Commensurate-incommensurate Transition Research Articles

Improved modeling of two-dimensional transitions in dense phases on crystalline surfaces. Krypton-graphite system.

This paper presents a refined technique to describe two-dimensional phase transitions in dense fluids adsorbed on a crystalline surface. Prediction of parameters of 2D liquid-solid equilibrium is known to be an extremely challenging problem, which is mainly due to a small difference in thermodynamic functions of coexisting phases and lack of accuracy of numerical experiments in case of their high density. This is a serious limitation of various attempts to circumvent this problem. To improve this situation, a new methodology based on the kinetic Monte Carlo method was applied. The methodology involves analysis of equilibrium gas-liquid and gas-solid systems undergoing an external potential, which allows gradual shifting parameters of the phase coexistence. The interrelation of the chemical potential and tangential pressure for each system is then treated with the Gibbs-Duhem equation to obtain the point of intersection corresponding to the liquid/solid-solid equilibrium coexistence. The methodology is demonstrated on the krypton-graphite system below and above the 2D critical temperature. Using experimental data on the liquid-solid and the commensurate-incommensurate transitions in the krypton monolayer derived from adsorption isotherms, the Kr-graphite Lennard-Jones parameters have been corrected resulting in a higher periodic potential modulation.

Demagnetization of K0.4(Cr(CN)6)(Mn((R/S)-pn))(R/S)-pnH0.6 Molecular Magnets Accompanied by Discrete Transitions in the Incommensurate Magnetic Phase

The magnetic moment serrated decrease was observed in K0.4(Cr(CN)6)(Mn((R/S)-pn))(R/S)-pnH0.6 chiral molecular magnet. We discussed observed magnetization jumps in terms of domain walls, spin chains and spin-soliton. Theoretical model of the commensurate-incommensurate transitions is in good agreement with experimental data. Contribution of the magnetic anisotropy to these transitions was experimentally confirmed.

The mechanism of domain-wall structure formation in Ar-Kr submonolayer films on graphite

Using Monte Carlo simulation method in the canonical ensemble, we have studied the commensurate-incommensurate transition in two-dimensional finite mixed clusters of Ar and Kr adsorbed on graphite basal plane at low temperatures. It has been demonstrated that the transition occurs when the argon concentration exceeds the value needed to cover the peripheries of the cluster. The incommensurate phase exhibits a similar domain-wall structure as observed in pure krypton films at the densities exceeding the density of a perfect $(\sqrt{3}\times\sqrt{3})R30^\circ$ commensurate phase, but the size of commensurate domains does not change much with the cluster size. When the argon concentration increases, the composition of domain walls changes while the commensurate domains are made of pure krypton. We have constructed a simple one-dimensional Frenkel-Kontorova-like model that yields the results being in a good qualitative agreement with the Monte Carlo results obtained for two-dimensional systems.

Effective and accurate approach for modeling of commensurate-incommensurate transition in krypton monolayer on graphite.

Commensurate-incommensurate (C-IC) transition of krypton molecular layer on graphite received much attention in recent decades in theoretical and experimental researches. However, there still exists a possibility of generalization of the phenomenon from thermodynamic viewpoint on the basis of accurate molecular simulation. Recently, a new technique was developed for analysis of two-dimensional (2D) phase transitions in systems involving a crystalline phase, which is based on accounting for the effect of temperature and the chemical potential on the lattice constant of the 2D layer using the Gibbs-Duhem equation [E. A. Ustinov, J. Chem. Phys. 140, 074706 (2014)]. The technique has allowed for determination of phase diagrams of 2D argon layers on the uniform surface and in slit pores. This paper extends the developed methodology on systems accounting for the periodic modulation of the substrate potential. The main advantage of the developed approach is that it provides highly accurate evaluation of the chemical potential of crystalline layers, which allows reliable determination of temperature and other parameters of various 2D phase transitions. Applicability of the methodology is demonstrated on the krypton-graphite system. Analysis of phase diagram of the krypton molecular layer, thermodynamic functions of coexisting phases, and a method of prediction of adsorption isotherms is considered accounting for a compression of the graphite due to the krypton-carbon interaction. The temperature and heat of C-IC transition has been reliably determined for the gas-solid and solid-solid system.

Moiré patterns as a probe of interplanar interactions for graphene on h-BN.

