Finite Film Thickness Research Articles

Instability of Magnetic Skyrmion Strings Induced by Longitudinal Spin Currents.

It is well established that spin-transfer torques exerted by in-plane spin currents give rise to a motion of magnetic skyrmions resulting in a skyrmion Hall effect. In films of finite thickness or in three-dimensional bulk samples the skyrmions extend in the third direction forming a string. We demonstrate that a spin current flowing longitudinally along the skyrmion string instead induces a Goldstone spin wave instability. Our analytical results are confirmed by micromagnetic simulations of both a single string as well as string lattices, suggesting that the instability eventually breaks the strings. A longitudinal current is thus able to melt the skyrmion string lattice via a nonequilibrium phase transition. For films of finite thickness or in the presence of disorder a threshold current will be required, and we estimate the latter assuming weak collective pinning.

Sum-frequency generation at interfaces: A Fresnel story. I. Designing high contrast in two interface systems.

When a homogeneous film of finite thickness is optically probed, interference due to multiple reflections modulates in amplitude the electric field of light. For optical processes located only at the interfaces between two media, as is common for Sum-Frequency Generation (SFG), interference also modulates the contrast between signals generated at the entrance and exit planes of the film. We introduce a universal formalism for Fresnel factors, which bear all the information about interference, valid at any point in a three-layer system and for the three beams involved in the SFG process. Their analysis provides general rules for obtaining a high contrast. In particular, we define four configurations leading to the cancellation of the SFG response from the entrance side of the film when its thickness or the angles of incidence are tuned. Cancellation conditions depend on the polarization of light and follow simple analytical rules, leading to a straightforward experimental implementation. Such a selective cancellation makes it possible to independently measure single components of the nonlinear susceptibility, for example, in a ppp experiment and to separate surface from bulk response by combining a few measurements.

Analytic theory for Néel skyrmion size, accounting for finite film thickness

The energy of a Néel skyrmion in a magnetic film with interfacial DMI is developed analytically, with the finite thickness of the film taken into account. Many theories for the energy of magnetic skyrmions use models that are only accurate in the limit that the film thickness vanishes. One theory [Büttner et al. Sci. Rep. 8, 4464 (2018)] provides exceptionally accurate expressions for the skyrmion energy for finite thickness films, but does not yield an analytic solution for the skyrmion size, plus it contains contributions which are found using fitting methods. Here, we approximate the demagnetizing energy of a skyrmion by examining the form of magnetostatic Green’s function expressions for the demagnetizing fields. Then, analytic expressions for the skyrmion radius and the skyrmion domain wall width are derived in the limit of zero applied field. Our methods are rigorously compared to other calculation methods and compare well to numerical calculations and experimental results, both with and without an applied magnetic field. The approximations that allow for an analytic result lead to a loss of accuracy for the skyrmion radius of up to 20% but this loss in accuracy may be offset by the simplicity of the developed physical expressions. Finite thickness is important to consider for skyrmions existing in multilayer stacks with total thickness of a few nanometers.

Low-Threshold Optical Bistability Based on Photonic Crystal Fabry–Perot Cavity with Three-Dimensional Dirac Semimetal

In this paper, we investigate theoretically the tunable low threshold optical bistability (OB) in the terahertz range based on photonic crystals’ Fabry–Perot (FP) cavity with a three-dimensional Dirac semimetal (3D DSM). On the one hand, a 3D DSM with a high nonlinear refractive index coefficient creates conditions for the generation of OB. Additionally, the finite film thickness of 3D DSMs leads to significantly a enhanced interaction volume compared to graphene, which allows easier preparation and has stable properties. On the other hand, the resonance of the FP cavity plays a positive role in promoting the tunable low-threshold OB. It was found that the OB threshold and hysteresis curve can be continuously adjusted by manipulating the Fermi energy and relaxation times of a 3D DSM. Additionally, the bistable curve of the composite structure is also closely related to the angle of incident light. Through parameter optimization, OB with a threshold approaching 105 V/m can be obtained. The photonic crystal’s FP cavity with a 3D DSM structure provides a feasible way to achieve low-threshold OB and a building block for future integrated all-optical devices.

