Papers by Stavros Komineas
arXiv: Mesoscale and Nanoscale Physics, 2020
We study the structure of an axially symmetric magnetic skyrmion in a ferromagnet with the Dzyalo... more We study the structure of an axially symmetric magnetic skyrmion in a ferromagnet with the Dzyaloshinskii-Moriya interaction. We examine the regime of large skyrmions and we identify rigorously the critical value of the dimensionless parameter at which the skyrmion radius diverges to infinity, while the skyrmion energy converges to zero. This critical value coincides with the expected transition point from the uniform phase, which accommodates the skyrmion as an excited state, to the helical phase, which has negative energy. We give the profile field at the skyrmion core, its outer field, and the intermediate field at the skyrmion domain wall. Moreover, we derive an explicit formula for the leading asymptotic behavior of the energy as well as the leading term and first asymptotic correction for the value of the critical parameter. The key leading to the results is a parity theorem that utilizes exact formulae for the asymptotic behavior of the solutions of the static Landau-Lifshitz...
Physical Review B, 2021
We study a vortex in a nanostripe of an antiferromagnet with easy-plane anisotropy and interfacia... more We study a vortex in a nanostripe of an antiferromagnet with easy-plane anisotropy and interfacial Dzyloshinskii-Moriya interaction. The vortex has hybrid chirality being Néel close to its center and Bloch away from it. Propagating vortices can acquire velocities up to a maximum value that is lower than the spin wave velocity. When the vortex is forced to exceed the maximum velocity, phase transitions occur to a nonflat spiral, vortex chain, and flat spiral, successively. The vortex chain is a topological configuration stabilised in the stripe geometry. Theoretical arguments lead to the general result that the velocity of localized excitations in chiral magnets cannot reach the spin wave velocity.
We find numerically skyrmionic textures with skyrmion number Q = 0 in ferromagnets with the Dzyal... more We find numerically skyrmionic textures with skyrmion number Q = 0 in ferromagnets with the Dzyaloshinskii-Moriya interaction and perpendicular anisotropy. These have the form of a skyrmionantiskyrmion pair and may be called chiral droplets. They are stable in an infinite film as well as in disc-shaped magnetic elements. Droplets are found for values of the parameters close to the transition from the ferromagnetic to the spiral phase. We study their motion under spin-transfer torque. They move in the direction of the spin flow and, thus, their dynamics are drastically different than the Hall dynamics of the standard Q = 1 skyrmion.
Chiral skyrmions are stable particle-like solutions of the Landau-Lifshitz equation for ferromagn... more Chiral skyrmions are stable particle-like solutions of the Landau-Lifshitz equation for ferromagnets with the Dzyaloshinskii-Moriya interaction (DMI), characterized by a topological number. We study the profile of an axially symmetric skyrmion and give exact formulas for the solution of the corresponding far field and near field equations, in the asymptotic limit of small DMI constant (alternatively large anisotropy). The matching of these two fields leads to a formula for the skyrmion radius as a function of the DMI constant. The derived solutions show the different length scales which are present in the skyrmion profiles. The picture is thus created of a chiral skyrmion that is born out of a Belavin-Polyakov solution with an infinitesimally small radius, as the DMI constant is increased from zero. The skyrmion retains the Belavin-Polyakov profile over and well-beyond the core before it assumes an exponential decay; the profile of an axially-symmetric Belavin-Polyakov solution of u...
Physical Review B, 2018
A strategy to drive skyrmion motion by a combination of an anisotropy gradient and spin-Hall effe... more A strategy to drive skyrmion motion by a combination of an anisotropy gradient and spin-Hall effect has recently been demonstrated. Here, we study the fundamental properties of this type of motion by combining micromagnetic simulations and a generalized Thiele's equation. We find that the anisotropy gradient drives the skyrmion mainly along the direction perpendicular to the gradient, due to the conservative part of the torque. There is some slower motion along the direction parallel to the anisotropy gradient due to damping torque. When an appropriate spin-Hall torque is added, the skyrmion velocity in the direction of the anisotropy gradient can be enhanced. This motion gives rise to acceleration of the skyrmion as this moves to regions of varying anisotropy. This phenomenon should be taken into account in experiments for the correct evaluation of the skyrmion velocity. We employ a Thiele-like formalism and derive expressions for the velocity and the acceleration of the skyrmion that match very well with micromagnetic simulation results.
