Finite Energy Barrier Research Articles

Tailoring energy barriers of Bloch-point-mediated transitions between topological spin textures

Magnetic skyrmions are nanoscale spin textures whose thermal stability originates from the nontrivial topology in nature. Recently, a plethora of topological spin textures have been theoretically predicted or experimentally observed, enriching the diversity of the skyrmionic family. In this work, we theoretically demonstrate the stabilities of various topological spin textures against homochiral states in chiral magnets, including chiral bobbers, dipole strings, and skyrmion tubes. They can be effectively classified by the associated topological Hall signals. Multiple transition paths are found among these textures, mediated by Bloch-point singularities, and the topological protection property here can be manifested by a finite energy barrier with the saddle point corresponding to the Bloch-point creation/destruction. By carefully modulating the local property of a surface, such as interfacial Dzyaloshinskii-Moriya interaction induced by breaking the structural symmetry, the energy landscape of a magnetic system can be tailored decisively. Significantly, the proposed scenario also enables the manipulation of stabilities and transition barriers of these textures, even accompanied by the discovery of ground-state chiral bobbers. This study may raise great expectations on the coexistence of topological spin textures as spintronics-based information carriers for future applications. Published by the American Physical Society 2024

Magnetic bubbles with alternating chirality in domain walls

In magnetic multilayers with perpendicular anisotropy, the competition of short-range and long-range interactions gives rise to the stability of cylindrical magnetic domains, also known as magnetic bubbles. The presence of Dzyaloshinsky-Moriya interaction induced by asymmetric interfaces between magnetic and nonmagnetic layers may lead to the formation of cylindrical bubble domains with Neel-type domain walls across the whole thickness of the multilayer. Such domain walls produce no contrast in Lorentz TEM under the normal incidence of the electron beam to the film. The latter is often used as an argument for the presence of Dzyaloshinskii-Moriya interaction in the system. Here we show that in magnetic multilayers, the absence of the Lorentz TEM contrast might also have another origin. In particular, in the absence of interfacial Dzyaloshinskii-Moriya interaction and weak interlayer exchange coupling, the magnetic bubbles might have Bloch-type domain walls of alternate chirality in adjacent layers. Such domain walls also do not produce magnetic contrast in Lorentz TEM at normal incidence of the electron beam. We show that, in the absence of interlayer exchange coupling, the magnetic bubble domains with the domain walls of fixed and alternate chirality have nearly identical energies and can coexist in the same range of magnetic fields. Using the geodesic nudged elastic band method, we prove that these states are separated by finite energy barriers. Furthermore, we demonstrate that magnetic multilayers with only dipolar coupling, besides the magnetic bubbles with nontrivial topology in all layers, can accommodate solutions with trivial topology within the internal layers.

Thermodynamics, formation dynamics, and structural correlations in the bulk amorphous phase of the phase-field crystal model.

We investigate bulk thermodynamic and microscopic structural properties of amorphous solids in the framework of the phase-field crystal (PFC) model. These are metastable states with a non-uniform density distribution, having no long-range order. From extensive numerical simulations, we determine the distribution of free energy density values in varying size amorphous systems and also the point-to-set correlation length, which is the radius of the largest volume of amorphous one can take while still having the particle arrangements within the volume determined by the particle ordering at the surface of the chosen volume. We find that in the thermodynamic limit, the free energy density of the amorphous tends toward a value that has a slight dependence on the initial state from which it was formed-i.e., it has a formation history dependence. The amorphous phase is observed to form on both sides of the liquid linear-stability limit, showing that the liquid to amorphous transition is first order, with an associated finite free energy barrier when the liquid is metastable. In our simulations, this is demonstrated when the noise in the initial density distribution is used to induce nucleation events from the metastable liquid. Depending on the strength of the initial noise, we observe a variety of nucleation pathways, in agreement with previous results for the PFC model, which show that amorphous precursor mediated multi-step crystal nucleation can occur in colloidal systems.

