Magnetic skyrmion
In physics, magnetic skyrmions (occasionally described as 'vortices,'[1] or 'vortex-like'[2] configurations) are statically stable solitons which have been predicted theoretically[1][3][4] and observed experimentally[5][6][7] in condensed matter systems.
1 a and b are both chiral skyrmions) in nature, and may exist both as dynamic excitations[10] or stable or metastable states.
[5] Although the broad lines defining magnetic skyrmions have been established de facto, there exist a variety of interpretations with subtle differences.
Most descriptions include the notion of topology – a categorization of shapes and the way in which an object is laid out in space – using a continuous-field approximation as defined in micromagnetics.
In skyrmion configurations the spatial dependence of the magnetisation can be simplified by setting the perpendicular magnetic variable independent of the in-plane angle (
It is worth observing that there are two different configurations which satisfy the topological index criterion stated above.
The distinction between these can be made clear by considering a horizontal cut across both of the skyrmions illustrated in figure 1, and looking at the progression of the local spin orientations.
[16] However, since the stability and behavioral attributes of skyrmions can vary significantly based on the type of interactions in a system, the word 'skyrmion' can refer to substantially different magnetic objects.
Which category one chooses to refer to depends largely on the emphasis one wishes to place on different qualities.
This definition finds a raison d'être because topology itself determines some properties of magnetic spin textures, such as their dynamical responses to excitations.
These qualities arise from stabilizing interactions which may be described in several mathematical ways, including for example by using higher-order spatial derivative terms[3] such as 2nd or 4th order terms to describe a field, (the mechanism originally proposed in particle physics by Tony Skyrme for a continuous field model),[22][23] or 1st order derivative functionals known as Lifshitz invariants[24]—energy contributions linear in first spatial derivatives of the magnetization—as later proposed by Alexei Bogdanov.
[28] In all cases the energy term acts to introduce topologically non-trivial solutions to a system of partial differential equations.
(2), the dipolar interaction is sometimes omitted in simulations of ultra-thin two-dimensional magnetic films, because it tends to contribute a minor effect in comparison with the others.
[29] If a skyrmion tube has finite length with Bloch points at either end, it has been called a toron [30] or a dipole string.
[31] A bound state of a skyrmion and a vortex of the XY-model, is in fact a type of screw dislocation of helimagnetic order in chiral magnets.
However, in physics, the free energy required to introduce a rupture enabling the transition of a system from one ‘topological’ state to another is always finite.
In order to draw a meaningful parallel between the concept of topological stability and the energy stability of a system, the analogy must necessarily be accompanied by the introduction of a non-zero phenomenological ‘field rigidity’ to account for the finite energy needed to rupture the field's topology[citation needed].
Applying the topological charge defined in a lattice,[33] the barrier height is theoretically shown to be proportional to the exchange stiffness.
=1 structures are in fact not stabilized by virtue of their ‘topology,’ but rather by the field rigidity parameters that characterize a given system.
While this distinction may at first seem pedantic, its physical motivation becomes apparent when considering two magnetic spin configurations of identical topology
This is to say that the most stable energy configuration of the field constituents, (in this case magnetic atoms), may in fact be to arrange into a topology which can be described as an
Note that from a point of view of practical applications this does not alter the usefulness of developing systems with Dzyaloshinskii–Moriya interaction, as such applications depend strictly on the topology [of the skyrmions, or lack thereof], which encodes the information, and not the underlying mechanisms which stabilize the necessary topology.
One must exercise caution when making inferences based on topology-related energy barriers, as it can be misleading to apply the notion of topology—a description which only rigorously applies to continuous fields— to infer the energetic stability of structures existing in discontinuous systems.
Giving way to this temptation is sometimes problematic in physics, where fields which are approximated as continuous become discontinuous below certain size-scales.
Such is the case for example when the concept of topology is associated with the micromagnetic model—which approximates the magnetic texture of a system as a continuous field—and then applied indiscriminately without consideration of the model's physical limitations (i.e. that it ceases to be valid at atomic dimensions).
In practice, treating the spin textures of magnetic materials as vectors of a continuous field model becomes inaccurate at size-scales on the order of < 2 nm, due to the discretization of the atomic lattice.
The dynamical magnetic skyrmion exhibits strong breathing which opens the avenue for skyrmion-based microwave applications.
[36] Thus, magnetic skyrmions also provide promising candidates for future racetrack-type in-memory logic computing technologies.
