The size of micromagnetic structures, such as domain walls or vortices, is comparable to the exchange length of the ferromagnet. Both, the exchange length of the stray field $l_s$ and the magnetocrystalline exchange length $l_k$ are material-dependen
t quantities that usually lie in the nanometer range. This emphasizes the theoretical challenges associated with the mesoscopic nature of micromagnetism: the magnetic structures are much larger than the atomic lattice constant, but at the same time much smaller than the sample size. In computer simulations, the smallest exchange length serves as an estimate for the largest cell size admissible to prevent appreciable discretization errors. This general rule is not valid in special situations where the magnetization becomes particularly inhomogeneous. When such strongly inhomogeneous structures develop, micromagnetic simulations inevitably contain systematic and numerical errors. It is suggested to combine micromagnetic theory with a Heisenberg model to resolve such problems. We analyze cases where strongly inhomogeneous structures pose limits to standard micromagnetic simulations, arising from fundamental aspects as well as from numerical drawbacks.
The one-dimensional problem of a static head-to-head domain wall structure in a thin soft-magnetic nanowire with circular cross-section is treated within the framework of micromagnetic theory. A radius-dependent analytic form of the domain wall profi
le is derived by decomposing the magnetostatic energy into a monopolar and a dipolar term. We present a model in which the dipolar term of the magnetostatic energy resulting from the transverse magnetization in the center of the domain wall is calculated with Osborns formulas for homogeneously magnetized ellipsoids [Phys. Rev. 67, 351 (1945)]. The analytic results agree almost perfectly with simulation data as long as the wire diameter is sufficiently small to prevent inhomogeneities of the magnetization along the cross-section. Owing to the recently demonstrated negligible Doring mass of these walls, our results should also apply to the dynamic case, where domain walls are driven by spin-transfer toque effects and/or an axial magnetic field.
Arrays of suitably patterned and arranged magnetic elements may display artificial spin-ice structures with topological defects in the magnetization, such as Dirac monopoles and Dirac strings. It is known that these defects strongly influence the qua
si-static and equilibrium behavior of the spin-ice lattice. Here we study the eigenmode dynamics of such defects in a square lattice consisting of stadium-like thin film elements using micromagnetic simulations. We find that the topological defects display distinct signatures in the mode spectrum, providing a means to qualitatively and quantitatively analyze monopoles and strings which can be measured experimentally.
We report on low-energy electron microscopy imaging of ferroelectric domains with submicron resolution. Periodic strips of up and down-polarized ferroelectric domains in bismuth ferrite -a room temperature multiferroic- serve as a model system to com
pare low-energy electron microscopy with the established piezoresponse force microscopy. The results confirm the possibility of full-field imaging of ferroelectric domains with short acquisition times by exploiting the sensitivity of ultraslow electrons to small variations of the electric potential near surfaces in the mirror operation mode.
The classical impact of electrical currents on magnetic nanostructures is analyzed with numerical calculations of current-density distributions and Oersted fields in typical contact geometries. For the Oersted field calculation, a hybrid finite eleme
nt / boundary element method (FEM/BEM) technique is presented which can be applied to samples of arbitrary shape. Based on the FEM/BEM analysis, it is argued that reliable micromagnetic simulations on spin-tranfer-torque driven magnetization processes should include precise calculations of the Oersted field, particularly in the case of pillar contact geometries. Similarly, finite-element simulations demonstrate that numerical calculations of current-density distributions are required, e.g., in the case of magnetic strips with an indentation. Such strips are frequently used for the design of devices based on current-driven domain-wall motion. A dramatic increase of the current density is found at the apex of the notch, which is expected to strongly affect the magnetization processes in such strips.
The antivortex is a fundamental magnetization structure which is the topological counterpart of the well-known magnetic vortex. We study here the ultrafast dynamic behavior of an isolated antivortex in a patterned Permalloy thin-film element. Using m
icromagnetic simulations we predict that the antivortex response to an ultrashort external field pulse is characterized by the production of a new antivortex as well as of a temporary vortex, followed by an annihilation process. These processes are complementary to the recently reported response of a vortex and, like for the vortex, lead to the reversal of the orientation of the antivortex core region. In addition to its fundamental interest, this dynamic magnetization process could be used for the generation and propagation of spin waves for novel logical circuits.