Formation of surface wrinkles and creases in constrained dielectric elastomers subject to electromechanical loading

This paper investigates issues that have arisen in experimental and theoretical studies of the stability of a dielectric elastomeric layer bonded to a stiff substrate and subject to a voltage difference across the top and bottom conducting surfaces of the layer. The role of equi-biaxial pre-stretch of the layer prior to bonding to the substrate is a central factor in the investigation. The focus is the competition between wrinkling and creasing and how this competition is affected by pre-stretch. A finite element model of the system is employed to generate wrinkling bifurcation and advanced post-bifurcation solutions in the form of localized modes, either crease-like or groove-like depending on the pre-stretch. The constitutive model includes elastic compressibility, but the formulation produces accurate solutions for nearly incompressible materials which coincide with the neo-Hookean solid in the incompressible limit. The numerical simulations reveal that localized crease solutions exist at voltages below the critical voltage for wrinkling bifurcation for equi-biaxial pre- stretches below about 2.4. In this range, the wrinkling bifurcation is highly unstable, creasing rather than wrinkling can be expected, and a discontinuous transition is predicted with a finite energy barrier that may be overcome due to the presence of surface defects. With an equi-biaxial pre-stretch greater than 2.4, a continuous transition is predicted with no energy barrier, forming a localized groove due to nonlinear interactions among the unstable wrinkling modes.

Surface stability of WN ultrathin films under O2 and H2O exposure: A first-principles study

Recently developed tungsten nitride (WN) ultrathin films are reported to be potentially good diffusion barriers in electronic and protective coatings and have exceptional mechanical strength. However, the surface interactions with the impurities in ambient conditions may play a crucial role in their stability, modifying the electronic and mechanical properties. In this paper, we investigate the molecular and dissociative adsorptions of O2 and H2O on both polar and nonpolar WN surfaces using density functional theory. The results show that the nonpolar and the W-terminated polar surfaces are highly reactive to O2. On the other hand, the N-terminated surfaces are stable on which the O2 dissociation occurs with finite energy barriers. Moreover, H2O dissociation on WN surfaces is not spontaneous irrespective of the surface direction or termination. The results, therefore, suggest that experiments growing the energetically stable W-terminated ultrathin films should employ the controlled conditions to obtain defect-free surfaces that offer excellent mechanical strength.

Friction and Plasticity in Contacts Between Amorphous Solids

Friction pervades nearly every aspect of our daily lives and has played a central role in technology ever since man created fire by rubbing sticks together. Despite its fundamental importance, a microscopic understanding of friction has remained elusive. Friction ultimately results from atomic-scale interactions between contacting bodies, but elastic and plastic deformations at larger scales and material transport control the area and composition of the contacting regions. Such atomic-scale interactions and geometry of contacting surface is difficult to characterize in experiments with sufficient accuracy. Here, we show the large-scale molecular dynamics simulations of contact and friction between two amorphous solids with self-affine fractal surfaces. We found that the plastic deformation on solid surfaces plays an important role in the interfacial friction that is much higher than expected for elastically deforming surfaces. Indeed, friction forces for different surface roughness collapse when plotted against the number of plastic rearrangements per unit sliding distance. Our results indicate that the microscopic friction origins from the overcome of finite energy barriers between plastically deformed local atomic structures.

The emergence of electroweak Skyrmions through Higgs bosons

Skyrmions are extended field configurations, initially proposed to describe baryons as topological solitons in an effective field theory of mesons. We investigate and confirm the existence of skyrmions within the electroweak sector of the Standard Model and study their properties. We find that the interplay of the electroweak sector with a dynamical Higgs field and the Skyrme term leads to a non-trivial vacuum structure with the skyrmion and perturbative vacuum sectors separated by a finite energy barrier. We identify dimension-8 operators that stabilise the electroweak skyrmion as a spatially localised soliton field configuration with finite size. Such operators are induced generically by a wide class of UV models. To calculate the skyrmion energy and radius we use a neural network method. Electroweak skyrmions are non-topological solitons but are exponentially long lived, and we find that the electroweak skyrmion is a viable dark matter candidate. While the skyrmion production cross section at collider experiments is suppressed, measuring the size of the Skyrme term in multi-Higgs-production processes at high-energy colliders is a promising avenue to probe the existence of electroweak skyrmions.