By atomistic modeling of moiré patterns of graphene on a substrate with a small lattice mismatch, we find qualitatively different strain distributions for small and large misorientation angles, corresponding to the commensurate-incommensurate transition recently observed in graphene on hexagonal BN. We find that the ratio of C-N and C-B interactions is the main parameter determining the different bond lengths in the center and edges of the moiré pattern. Agreement with experimental data is obtained only by assuming that the C-B interactions are at least twice weaker than the C-N interactions. The correspondence between the strain distribution in the nanoscale moiré pattern and the potential energy surface at the atomic scale found in our calculations makes the moiré pattern a tool to study details of dispersive forces in van der Waals heterostructures.

Commensurate-incommensurate solid transition in theHe4monolayer onγ-graphyne

Path-integral Monte Carlo calculations have been performed to study the $^4$He adsorption on $\gamma$-graphyne, a planar network of benzene rings connected by acetylene bonds. Assuming the $^4$He-substrate interaction described by a pairwise sum of empirical $^4$He-carbon interatomic potentials, we find that unlike $\alpha$-graphyne, a single sheet of $\gamma$-graphyne is not permeable to $^4$He atoms in spite of its large surface area. One-dimensional density distributions computed as a function of the distance from the graphyne surface reveal a layer-by-layer growth of $^4$He atoms. A partially-filled $^4$He monolayer is found to exhibit different commensurate solid structures depending on the helium coverage; it shows a C$_{2/3}$ commensurate structure at an areal density of 0.0491\AA$^{-2}$, a C$_{3/3}$ structure at 0.0736\AA$^{-2}$, and a C$_{4/3}$ structure at 0.0982\AA$^{-2}$. While the promotion to the second layer starts beyond the C$_{4/3}$ helium coverage, the first $^4$He layer is found to form an incommensurate triangular solid when compressed with the development of the second layer.

Atomic simulations of effects of contact size and interfacial interaction strength on superlubricity in incommensurate sliding interface

Understanding the effects of contact size and interfacial interaction strength on superlubricity in incommensurate sliding interface is critically needed for the design and development of nanoscale ultra-low friction devices. This study uses molecular dynamics simulations to explore the sliding friction behaviors of an incommensurate interface consisting of a diamond slider and a silver substrate. The instantaneous relative lattice constant is proposed to quantitatively describe the commensurability of contacting surfaces in the sliding process. It is found that when the contact size is large, the slider exhibits ultra-low friction force. While for small contact size, superlubricity behavior breaks down,which is due to the transition of incommensurate–commensurate interfacial configuration in the local contact region. It is also found that when the interfacial interaction strength is reduced below a critical value, the obvious stick–slip motion observed for the small slider with large interfacial interaction strength disappears and superlubricity behavior occurs, which results from the incommensurate interfacial configuration in the contact region maintained during the sliding process. These results provide a first demonstration that the instantaneous incommensurate–commensurate transition in the local contact region can result in the breakdown of superlubricity in a realistic three-dimensional sliding system. The obtained results not only may guide the design of nanoscale ultra-low friction devices, but also provide some insights into the origins of friction at macroscopic interfaces which usually consists of many small nanoscale contacts.

Commensurate-incommensurate magnetic phase transition in the Fe-doped bilayer ruthenateCa3Ru2O7

Neutron diffraction studies have revealed an uncommon commensurate-incommensurate magnetic phase transition with decreasing temperature in the (\ensuremath{\sim}5%) Fe-doped bilayer ruthenate ${\mathrm{Ca}}_{3}(\mathrm{Ru},\mathrm{Fe}{)}_{2}{\mathrm{O}}_{7}$. An incommensurate phase formed of a cycloidal spiral spin structure coexists with a commensurate one below the phase transition at 42 K and persists down to the lowest temperature, accompanied by higher-order magnetic satellite peaks which indicate the formation of a magnetic soliton lattice. We ascribe these findings to the competing magnetic interactions in this system. This study demonstrates an effective approach to tune novel magnetic and electronic properties of ruthenates via $3d$ magnetic transition-metal substitution.

Commensurate–incommensurate transition in graphene on hexagonal boron nitride

When a crystal is subjected to a periodic potential, under certain circumstances (such as when the period of the potential is close to the crystal periodicity; the potential is strong enough, etc.) it might adjust itself to follow the periodicity of the potential, resulting in a, so called, commensurate state. Such commensurate-incommensurate transitions are ubiquitous phenomena in many areas of condensed matter physics: from magnetism and dislocations in crystals, to vortices in superconductors, and atomic layers adsorbed on a crystalline surface. Of particular interest might be the properties of topological defects between the two commensurate phases: solitons, domain walls, and dislocation walls. Here we report a commensurate-incommensurate transition for graphene on top of hexagonal boron nitride (hBN). Depending on the rotational angle between the two hexagonal lattices, graphene can either stretch to adjust to a slightly different hBN periodicity (the commensurate state found for small rotational angles) or exhibit little adjustment (the incommensurate state). In the commensurate state, areas with matching lattice constants are separated by domain walls that accumulate the resulting strain. Such soliton-like objects present significant fundamental interest, and their presence might explain recent observations when the electronic, optical, Raman and other properties of graphene-hBN heterostructures have been notably altered.

