Minimal radius of magnetic skyrmions: statics and dynamics

Abstract

In a broad range of applied magnetic fields and material parameters isolated magnetic skyrmions condense into skyrmion lattices. While the geometry of isolated skyrmions and their lattice counterparts strongly depend on field and Dzyaloshinski-Moriya interaction, this issue has not been adequately addressed in previous studies. Meanwhile, this information is extremely important for applications, because the skyrmion size and the interskyrmion distance have to be tuned for skyrmion based memory and logic devices. In this investigation we elucidate the size and density-dependent phase diagram showing traditional phases in field versus material parameters space by means of Monte-Carlo simulations on a discrete lattice. The obtained diagram permits us to establish that, in contrast to the continuum limit, skyrmions on a discrete lattice cannot be smaller than some critical size and have a very specific shape. These minimal skyrmions correspond to the micromagnetic configuration at the energy barrier between the ferromagnetic and the skyrmionic states. Furthermore, we use atomistic Landau-Lifshitz-Gilbert simulations to study dynamics of the skyrmion annihilation. It is shown that this procees consists of two stages: the continuous skyrmion contraction and its discontinuous annihilation. The detailed analysis of this dynamical process is given.

Interplay between size and stability of magnetic skyrmions

“…Analysis involving both numerical calculations and asymptotic methods have previously revealed basic properties of isolated skyrmion solutions. In particular, it has been shown that the equilibrium size of an isolated skyrmion decreases with the anisotropy parameter but increases as the DM interaction strength increases [2,3,25,43]. This behavior is consistent with analytical solutions based on ansatzes such as the one in Eq.…”

“…The curves are characterized by a certain critical value of the anisotropy parameter, at which the skyrmion size diverges. Observe that confined skyrmions can demonstrate opposite trends for the skyrmion size compared to the isolated skyrmions considered here [2,42,43,45]. Figure 1(b) shows results of GNEB calculations of the energy barrier ∆E for the skyrmion collapse into the FM background.…”

“…1). The fact that skyrmions collapse with finite radii is a consequence of the discreteness of the model used here [25,43]. At the upper critical line, isolated skyrmions strip out into spiral states [24,25].…”

Universality of annihilation barriers of large magnetic skyrmions in chiral and frustrated magnets

“…Here, the length scale ξ is given in Eq. (17) which yields an expression for the next-nearest neighbor interaction J 2 :…”

Eigenmodes of Néel skyrmions in ultrathin magnetic films

“…16 In contrast, the dynamics of the internal structure of the skyrmion has not been intensively explored. [17][18][19][20] This is particularly so for the Néel skyrmion whose internal dynamics is much less researched than that of its Bloch counterpart. Three ac magnetic-field-induced fundamental collective eigenmodes of the Bloch skyrmion lattice were theoretically predicted by Mochizuki.…”