Comparative analysis of two models for the optical response of a thin slab: a film of finite thickness versus a surface current sheet.

An accurate description of the electromagnetic properties of materials is fundamental to optical and electric devices. As a current research hotspot, thin slabs generally are modeled as a film of finite thickness with a dielectric function. However, inspired by two-dimensional materials, thin slabs can be regarded as surface current sheets with conductivity. Due to the convenience of the latter in simplifying the calculations, it becomes increasingly significant to determine the equivalent conditions of the two models. In this work, we compare the differences between the thin film and surface current models in calculating the transmissivity, reflectivity, and absorptivity of a SiC film. For normal incidence, the difference between the calculations of the two models is only non-negligible when the thickness is large (500 nm), because of the invalidation of surface current models and the excitation of Fabry-Perot resonance. In particular, we derive analytical formulas for the relative error in transmittance versus phase difference, which can be used to predict the difference between the two models as a function of film thickness. For oblique incidence, the two models have significant differences in the vicinity of epsilon-near-zero (ENZ) frequency. The excitation of the Berreman leaky mode in a thin film model causes a narrow blank absorption peak close to the ENZ frequency. However, we found that the surface current model is unable to form this resonance mode and further demonstrate it theoretically. In addition, it is found that the two models are equivalent in the case of a transverse electric wave even though the incidence is oblique. This work can enhance the awareness of the light-matter interaction and open unprecedented avenues for designing ultrathin optical devices.

Spontaneous emission modulation in biaxial hyperbolic van der Waals material

As a natural van der Waals crystal, α-MoO3 has excellent in-plane hyperbolic properties and essential nanophotonics applications. However, its tunable properties are generally neglected. Here, we achieve effective modulation of spontaneous emission (SE) from a single-layer flat plate by changing the crystal directions. Numerical results and theoretical analysis show that α-MoO3 exhibits good tunability when the crystal directions of α-MoO3 are different in y–z or x–y planes. A modulation factor of more than three orders of magnitude is obtained at 634 cm−1. This phenomenon is caused by the excitation of hyperbolic phonon polaritons in α-MoO3 at specific bands. However, when the crystal directions of α-MoO3 are different in the x–z plane, the SE of the material exhibits strong angle independence. Additionally, for the semi-infinite α-MoO3 flat structure, we determine the distribution of the modulation factor of SE using the wavenumber and rotation angle. Finally, we extend the calculation results from semi-infinite media to finite thickness films. We obtain the general evolution law of the peak angle of the modulation factor with thickness, increasing the modulation factor to approximately 2000, which exceeds the maximum modulation factor observed in previous works by 48 times. We believe this work could guide the SE modulation of anisotropic materials and benefit the field of micro-/nano-lasers and quantum computing.

Resonance damping of gravity–capillary waves on water covered with a visco-elastic film of finite thickness: A reappraisal

A new approach to the problem of damping of gravity–capillary waves (GCW) on water covered with a layer of viscous liquid (a film) of finite thickness with two elastic boundaries is developed. It is shown that the rotational component of GCW can be described formally as a “forced” longitudinal or Marangoni wave (MW), and the potential component of GCW plays a role of the “external force.” The resonance-like excitation of the forced MW is demonstrated when the GCW and MW frequencies and wave numbers are approximately close to each other. For a film that is thinner than the viscous boundary layers in film, a single forced MW exists that is located within the boundary layer beneath the water surface. For a thick film, the forced MW is characterized by the existence of two spatially separated MW modes: one is localized in the boundary layer below the upper, air–film interface and another within the boundary layers in the vicinity of the water–film interface. Then, at different elasticities of the interfaces, a double peak dependence of the GCW damping coefficient on wave number can occur due to the resonance with the two forced MW modes. The dependence of the damping coefficient on film thickness is characterized by a strong maximum appearing when the film and boundary layer thickness values are comparable to each other. The developed theory is consistent with existing numerical studies and experiment.

