2,357 research outputs found
Variational principles of micromagnetics revisited
We revisit the basic variational formulation of the minimization problem
associated with the micromagnetic energy, with an emphasis on the treatment of
the stray field contribution to the energy, which is intrinsically non-local.
Under minimal assumptions, we establish three distinct variational principles
for the stray field energy: a minimax principle involving magnetic scalar
potential and two minimization principles involving magnetic vector potential.
We then apply our formulations to the dimension reduction problem for thin
ferromagnetic shells of arbitrary shapes
Moving toward an atomistic reader model
With the move to recording densities up to and beyond 1 Tb/in/sup 2/, the size of read elements is continually reducing as a requirement of the scaling process. The expectation is for read elements containing magnetic films as thin as 1.5 nm, in which finite size effects, and factors such as interface mixing might be expected to become of increasing importance. Here, we review the limitations of the current (micromagnetic) approach to the theoretical modeling of thin films and develop an atomistic multiscale model capable of investigating the magnetic properties at the atomic level. Finite-size effects are found to be significant, suggesting the need for models beyond the micromagnetic approach to support the development of future read sensors
Geometric integration on spheres and some interesting applications
Geometric integration theory can be employed when numerically solving ODEs or
PDEs with constraints. In this paper, we present several one-step algorithms of
various orders for ODEs on a collection of spheres. To demonstrate the
versatility of these algorithms, we present representative calculations for
reduced free rigid body motion (a conservative ODE) and a discretization of
micromagnetics (a dissipative PDE). We emphasize the role of isotropy in
geometric integration and link numerical integration schemes to modern
differential geometry through the use of partial connection forms; this
theoretical framework generalizes moving frames and connections on principal
bundles to manifolds with nonfree actions.Comment: This paper appeared in prin
Boundary twists, instabilities, and creation of skyrmions and antiskyrmions
We formulate and study the general boundary conditions dictating the
magnetization profile in the vicinity of an interface between magnets with
dissimilar properties. Boundary twists in the vicinity of an edge due to
Dzyaloshinskii-Moriya interactions have been first discussed in [Wilson et al.,
Phys. Rev. B 88, 214420 (2013)] and in [Rohart and Thiaville, Phys. Rev. B 88,
184422 (2013)]. We show that in general case the boundary conditions lead to
the magnetization profile corresponding to the N\'eel, Bloch, or intermediate
twist. We explore how such twists can be utilized for creation of skyrmions and
antiskyrmions, e.g., in a view of magnetic memory applications. To this end, we
study various scenarios how skyrmions and antiskyrmions can be created from
interface magnetization twists due to local instabilities. We also show that a
judicious choice of Dzyaloshinskii-Moriya tensor (hence a carefully designed
material) can lead to local instabilities generating certain types of skyrmions
or antiskyrmions. The local instabilities are shown to appear in solutions of
the Bogoliubov-de-Gennes equations describing ellipticity of magnon modes bound
to interfaces. In one considered scenario, a skyrmion-antiskyrmion pair can be
created due to instabilities at an interface between materials with properly
engineered Dzyaloshinskii-Moriya interactions. We use micromagnetics
simulations to confirm our analytical predictions.Comment: 9 pages, 8 figure
Computation of the magnetostatic interaction between linearly magnetized polyhedrons
In this paper we present a method to accurately compute the energy of the
magnetostatic interaction between linearly (or uniformly, as a special case)
magnetized polyhedrons. The method has applications in finite element
micromagnetics, or more generally in computing the magnetostatic interaction
when the magnetization is represented using the finite element method (FEM).
The magnetostatic energy is described by a six-fold integral that is singular
when the interaction regions overlap, making direct numerical evaluation
problematic. To resolve the singularity, we evaluate four of the six iterated
integrals analytically resulting in a 2d integral over the surface of a
polyhedron, which is nonsingular and can be integrated numerically. This
provides a more accurate and efficient way of computing the magnetostatic
energy integral compared to existing approaches.
The method was developed to facilitate the evaluation of the demagnetizing
interaction between neighouring elements in finite-element micromagnetics and
provides a possibility to compute the demagnetizing field using efficient fast
multipole or tree code algorithms
Chiral magnet models and boundary condition geometry in Skyrmion electronics
Field theoretic techniques are used to relate (i) the
Landau-Lifschitz approach to Skyrmion devices based on
Dzyaloshinskii-Moriya (D-M) chiral magnets, and (ii) the
mathematical approaches to quantum magnetism. This results in a
geometric understanding of micromagnetic singularities and
boundary conditions without the usual thin-film assumptions.First author draf
Computing the demagnetizing tensor for finite difference micromagnetic simulations via numerical integration
In the finite difference method which is commonly used in computational
micromagnetics, the demagnetizing field is usually computed as a convolution of
the magnetization vector field with the demagnetizing tensor that describes the
magnetostatic field of a cuboidal cell with constant magnetization. An
analytical expression for the demagnetizing tensor is available, however at
distances far from the cuboidal cell, the numerical evaluation of the
analytical expression can be very inaccurate.
Due to this large-distance inaccuracy numerical packages such as OOMMF
compute the demagnetizing tensor using the explicit formula at distances close
to the originating cell, but at distances far from the originating cell a
formula based on an asymptotic expansion has to be used. In this work, we
describe a method to calculate the demagnetizing field by numerical evaluation
of the multidimensional integral in the demagnetization tensor terms using a
sparse grid integration scheme. This method improves the accuracy of
computation at intermediate distances from the origin.
We compute and report the accuracy of (i) the numerical evaluation of the
exact tensor expression which is best for short distances, (ii) the asymptotic
expansion best suited for large distances, and (iii) the new method based on
numerical integration, which is superior to methods (i) and (ii) for
intermediate distances. For all three methods, we show the measurements of
accuracy and execution time as a function of distance, for calculations using
single precision (4-byte) and double precision (8-byte) floating point
arithmetic. We make recommendations for the choice of scheme order and
integrating coefficients for the numerical integration method (iii)
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