Universal logarithmic temperature dependence of magnetic susceptibility of one-dimensional electrons at critical values of magnetic field

We study the leading low-temperature dependence of magnetic susceptibility of one-dimensional electrons with a fixed total number of particles at the magnetic fields equal to zero-temperature critical values where the magnetic field induces commensurate-incommensurate quantum phase transitions. For free and repulsively interacting electrons there is only one such critical field corresponding to the transition to the fully polarized state. For attractively interacting electrons besides saturation field there is another critical field equal to the spin gap where zero-temperature magnetization sets in. For all cases, except for the lattice models at half filling, the magnetic susceptibility at critical values of magnetic field has a universal logarithmic temperature dependence, $\ensuremath{\chi}(T)=\ensuremath{\chi}(0)(1+2/ln\phantom{\rule{0.16em}{0ex}}T+\ensuremath{\cdots})$ for $T\ensuremath{\rightarrow}0$.

Domain-walls formation in binary nanoscopic finite systems

Using a simple one-dimensional Frenkel-Kontorowa type model, we have demonstrated that finite commensurate chains may undergo the commensurate-incommensurate (C-IC) transition when the chain is contaminated by isolated impurities attached to the chain ends. Monte Carlo (MC) simulation has shown that the same phenomenon appears in two-dimensional systems with impurities located at the peripheries of finite commensurate clusters.

The 1D Spin-1/2 XXZ Model in Transverse Uniform and Staggered Magnetic Fields

We have studied the ground state magnetic phase diagram of the one-dimensional anisotropic spin-1/2 XXZ model in the presence of transverse uniform and staggered magnetic fields. We have suggested that the presence study can be applied to a real magnet with the Dzyaloshinskii–Moriya interaction. In the absence of the staggered magnetic field, the phase diagram is divided into four regions. Using the numerical Lanczos method, we have done an accurate numerical experiment. We have presented a detailed numerical analysis of the low energy spectrum and the ground state magnetic phase diagram. Our numerical results show the staggered-field-induced effects depend on in which one of the four regions the system is. In one of the regions, we have identified two quantum phase transitions, which belong to the universality class of the commensurate-incommensurate phase transition.

Magnetic orders, excitations, and phase transitions in Fe1+yTe

We study the magnetic properties of Fe_1+y Te, a parent compound of the iron-based high-temperature superconductors. Motivated by recent neutron scattering experiments, we show that a spin-1 exchange model, supplemented by a single-ion spin anisotropy, accounts well for the experimentally observed low temperature magnetic phase diagram, that exhibits a commensurate bicollinear order at low Fe dopings (y < 0.12) and an incommensurate spin-spiral order at high Fe dopings (y > 0.12). We suggest that the commensurate-incommensurate transition at y = 0.12 is due to the competition between the exchange interaction and the local spin anisotropy. At low Fe dopings, the single-ion spin anisotropy is strong and pins the spins along the easy axis, which, together with the spatially anisotropic exchanges, induces a unusual bicollinear commensurate magnetic order. The low-energy spin-wave excitation is gapped due to the explict breaking of spin-rotational symmetry by the local spin anisotropy. At high Fe dopings, the single-ion anisotropy is weak, and the exchange favors an incommensurate coplanar state. The incommensurate magnetic wavevector averages out the spin anisotropy so that a gapless low-energy spin-wave excitation is obtained. We also analyze the low-energy hydrodynamic model and use it to describe the magneto-structural transition and the static and dynamical spin structure factors across the magnetic ordering transitions.