Stability and post-bifurcation of film-substrate systems

Morphological instabilities in soft solids with free surfaces lead to an array of deformation modes including wrinkling, creasing, folding and ridge localization. While homogeneous systems tend to form creases, stiff films over soft substrates usually exhibit surface waves. Here, we look to analytically investigate this transition through the effects of film stiffness and finite thickness on the post-bifurcation stability of these surface waves. By considering both the film and substrate as compressible Neo-Hookean solids, we apply bifurcation theory and Lyaponov–Schmidt–Koiter asymptotics to produce a phase diagram of the surface wave stability over the parameter space. While earlier works have studied the effect of film-to-substrate stiffness ratios for thin films on deep substrates in the incompressible setting, we consider the additional effects of both finite film thickness and Poisson ratio. To investigate the further evolution of these surface waves, we turn to computational methods through finite-element simulations with bifurcation branch-following techniques. We see that as the unstable surface waves evolve, they eventually lead to the beginnings of crease formation. Thus, when the surface waves are unstable, we would expect snap-back or snap-through behaviour leading to creases.

Structured viscoelastic substrates as linear foundations.

The linear (Winkler) foundation is a simple model widely used for decades to account for the surface response of elastic bodies. It models the response as purely local, linear, and perpendicular to the surface. We extend this model to the case in which the foundation is made of a structured material such as a polymer network, which has characteristic scales of length and time. We use the two-fluid model of viscoelastic structured materials to treat a film of finite thickness, supported on a rigid solid and subjected to a concentrated normal force at its free surface. We obtain the foundation modulus (Winkler constant) as a function of the film's thickness, intrinsic correlation length, and viscoelastic moduli, for three choices of boundary conditions. The results can be used to readily extend earlier applications of the Winkler model to more complex, microstructured substrates. They also provide a way to extract the intrinsic properties of such complex materials from mechanical surface measurements.

Effect of a Conducting Film of Finite Thickness Deposited on a Resonator with a Lateral Electric Field on Its Characteristics

Effect of a Conducting Film of Finite Thickness Deposited on a Resonator with a Lateral Electric Field on Its Characteristics

Skyrmions near defects

We study the impact of an exchange-reducing defect on a skyrmion in a thin film of finite thickness. Attraction of the skyrmion to a defect is demonstrated in a lattice model by computing the micromagnetic energy accounting for the exchange, Dzyaloshinskii–Moriya interaction, magnetic anisotropy, and dipole–dipole coupling. The spiraling dynamics of the skyrmion toward the defect is illustrated by solving numerically the full Landau–Lifshitz–Gilbert equations on a lattice and, independently, by solving the Thiele equation, with the two methods in agreement with each other. Depinning of the skyrmion by the current is investigated. We find that the skyrmion deforms when it is close to the defect. Deformation is small in the parameter space far from the phase boundary that determines stability of skyrmions. It increases dramatically near the phase boundary, leading to the transformation of the skyrmion by the defect into a snake-like magnetic domain.

Influence of boundary roughness on the saturation of electrohydrodynamic Rayleigh-Taylor instability in two superposed fluids in the presence of nanostructured porous layer

Using linear stability analysis, the influence of boundary roughness on electro-hydrodynamic Rayleigh-Taylor instability (EHRTI), in a poorly electrically conducting fluid film of finite thickness, is studied. It is a theoretical study, based on the assumption of densely packed porous lining, prepared with smart material of nanostructure, that permits the use of modified Darcy equation with Saffman-slip condition at the interface. Modify means the addition of Lorentz forces due to magnetic and electric fields. A dispersion that accounts for the growth rate of perturbed waves is derived and stability discussed theoretically. The effects of electromagnetic fields, surface tension, boundary roughness, and porous layer are demonstrated using Stokes and lubrication approximations and shown graphically for the above-said physical parameters on the stability of the system. The strength of electromagnetic fields, porous layer and boundary roughness decreases the unstable growth rate for finitely conducting fluids, while surface tension stabilizes the system for a lower Bond number.