Mechanics of nanoscale crumpled graphene measured by Atomic Force Microscopy

Crumpling profoundly alters the chemical, electrical, mechanical and tribological properties of 2D materials. Structural deformations at these scales can correlate to the local chemical composition, thereby providing a novel method to tune their properties. In order to leverage the unique characteristics of these compact, high surface area structures, it is crucial to understand the mechanical behavior of crumples at the nanoscale and the effect of chemical composition on the crumpling mechanics. Here, we explore the mechanics of crumpled graphene and graphene oxide nanostructures through force-indentation routines using Atomic Force Microscopy. Crumpled graphene and crumpled graphene oxide show a multi-regime power law force deflection response with exponents ranging between 1.2–2.5. Pushing on the crumpled nano-structures induces both reversible and irreversible energy dissipation, which can be observed through changes in the hysteresis between the loading and unloading curves. Describing folding as a structural transformation passing through a metastable transition state with a finite energy barrier, the total energy imparted during force-indentation routines can be quantitatively related to the energy required to bend monolayer graphene. We also demonstrate that the chemical composition of the crumples can strongly influence the energy dissipation, where crumpled graphene consistently dissipated a smaller amount of energy irreversibly compared to crumpled graphene oxide.

Bose–Einstein-like condensation due to diffusivity edge under periodic confinement

A generic class of scalar active matter, characterized at the mean field level by the diffusivity vanishing above some threshold density, was recently introduced [Golestanian R 2019 Phys. Rev. E 100 010601(R)]. In the presence of harmonic confinement, such ‘diffusivity edge’ was shown to lead to condensation in the ground state, with the associated transition exhibiting formal similarities with Bose–Einstein condensation (BEC). In this work, the effect of a diffusivity edge is addressed in a periodic potential in arbitrary dimensions, where the system exhibits coexistence between many condensates. Using a generalized thermodynamic description of the system, it is found that the overall phenomenology of BEC holds even for finite energy barriers separating each neighbouring pair of condensates. Shallow potentials are shown to quantitatively affect the transition, and introduce non-universality in the values of the scaling exponents.

Stable and metastable kinetic ferromagnetism on a ring

Performing an exact diagonalization of the effective spin problem, a ferromagnetic ground state of kinetic origin is shown to emerge in a system of $N$ strongly correlated electrons on a $L$-site ring ($L > N$). This phenomenon is brought about by the quantum necklace statistics originated from the no double occupancy constraint leading to a fractional shifted electron momentum quantization. As a consequence of such special energy level distribution, the kinetic ferromagnetism is stable only for $N=3$. For odd $N>3$ the fully polarized FM state energy is only a local minimum but it is protected by a finite energy barrier that inhibits one spin-flip processes. The metastable ferromagnetic state survives perturbations of small magnitude opening up a possibility of being experimentally observed by an appropriate tuning of the interdot tunneling amplitudes in currently available quantum dot arrays.