Role of magnetic chirality in polarization flip upon a commensurate-incommensurate magnetic phase transition in YMn2O5

We have performed simultaneous measurements of magnetic chirality by using polarized neutrons and electric polarization along the b-axis of single crystals of YMn$^{4+}$(Mn$_{1-x}$Ga$_{x}$)$^{3+}$O$_{5}$ with $x=0.047$ and 0.12, in which nonmagnetic Ga-ions dilute Mn$^{3+}$ spins. The $x=0.047$ sample exhibits high-temperature incommensurate (HT-ICM), commensurate (CM), and low-temperature incommensurate (LT-ICM) magnetic phases in order of decreasing temperature, whereas the $x=0.12$ sample exhibits only HT-ICM and LT-ICM phases. Here, the CM and LT-ICM phases are ferroelectric and weak-ferroelectric, respectively. Measurements conducted under zero field heating after various field-cooling conditions evidence that the microscopic mechanisms of the spin-driven ferroelectricity in the CM and LT-ICM phases are different: the magnetic chirality of Mn$^{4+}$ cycloidal spins plays a dominant role in the LT-ICM phase, whereas the magnetic exchange striction by the Mn$^{4+}$-Mn$^{3+}$ chain plays a dominant role in the CM phase. The polarization of YMn$_{2}$O$_{5}$ flips upon CM to LT-ICM phase transition because the ferroelectricity driven by the magnetic chirality and the exchange striction provides opposite directions of polarization.

ChemInform Abstract: Application of X‐Ray Resonant Diffraction to Structural Studies of Liquid Crystals

AbstractReview: 39 refs.

Commensurate-Incommensurate Transition with 2x2 Structure in the Mean-Field Approximation

Disordered-Incommensurate-Commensurate transitions with a 2 × 2 structure are analyzed in terms of the Ising model on a triangular lattice with conserved magnetization. In the mean-field approximation one finds that for a certain range of antiferromagnetic nearest and next nearest neighbour interactions paramagnetic-incommensurate-commensurate transitions take place in this order on lowering the temperature, which corresponds to the experimental situation on β-eucryptite.

Entropic commensurate-incommensurate transition.

The equilibrium properties of a minimal tiling model are investigated. The model has extensive ground state entropy, with each ground state having a quasiperiodic sequence of rows. It is found that the transition from the ground state to the high temperature disordered phase proceeds through a sequence of periodic arrangements of rows, in analogy with the commensurate-incommensurate transition. We show that the effective free energy of the model resembles the Frenkel-Kontorova Hamiltonian, but with temperature playing the role of the strength of the substrate potential, and with the competing lengths not explicitly present in the basic interactions.

Manipulating Majorana fermions in quantum nanowires with broken inversion symmetry

We study a Majorana-carrying quantum wire, driven into a trivial phase by breaking the spatial inversion symmetry with a tilted magnetic field. Interestingly, we predict that a supercurrent applied in the proximate superconductor is able to restore the topological phase and therefore the Majorana end states. Using Abelian bosonization, we further confirm this result in the presence of electron-electron interactions and show a profound connection of this phenomenon to the commensurate-incommensurate transition in one-dimensional doped Mott insulators. These results have important applications in, e.g., realizing a supercurrent-assisted braiding of Majorana fermions, which proves highly useful in topological quantum computation with realistic Majorana networks.

Atomistic and Coarse-Grained Modeling Strategies for Thin Film Nucleation and Growth on Quasicrystalline Surfaces

ABSTRACTStrategies are described for modeling the kinetics of non-equilibrium film growth during deposition of metals on quasicrystalline substrates. We review previous atomistic-level lattice-gas modeling and Kinetic Monte Carlo simulation for pseudomorphic (or commensurate) submonolayer growth based on a “disordered or irregular bond-network” (DBN) of neighboring adsorption sites. We describe extensions to treat strain effects and multilayer growth, and discuss a type of commensurate-incommensurate transition expected around 2-3 layers. We also describe a coarse-grained “step dynamics” modeling which tracks the dynamics of island edges in each layer rather than individual atoms. Step dynamics models can also include key aspects of the physics such as layer-dependent energetics, including quantum size effects, and strain effects.

Vanishing of the metal-insulator Peierls transition in pressurized BaVS3

BaVS${}_{3}$ presents a metal-to-insulator (MI) transition at ambient pressure due to the stabilization of a 2k${}_{\mathrm{F}}$ commensurate charge density wave (CDW) Peierls ground state built on the $d{z}^{2}$ V orbitals. The MI transition vanishes under pressure at a quantum critical point (QCP) where the electronic properties exhibit a non-Fermi liquid behavior. In this paper, we determine the CDW phase diagram under pressure and show that it combines both the vanishing of the second-order Peierls transition and a commensurate-incommensurate first-order delocking transition of the 2k${}_{\mathrm{F}}$ wave vector. We explain quantitatively the drop of the MI critical temperature by the decrease of the electron-hole pair lifetime of the CDW condensate due to an enhancement of the hybridization between the $d{z}^{2}$ and $e$(${t}_{2g}$) levels of the V under pressure.