Shapes of large, static soap bubbles

Standard predictions induced by the balance of surface tension and pressure dictate that static soap bubbles must be spherical. However, definite non-spherical shapes appear in large bubbles, where noticeable oblate or prolate deformations occur. Gravity is the principal cause of such deformations, and multiple approaches for including its influence appear in recent literature. This paper derives a general surface-theoretic model by applying asymptotic and variational methods to a fully three-dimensional set-up where the soap bubble is a finite-thickness film. The procedure illuminates implicit assumptions, clarifying the discrepancies seen in previous models. Then the model is studied in four physical situations. In three of these situations, results show that there is a maximum stable span and volume of the soap bubbles, implying that their behaviour is qualitatively more similar to liquid drops than standard soap bubbles. Also, the model presented is directly analogous to the two-dimensional version of a hanging chain, and the derived predictions give practical insights into the construction of heavy containment vessels.

Determination of Stresses in Incrementally Deposited Films From Wafer-Curvature Measurements

Abstract We report closed-form formulas to calculate the incremental-deposition stress, the elastic relaxation stress, and the residual stress in a finite-thickness film from a wafer-curvature measurement. The calculation shows how the incremental deposition of a new stressed layer to the film affects the amount of the film/wafer curvature and the stress state of the previously deposited layers. The formulas allow the incremental-deposition stress and the elastic relaxation to be correctly calculated from the slope of the measured curvature versus thickness for arbitrary thicknesses and biaxial moduli of the film and the substrate. Subtraction of the cumulative elastic relaxation from the incremental-deposition stress history results in the residual stress left in the film after the whole deposition process. The validities of the formulas are confirmed by curvature measurements of electrodeposited Ni films on substrates with different thicknesses.

Decohesion of a rigid flat punch from an elastic layer of finite thickness

Interfacial bond strength is a crucial mechanical property of solid adhesive joints that plays an important role in a wide range of applications. A common way of quantifying mechanical strength of an adhered interface is to measure the apparent adhesion strength by finding the maximum pulling force in a tensile bond test and dividing it by the area. Despite the simplicity of this method, there is growing evidence suggesting that the measured quantity is not necessarily an intrinsic attribute of the interface but depends on thickness of the adhesive film and size of the interface. In this work, the critical pull-off force of a flat rigid punch adhered to an elastic film of finite thickness is studied via asymptotic analysis as well as finite element (FE) simulations. The decohesion behavior is found to be governed by two dimensionless parameters η and φ: the former represents the deformation of the interface relative to the interaction distance of interfacial forces, while the latter denotes a correction factor due to finite thickness of the film. As η changes from 0 to infinity, the interface decohesion would take place from uniform detachment (DMT-like) to crack-like propagation (JKR-like). The transition behavior can be well described by an empirical solution, which suggests a new rational procedure to consistently characterize the intrinsic adhesion properties of an adhered interface from tensile bond tests. Finally, the general empirical solution and the adhesion characterization procedure are directly validated by a series of experiments via detaching a stainless-steel flat punch from adhesive Polydimethylsiloxane (PDMS) films. This work not only offers a clear and explicit solution to capture the transition behavior of interface decohesion but also provides a guideline for modulating adhesion performance via geometry rather than chemistry of the adhesives.

Flow Regimes for Laminar Film Condensation on a Vertical Plate With an Upward Vapor Flow

Abstract Laminar film condensation on a vertical plate with an upward vapor flow is studied. An approximate integral model of the condensate film and the boundary layer of the vapor is numerically solved, taking into account both gravity and interfacial shear. Here, three types of solution are examined: (i) zero film thickness at the bottom; (ii) zero flowrate with a finite film thickness at the bottom; and (iii) negative flowrates at the bottom. The film thickness and the average Nusselt number are shown as functions of the distance along the plate and the plate length, respectively. The terminal lengths of the solutions of the types (i) and (ii) are calculated against the degree of the subcooling. Moreover, the results are compared with those derived using the approximation method where the shearing stress on the vapor–liquid interface is composed of only the momentum transferred by the suction mass (the Shekriladze–Gomelauri approach). It is found that the average Nusselt number is well described by the Shekriladze–Gomelauri model in the range of the solution type (ii), while the average Nusselt number for the thinnest-film solution of the type (iii) is asymptotically consistent with the Shekriladze–Gomelauri value for long plates.

