Thermal stability of metastable magnetic skyrmions

Magnetic skyrmions are two-dimensional, localized, particle-like, topologically non-trivial magnetic spin textures. In recent years, they have attracted a lot of interest as potential candidates for novel spintronics applications. Isolated skyrmions are metastable excitations of the ferromagnetic ground state. They are separated from it by an activation energy, which may be overcome at finite temperature under the effect of thermal fluctuations. In this thesis, we study the thermal stability of metastable magnetic skyrmions on the two-dimensional square lattice, for which we use an atomistic spin model. This task is firstly carried out via a numerical implementation of Langer's statistical theory for the decay of metastable states. The paths of minimum energy that lead to the skyrmion annihilation are computed via the geodesic nudged elastic band method. The transition state at the barrier top, which is a saddle point (SP), is precisely identified by a climbing image algorithm. We focus on chiral magnetic skyrmions and we look at two types of annihilation mechanisms: collapse, in which the skryrmion progressively shrinks in size until it annihilates, and escape through a boundary. We find that the thermally significant modes are the modes localized to the skyrmion, in contrast to the rest of the collective spin-wave modes, which extend to the entire lattice and contribute weakly. Important variations of the attempt frequency over several orders of magnitude are found, depending on the mechanism and on the value of the external magnetic field. They originate from strong entropic effects which come from the difference in configurational entropy between the metastable skyrmion state and the saddle point. In the cases we studied, the configurational entropy decreases at the SP (Delta S < 0), which results in lowered attempt frequencies, and enhanced skyrmion stability. We refer to this effect as entropic narrowing in the SP region. The strong entropic contribution mainly originates from the skyrmion's internal modes, and is generally more pronounced for collapse mechanisms. Next, we use forward flux sampling (FFS) to compute skyrmion collapse rates as a function of the applied field, and compare them with the previous results from Langer's theory. This is an important step, because the use of Langer's theory is based on many assumptions. We obtain a good agreement between both methods, thus confirming the strong dependence of the attempt frequency on the external field. While in magnetism, it is common practice to only focus on activation barriers and assume a characteristic value of the prefactor in the gigahertz regime, we conclude that due to a strong entropic contribution, internal energy barriers are not enough in order to correctly predict the lifetime of magnetic skyrmions, and it is essential to also evaluate a rate prefactor. Lastly, we look at paths to annihilation of first- and second-order skyrmions and antiskyrmions on the frustrated square lattice. Frustrated exchange has been found to arise from interface effects in certain systems where nanoscale interface skyrmions have been observed. We find that, in certain regions of parameter space, the annihilation of skyrmionic solutions no longer occurs through an isotropic type of collapse, and instead involves the injection of the opposite topological charge into the system, by means of the nucleation of merons and antimerons. Alternatively, the second-order (anti)skyrmion may split into a bound (anti)skyrmion pair, which involves no change in the total topological charge

Thermal stability of metastable magnetic skyrmions: Entropic narrowing and significance of internal eigenmodes

We compute annihilation rates of metastable magnetic skyrmions using a form of Langer's theory in the intermediate-to-high damping (IHD) regime. For a N\'eel skyrmion, a Bloch skyrmion, and an antiskyrmion, we look at two possible paths to annihilation: collapse and escape through a boundary. We also study the effects of a curved vs. a flat boundary, a second skyrmion and a non-magnetic defect. We find that the skyrmion's internal modes play a dominant role in the thermally activated transitions compared to the spin-wave excitations and that the relative contribution of internal modes depends on the nature of the transition process. Our calculations for a small skyrmion stabilized at zero-field show that collapse on a defect is the most probable path. In the absence of a defect, the annihilation is largely dominated by escape mechanisms, even though in this case the activation energy is higher than that of collapse processes. Escape through a flat boundary is found more probable than through a curved boundary. The potential source of stability of metastable skyrmions is therefore found not to lie in high activation energies, nor in the dynamics at the transition state, but comes from entropic narrowing in the saddle point region which leads to lowered attempt frequencies. This narrowing effect is found to be primarily associated with the skyrmion's internal modes.Comment: 14 pages, 9 figure