DNA-conjugated layered double hydroxides penetrating into a plasma membrane: Layer size, thickness and DNA grafting density matter

Layered double hydroxides (LDHs) are promising as carriers delivering active molecules into cells via endocytosis which, however, is disadvantageous because contents are easily digested by the acid hydrolase upon entering the lysosomal system. Our earlier experiments have demonstrated that, when conjugated with DNA molecules on the LDH surface, the DNA-LDH-DNA nanocomposite can be formed and effectively enter cells via a non-endocytic pathway. Here, we combine dissipative particle dynamics simulations and free energy analysis to reveal the pathway and mechanism of DNA-LDH-DNA nanocomposites penetrating into a plasma membrane, and answer how the translocation is influenced by properties including the LDH size, thickness, and DNA grafting density. First, membrane anchorage is a spontaneous leading step of penetration via gaining favorable contacts with lipid headgroups and tails respectively by LDH and grafted DNA. Further insertion creates unfavorable contacts between LDH and lipid tails, generating a finite energy barrier with the magnitude depending on the LDH lateral size. Increasing the layer thickness can ease tilting of small nanocomposites to facilitate translocation, while for laterally larger nanocomposites especially than the membrane thickness, increase of the thickness contrarily makes translocation more difficult due to the enhanced membrane perturbation. Grafting more DNA molecules increases the LDH surface hydrophobicity to promote translocation into a membrane.

Duality of singularities of multiscale damage localization and crack advance: length variety in Theory of Critical Distances

The existence of two singularities related to the stress field at the crack tip and blow-up kinetics of damage localization is considered as the physical basis for the interpretation of the Theory of Critical Distances. The free energy metastability of solid with defects and corresponding free energy release explain the conception of the Finite Fracture Mechanics in the presence of the finite amplitude energy barrier. The variety of crack paths is analyzed as duality of inherently linked two types of singularities related to the singularity of multiscale damage kinetics under crack nucleation and singularity of stress field at the crack tip as the classical framework of fracture mechanics. The singularity of multiscale damage kinetics is a natural precursor of crack nucleation that could provide in some cases the totally independent scenario of fracture from the stress singularity at the crack tips. The influence of two singularities with the nature of intermediate asymptotical solutions for stress at the crack tip and damage localization kinetics over the set of spatial scales represents two attractors, which provides the variety of crack paths for corresponding loading conditions.

Shape stability of pasta phases: Lasagna case

.The stability of periodically placed slabs occurring in neutron stars (lasagna phase) is examined by exact geometrical methods for the first time. It appears that the slabs are stable against any shape perturbation modes for the whole range of volume fraction occupied by the slab. The calculations are done in the framework of the liquid drop model and obtained results are universal --they do not depend on model parameters like surface tension or charge density. The results shows that the transition to other pasta shapes requires crossing the finite energy barrier.

Crowding of Interacting Fluid Particles in Porous Media through Molecular Dynamics: Breakdown of Universality for Soft Interactions.

Molecular dynamics simulations of interacting soft disks confined in a heterogeneous quenched matrix of soft obstacles show dynamics which is fundamentally different from that of hard disks. The interactions between the disks can enhance transport when their density is increased, as disks cooperatively help each other over the finite energy barriers in the matrix. The system exhibits a transition from a diffusive to a localized state, but the transition is strongly rounded. Effective exponents in the mean-squared displacement can be observed over three decades in time but depend on the density of the disks and do not correspond to asymptotic behavior in the vicinity of a critical point, thus, showing that it is incorrect to relate them to the critical exponents in the Lorentz model scenario. The soft interactions are, therefore, responsible for a breakdown of the universality of the dynamics.

Skyrmion-Anti-Skyrmion Pair Creation by in-Plane Currents.

Magnetic Skyrmions can be considered as localized vortexlike spin textures which are topologically protected in continuous systems. Because of their stability, their small size, and the possibility to move them by low electric currents, they are promising candidates for spintronic devices. Without changing the topological charge, it is possible to create Skyrmion-anti-Skyrmion pairs. We derive a Skyrmion equation of motion which reveals how spin-polarized charge currents create Skyrmion-anti-Skyrmion pairs. It allows us to identify general prerequisites for the pair creation process. We corroborate these general principles by numerical simulations. On a lattice, where the concept of topological protection has to be replaced by that of a finite energy barrier, the anti-Skyrmion partner of the pairs is annihilated and only the Skyrmion survives. This eventually changes the total Skyrmion number and yields a new way of creating and controlling Skyrmions.