Biskyrmion lattices in centrosymmetric magnetic films

Abstract Theoretical framework is developed that explains biskyrmion lattices observed in non-chiral magnetic films. We study films of finite thickness containing up to $1000\times1000\times100$ spins. Hexatic biskyrmion lattices in a pure 2D exchange model are naturally described by the Weierstrass $\wp$ and $\zeta$ elliptic functions. Starting with such a lattice as an initial state we investigate how it evolves towards the minimum-energy state in the presence of perpendicular magnetic anisotropy and dipole-dipole interaction. In accordance with experiments, we find that the final state is a triangular lattice of biskyrmion bubbles containing Bloch lines.

Stabilty of biskyrmions in centrosymmetric magnetic films

Motivated by the observation of biskyrmions in centrosymmetric magnetic films (Yu et al. Nature Communications 2014, Wang et al. Advanced Materials 2016), we investigate analytically and numerically the stability of biskyrmions in films of finite thickness, taking into account the nearest-neighbor exchange interaction, perpendicular magnetic anisotropy (PMA), dipole-dipole interaction (DDI), and the discreteness of the atomic lattice. The biskyrmion is characterized by the topological charge $Q=2$, the spatial scale $\lambda$, and another independent length $d$ that can be interpreted as a separation of two $Q=1$ skyrmions inside a $Q=2$ topological defect in the background of uniform magnetization. We find that biskyrmions with $d$ of order $\lambda$ can be stabilized by the magnetic field within a certain range of the ratio of PMA to DDI in a film having a sufficient number of atomic layers $N_{z}$. The shape of biskyrmions has been obtained by the numerical minimization of the energy of interacting spins in a $1000\times1000\times N_{z}$ atomic lattice. It is close to the exact solution of Belavin-Polyakov model when $d$ is below the width of the ferromagnetic domain wall. We compute the magnetic moment of a biskyrmion and discuss ways of creating biskyrmions in experiment.

The effects of a horizontal magnetic field on the Rayleigh–Taylor instability

The stability of a thin conductive liquid film flowing along a solid wall is an important problem that occurs in many proposed fusion device designs. In this paper we investigate the linear stability of an electrically conductive liquid film of finite thickness in the presence of a strong magnetic field. Inviscid flows of finite and infinite electric conductivity are considered. The magnetic field is found to decrease the unstable growth rate for both finite and infinite conductivity fluids but only narrows the unstable modes for infinite conductivity fluids. Our theory serves as an extension to the classical theory by Chandrasekhar (1961) [1] by considering the finite-thickness and finite-conductivity effects.

Magnetism of Bi2Se3 thin films with Eu-rich flat inclusions

We report the results of experimental and theoretical studies of Eu-doped Bi2Se3 thin films with extremely inhomogeneous distribution of magnetic component. The obtained electron microscopy images suggest that Eu atoms are concentrated within platelet-like nanoinclusions. The number of inclusions grows with the increase in Eu content, x. Moreover, at relatively high x values, the stacks of platelets (inclusions located one under another) become rather frequent. A comparative analysis of magnetic properties of the films under study reveals no pronounced changes of their temperature dependence with the increase in x, which, however, leads to the decrease in the average magnetic moment per Eu atom. A theoretical analysis of different mechanisms contributing to a possible magnetic ordering in the Eu-doped films demonstrates that at small distances (i.e. within a platelet) a dominant contribution is related to the RKKY interaction via electrons in the bulk, while the ordering at inter-platelet distances is governed by magnetic dipole–dipole interaction. The latter implies the antiferromagnetic ordering within the stacks of platelets explaining a drop of per Eu atom. We employ the model of a metallic spin glass to estimate the transition temperature, characterising the interaction within the ensemble of randomly distributed magnetic platelets. This estimate gives satisfactory agreement with the experiment, even if we take into account a finite film thickness, thus, neglecting the interaction anisotropy and including only the antiferromagnetism related to the stacking. While the overall contribution of interface Dirac electrons is damped in the systems under study, we argue that the obtained results can be used for the investigation of ultrathin films with analogous impurity profile, where this contribution should be clearly pronounced.