Physical Review B, 2015
We study the dynamics of skyrmions under spin-transfer torque in Dzyaloshinskii-Moriya materials ... more We study the dynamics of skyrmions under spin-transfer torque in Dzyaloshinskii-Moriya materials with easy-axis anisotropy. In particular, we study the motion of a topological skyrmion with skyrmion number Q = 1 and a non-topological skyrmionium with Q = 0 using their linear momentum, virial relations, and numerical simulations. The non-topological Q = 0 skyrmionium is accelerated in the direction of the current flow and it either reaches a steady state with constant velocity, or it is elongated to infinity. The steady-state velocity is given by a balance between current and dissipation and has an upper limit. In contrast, the topological Q = 1 skyrmion converges to a steady-state with constant velocity at an angle to the current flow. When the spin current stops the Q = 1 skyrmion is spontaneously pinned whereas the Q = 0 skyrmionium continues propagation. Exact solutions for the propagating skyrmionium are identified as solutions of equations given numerically in a previous work. Further exact results for propagating skyrmions are given in the case of the pure exchange model. The traveling solutions provide arguments that a spin polarized current will cause rigid motion of a skyrmion or a skyrmionium.
Physical Review Letters, 2005
Interactions of solitary waves in a cylindrically confined Bose-Einstein condensate are investiga... more Interactions of solitary waves in a cylindrically confined Bose-Einstein condensate are investigated by simulating their head-on collisions. Slow vortex rings and fast solitons are found to collide elastically contrary to the situation in the three-dimensional homogeneous Bose gas. Strongly inelastic collisions are absent for low density condensates but occur at higher densities for intermediate velocities. The scattering behavior is rationalized by use of dispersion diagrams. During inelastic collisions, spherical shell-like structures of low density are formed and they eventually decay into depletion droplets with solitary-wave features. The relation to similar shells observed in a recent experiment by Ginsberg et al. [Phys. Rev. Lett. 94, 040403 (2005)] is discussed.
Nonlinearity, May 30, 2019
We show that chiral symmetry breaking enables traveling domain wall solution for the conservative... more We show that chiral symmetry breaking enables traveling domain wall solution for the conservative Landau-Lifshitz equation of a uniaxial ferromagnet with Dzyaloshinskii-Moriya interaction. In contrast to related domain wall models including stray-field based anisotropy, traveling wave solutions are not found in closed form. For the construction we follow a topological approach and provide details of solutions by means of numerical calculations.
Physical Review B
We find numerically skyrmionic textures with skyrmion number Q = 0 in ferromagnets with the Dzyal... more We find numerically skyrmionic textures with skyrmion number Q = 0 in ferromagnets with the Dzyaloshinskii-Moriya interaction, perpendicular anisotropy, and the magnetostatic field. These have a skyrmion part and an antiskyrmion part, and they may be called chiral droplets. They are stable in an infinite film as well as in disk-shaped magnetic elements. Droplets are found in films for values of the parameters close to the transition from the ferromagnetic to the spiral phase. Under spin-transfer torque, they move in the direction of the spin flow and behave as solitary waves of Newtonian character, in stark contrast to the Hall dynamics of the standard Q = 1 skyrmion.
We study numerically the dynamics of a magnetic bubble in a disc-shaped magnetic element which is... more We study numerically the dynamics of a magnetic bubble in a disc-shaped magnetic element which is probed by a pulse of a magnetic field gradient. Magnetic bubbles are nontrivial magnetic configurations which are characterized by a topological (skyrmion) number N and they have been observed in mesoscopic magnetic elements with strong perpendicular anisotropy. For weak fields we find a skew deflection of the axially symmetric N = 1 bubble and a subsequent periodic motion around the center of the dot. This gyrotropic motion of the magnetic bubble is shown here for the first time. Stronger fields induce switching of the N = 1 bubble to a bubble which contains a pair of Bloch lines and has N = 0. The N = 0 bubble can be switched back to a N = 1 bubble by applying again an external field gradient. Detailed features of the unusual bubble dynamics are described by employing the skyrmion number and the moments of the associated topological density.
SciPost Physics
Skyrmions in antiferromagnetic (AFM) materials with the Dzyaloshinskii-Moriya (DM) interaction ar... more Skyrmions in antiferromagnetic (AFM) materials with the Dzyaloshinskii-Moriya (DM) interaction are expected to exist for essentially the same reasons as in DM ferromagnets (FM). It is shown that skyrmions in antiferromagnets with the DM interaction can be traveling as solitary waves with velocities up to a maximum value that depends on the DM parameter. Their configuration is found numerically. The energy and the linear momentum of an AFM skyrmion lead to a proper definition of its mass. We give the details of the energy-momentum dispersion of traveling skyrmions and explore their particle-like character based on exact relations. The skyrmion number, known to be linked to the dynamics of topological solitons in FM, is, here, unrelated to the dynamical behavior. As a result, the solitonic behavior of skyrmions in AFM is in stark contrast to the dynamical behavior of their FM counterparts.
