The Theory of Cylindrical Magnetic Domains

Abstract

The theory of cylindrical magnetic domains provides conditions governing the size and stability of circular cylindrical magnetic domains in plates of uniaxial magnetic materials together with an estimate of the range of applicability of these conditions. The results of the theory are directly applicable to the design of cylindrical domain devices. Computation to first and second order of the energy variation resulting from general small deviation in the domain shape from an initially circular shape yields the conditions governing domain size and stability. The physical origin of the various terms in the energy expansion is examined in detail. A graph from which many domain size and stability properties may be obtained summarizes the results of the energy variation calculation. The minimum theoretically attainable domain diameter is approximately σw/πMs2, where σw is the wall energy density and Ms is the saturation magnetization. For domains to exist, the effective anisotropy field must be greater than 4πMs.

Data retention in organic ferroelectric resistive switches

“…The driving force for retracting from the semiconductor domains is counteracted by the energy penalty associated with increasing the perimeter of the depolarized area -the latter mechanism is responsible for the instability of inverted domains below a critical size upon polarization reversal of a ferroelectric. [21][22][23][24] Growth of the depolarized area is therefore self-limiting. Once the stray field at its perimeter sits predominantly in the ferroelectric phase, there is no longer a driving force for further depolarization.…”

“…As mentioned above there are two contributions to the total energy of the system: the domain wall (DW) energy and the electrostatic (E) energy. Hence the total energy of the simulated system is calculated as [21][22][23]:…”

Periodic Modulations of Magnetostatic Field in Ferromagnetic Cylinder and Their Influence on Etching Figure Formation in Acid Solutions

“…The parameters of certain types of domain structures (DS) and their separate elements have been widely studied both by experimental and theoretical methods, for example [1][2][3][4][5][6]. These papers report on thermodynamic properties of ferromagnetic materials, the influence of DS on their magnetization processes and their practical use in magnetic devices.…”

“…On the one hand, it is the energy of a magnetic anisotropy and exchange interaction; on the other hand, it is dipole-dipole interaction of magnetic moments of the system. Domain structure acquires the various forms depending on the contribution of the mentioned interactions, a specimen shape and characteristics of external magnetic field [1][2][3][4]. It can be a system of stripe domains, serpentine domain structure, a lattice of cylindrical domains, spiral domains, etc.…”

Propagation of cylindrical magnetic domains

“…The method used to take dissipative effects into account is to compute The material requirements are also determined from a combination of such engineering requirements as cost, room temperature operation, the avail ability of materials, and the restrictions arising from the static stability and mobility condition (7,8 …”