study we use Lorentz microscopy to image magnetic domain patterns in the prototypical magnetic oxide-M-type hexaferrite with a hint of scandium. Surprisingly, we find that the magnetic bubbles and stripes in the hexaferrite have a much more complex structure than the skyrmions and spirals in helimagnets, which we associate with the new degree of freedom--helicity (or vector spin chirality) describing the direction of spin rotation across the domain walls. We observe numerous random reversals of helicity in the stripe domain state. Random helicity of cylindrical domain walls coexists with the positional order of magnetic bubbles in a triangular lattice. Most unexpectedly, we observe regular helicity reversals inside skyrmions with an unusual multiple-ring structure.

Topology-change surgery for crystals

We performed the topology-change surgery for ring-shaped crystals of tantalum triselenide (TaSe${}_{3}$) to investigate the interplay between the closed-ring topology and elasticity/plasticity of the crystals. We cut the TaSe${}_{3}$ rings using a focused ion beam and observed that the curvatures of the open rings increased from their initial curvatures. We found that a change in the radius is proportional to inverse square of the thickness of the crystals, which corresponds to an inhomogeneous distribution of edge dislocations. From the distribution, we suggest the existence of cylindrical domain walls in the ring-shaped crystals as a result of the crystal topology.

Dynamics of cylindrical domain walls in smectic C liquid crystals

An analysis of the dynamics of cylindrical domain walls in planar aligned samples of smectic C liquid crystals is presented. A circular magnetic field, induced by an electric current, drives a time-dependent reorientation of the corresponding radially dependent director field. Nonlinear approximations to the relevant nonlinear dynamic equation, derived from smectic continuum theory, are solved in a comoving coordinated frame: exact solutions are found for a π-wall and numerical solutions are calculated for -walls. Each calculation begins with an assumed initial state for the director that is a prescribed cylindrical domain wall. Such an initial wall will proceed to expand or contract as its central core propagates radially inwards or outwards, depending on the boundary conditions for the director, the elastic constants, the magnitude of the field and the sign of the magnetic anisotropy of the liquid crystal.

Casimir Forces for Robin Scalar Field on Cylindrical Shell in de Sitter Space

The Casimir stress on a cylindrical shell in background of conformally flat spacetime for massless scalar field is investigated. In the general case of Robin (mixed) boundary condition, formulae are derived for the vacuum expectation values of the energy–momentum tensor and vacuum forces acting on boundaries. The special case of the dS bulk is considered then different cosmological constants are assumed for the space inside and outside of the shell to have general results applicable to the case of cylindrical domain wall formations in the early universe.

Dynamics of cylindrical domain walls in nematic liquid crystals

Analytical calculations of the dynamics of a curved domain wall in a nematic liquid crystal are performed. The core of the wall is assumed to form a cylinder, whose axis coincides with the direction of an external magnetic field. The equation of motion for the nematic director field is solved in a comoving coordinate frame by applying a polynomial expansion of the tilt angle with respect to the radial distance from the wall core. Starting from a cylindrical domain wall at rest as initial conditions, the shrinking of the cylinder and the change of the wall width is analysed in detail. In particular, we find that the Neel wall decays faster than the Bloch wall, in agreement with energy considerations.

The magnetic domain structures of small crystals

Abstract The first part of the article describes the calculation of magnetostatic energies (which are necessary to predict the critical sizes of crystals below which domains cease to form) and of the domain spacing or number of domains per crystal. Methods suitable for periodic ‘magnetic charge’ distributions in semi-infinite crystals and for finite distributions are described, and both planar and cylindrical domain walls are included. The reasons for the special interest in small crystals is discussed. The second part presents results on thin crystals of barium ferrite with both extensive and discrete structures; orthoferrite crystals with extensive walls and containing one or two cylindrical domains; and small crystals of gadolinium iron garnet near to the compensation temperature, in which the number of domains is a function of temperature. These results are discussed in the light of the theories outlined.

Direct Measurement of Domain Wall Energy

Attempts have been made to measure the energy of a Bloch domain wall in a Perminvar ring by a modification of a method suggested by Williams and Goertz based on the fact that a cylindrical domain wall within a ring tends to shrink in order to reduce the total energy of the wall.