Colloidal Jamming at Interfaces: a Route to Fluid-bicontinuous Gels

Colloidal particles or nanoparticles, with equal affinity for two fluids, are known to adsorb irreversibly to the fluid-fluid interface. We present large-scale computer simulations of the demixing of a binary solvent containing such particles. The newly formed interface sequesters the colloidal particles; as the interface coarsens, the particles are forced into close contact by interfacial tension. Coarsening is dramatically curtailed, and the jammed colloidal layer seemingly enters a glassy state, creating a multiply connected, solid-like film in three dimensions. The resulting gel contains percolating domains of both fluids, with possible uses as, for example, a microreaction medium

Path sampling for lifetimes of metastable magnetic skyrmions and direct comparison with Kramers' method

We perform a direct comparison between Kramers' method in many dimensions -- i.e., Langer's theory -- adapted to magnetic spin systems, and a path sampling method in the form of forward flux sampling, as a means to compute collapse rates of metastable magnetic skyrmions. We show that a good agreement is obtained between the two methods. We report variations of the attempt frequency associated with skyrmion collapse by three to four orders of magnitude when varying the applied magnetic field by 5$\%$ of the exchange strength, which confirms the existence of a strong entropic contribution to the lifetime of skyrmions. This demonstrates that in complex systems, the knowledge of the rate prefactor, in addition to the internal energy barrier, is essential in order to properly estimate a lifetime.Comment: 5 pages, 5 figures (main text), 8 pages including supplemental materia

Nonequilibrium steady states in sheared binary fluids

We simulate by lattice Boltzmann the steady shearing of a binary fluid mixture undergoing phase separation with full hydrodynamics in two dimensions. Contrary to some theoretical scenarios, a dynamical steady state is attained with finite domain lengths $L_{x,y}$ in the directions ($x,y)$ of velocity and velocity gradient. Apparent scaling exponents are estimated as $L_{x}\sim\dot{\gamma}^{-2/3}$ and $L_{y}\sim\dot{\gamma}^{-3/4}$. We discuss the relative roles of diffusivity and hydrodynamics in attaining steady state.Comment: 4 pages, 3 figure

Inertial effects in three dimensional spinodal decomposition of a symmetric binary fluid mixture: A lattice Boltzmann study

The late-stage demixing following spinodal decomposition of a three-dimensional symmetric binary fluid mixture is studied numerically, using a thermodynamicaly consistent lattice Boltzmann method. We combine results from simulations with different numerical parameters to obtain an unprecendented range of length and time scales when expressed in reduced physical units. Using eight large (256^3) runs, the resulting composite graph of reduced domain size l against reduced time t covers 1 < l < 10^5, 10 < t < 10^8. Our data is consistent with the dynamical scaling hypothesis, that l(t) is a universal scaling curve. We give the first detailed statistical analysis of fluid motion, rather than just domain evolution, in simulations of this kind, and introduce scaling plots for several quantities derived from the fluid velocity and velocity gradient fields.Comment: 49 pages, latex, J. Fluid Mech. style, 48 embedded eps figs plus 6 colour jpegs for Fig 10 on p.2

Binary fluids under steady shear in three dimensions

We simulate by lattice Boltzmann the steady shearing of a binary fluid mixture with full hydrodynamics in three dimensions. Contrary to some theoretical scenarios, a dynamical steady state is attained with finite correlation lengths in all three spatial directions. Using large simulations we obtain at moderately high Reynolds numbers apparent scaling expon ents comparable to those found by us previously in 2D. However, in 3D there may be a crossover to different behavior at low Reynolds number: accessing this regime requires even larger computational resource than used here.Comment: 4 pages, 3 figure