Physical Review B
A skyrmion can be stabilized in a nanodisk geometry in a ferromagnetic material with Dzyaloshinsk... more A skyrmion can be stabilized in a nanodisk geometry in a ferromagnetic material with Dzyaloshinskii-Moriya (DM) interaction. We apply spin torque uniform in space and time and observe numerically that the skyrmion is set in steady rotational motion around a point off the nanodisk center. We give a theoretical description of the emerging auto-oscillation dynamics based on the coupling of the rotational motion to the breathing mode of the skyrmion and to the associated oscillations of the in-plane magnetization. The analysis shows that the achievement of auto-oscillations in this simple setup is due to the chiral symmetry breaking. Thus, we argue that the system is turned into a spin-torque oscillator due to the chiral DM interaction. We also show injection locking of this skyrmion oscillator demonstrating feasibility of application by using synchronization of multiple skyrmion auto-oscillators.
The dynamics of vortices in a 2D Heisenberg antiferromagnet with an easy-plane anisotropy is stud... more The dynamics of vortices in a 2D Heisenberg antiferromagnet with an easy-plane anisotropy is studied numerically within the discrete spin model as well as analytically within a continuum approximation based on a suitable extension of the relativistic nonlinear sigma model. We find that two like vortices scatter at 90 degrees during a head-on collision, whereas a vortex-antivortex pair is annihilated into spinwave radiation emitted mainly at 90 degrees. When a uniform bias field is applied, vortex dynamics is affected rather profoundly and acquires the characteristic features of the Hall effect of electrodynamics or the Magnus effect of fluid dynamics. In particular, a single vortex is always spontaneously pinned, two like vortices form a rotating bound state, and a vortex-antivortex pair undergoes Kelvin motion. Finally, in the presence of a bias field, vortices are shown to be the prominent topological excitations even for an isotropic antiferromagnet.
Aps Meeting Abstracts, Mar 1, 2006
... Authors: Stavros Komineas Nigel Cooper (University of Cambridge). Nikos Papanicolaou (Univers... more ... Authors: Stavros Komineas Nigel Cooper (University of Cambridge). Nikos Papanicolaou (University of Crete). We derive a class of virial theorems which provide stringent tests of both analytical and numerical calculations of vortex states in a confined Bose-Einstein condensate. ...
The dynamics of N point vortices in a fluid is described by the Helmholtz-Kirchhoff (HK) equation... more The dynamics of N point vortices in a fluid is described by the Helmholtz-Kirchhoff (HK) equations which lead to a completely integrable Hamiltonian system for N=2 or 3 but chaotic dynamics for N>3. Here we consider a generalization of the HK equations to describe the dynamics of magnetic vortices within a collective-coordinate approximation. In particular, we analyze in detail the dynamics of a system of three magnetic vortices by a suitable generalization of the solution for three point vortices in an ordinary fluid obtained by Groebli more than a century ago. The significance of our results for the dynamics of ferromagnetic elements is briefly discussed.
Aps Meeting Abstracts, Mar 1, 2008
The dynamics of N point vortices in a fluid is described by the Helmholtz-Kirchhoff (HK) equation... more The dynamics of N point vortices in a fluid is described by the Helmholtz-Kirchhoff (HK) equations which lead to a completely integrable Hamiltonian system for N = 2 or 3 but chaotic dynamics for N > 3. Here we consider a generalization of the HK equations to describe the dynamics of magnetic vortices within a collective-coordinate approximation. In particular, we analyze in detail the dynamics of a system of three magnetic vortices by a suitable generalization of the solution for three point vortices in an ordinary fluid obtained by Gröbli more than a century ago. The significance of our results for the dynamics of ferromagnetic elements is briefly discussed.
Journal of Physics A: Mathematical and General, 2006
We derive a virial theorem for a disc-shaped ferromagnetic particle with an axially symmetric mag... more We derive a virial theorem for a disc-shaped ferromagnetic particle with an axially symmetric magnetic configuration. This is a generalization of Derrick's scaling theorem which is now valid in the presence of surfaces. The relation gives simple results when applied to elementary magnetic states such as a single domain in an infinitely-elongated cylinder. We further calculate the vortex state and verify numerically that it satisfies the virial relation. The vortex profile has a simple form in the limit of a very thin particle where also the virial relation simplifies and effectively gives the vortex core radius. Away from the very thin limit the vortex configuration becomes more complicated with a varying vortex core radius along the thickness of the particle.
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Papers by Stavros Komineas