Droplet clusters: exploring the phase space of soft mesoscale atoms.

We report three-dimensional structures--mesoscale "atoms"--comprising up to N=8 aqueous droplets compressed in a liquid shell. In contrast to hard colloids that self-assemble into structures unique for a given N, we observe multiple metastable states. We attribute this unexpected richness of metastable structures to the deformability of the cores that introduces irreducible many-body interactions between the droplets. These exotic, often highly anisotropic, structures are locally stable. The structures displaying highly nonoptimum packing-and hence interfacial energy much higher than that of the lowest-energy state-exhibit finite energy barriers that prevent restructuring and relaxation of energy.

Thermal Activation in Permanent Magnets

The coercive field of permanent magnets decays with temperature. At non-zero temperatures, the system can overcome a finite energy barrier through thermal fluctuations. Using finite element micromagnetic simulations, we quantify this effect, which reduces coercivity in addition to the decrease of the coercive field associated with the temperature dependence of the anisotropy field, and validate the method through comparison with existing experimental data.

A comparative first-principles study of martensitic phase transformations in TiPd2 and TiPd intermetallics

Martensitic phase transformations in TiPd2 and TiPd alloys are studied employing density-functional, first-principles calculations. We examine the transformation of tetragonal C11b TiPd2 to the low-temperature orthorhombic phase (C11b → oI6), and the transformation of cubic B2 TiPd under orthorhombic (B2→B19) and subsequent monoclinic transformations (B19→B19′) as the system is cooled. We employ a theoretical approach based on a phenomenological Landau theory of the structural phase transitions and a mean-field approximation for the free energy, utilizing first-principles calculations to obtain the deformation energy as a function of strains and to deduce parameters for constructing the free energy. The predicted transition temperature for the TiPd2 C11b → oI6 transition is in good agreement with reported experimental results. To investigate the TiPd B2→B19 transformation, we employ both the Cauchy–Born rule and a soft-mode-based approach, and elucidate the importance of the coupling between lattice distortion and atomic displacements (i.e. shuffling) in the formation of the final structure. The calculated B2→B19 transition temperature for TiPd alloy agrees well with the experimental results. We also find that there exists a very small but finite (0.0005 eV/atom) energy barrier of B19 TiPd under monoclinic deformation for B19→B19′ structural phase transformation.

Role of the van der Waals forces in the ability of a double-walled carbon nanotube to accommodate a C60molecule: The example of C60@(15,0)@(24,0)

We report the first nonempirical inclusion of the van der Waals interaction in the study of the ability of a double-walled carbon nanotube to accommodate a C${}_{60}$ molecule. In agreement with the experiments reported by Khlobystov et al. [A. N. Khlobystov, D. A. Britz, A. Ardavan, and G. A. D. Briggs, Phys. Rev. Lett. 92, 245507 (2004)] this ability is confirmed even when the diameter of the inner tube is small. The study considered for the prototype case of C${}_{60}@(15,0)@(24,0)$ suggests that when and only when the van der Waals interactions are included the encapsulation becomes exothermic, although it may require a finite energy barrier.

Oscillator strengths of the intersubband electronic transitions in the hydrogenic nano-antidots

We calculate the oscillator strengths of the quantum antidots with hydrogenic donor impurity at the center, for transitions from the ground state to the first as well as the second excited state, in two and three dimensions, with both finite and infinite potential energy barriers. For this purpose, the binding energy spectrum and the corresponding wavefunctions, are first determined in terms of the Whittaker and the hypergeometric functions. The results are tested against the well understood limiting cases such as the free hydrogen atom in the bulk material, and also compared with the previously reported work. It is found, in particular, that the oscillator strength characterizing the transitions from the ground state to the second excited state, though negligible for small antidot radii, becomes significantly large and indeed comparable with that of the transitions to the first excited state for large enough antidot radii.