Commensurate-incommensurate Phase Transition Research Articles

The electric conductivity and dielectric properties of Tl(GaS2)1 – x (InSe2) x solid solutions

The effect of composition and temperature on the electrical conductivity and the permittivity of the Tl(GaS2)1 – x (InSe2) x has been studied. It is found that the permittivity and the conductivity increase with temperature and vary linearly as the InSe2 concentration increases: in this case, the conductivity decreases and the permittivity increases. It is confirmed that the system under study contains two series of solid solutions. It is shown that the commensurate–incommensurate phase transition temperatures shift to lower values as the InSe2 concentration increases.

Refractometry of Rb2ZnCl4 crystals under uniaxial pressure

The influence of uniaxial pressures applied along the main crystallophysical directions on the dispersion and temperature dependences of the refractive index n i of Rb2ZnCl4 crystals has been investigated. The n i value is found to be rather sensitive to uniaxial pressures, whereas uniaxial stress does not change the character of the dispersion and temperature dependences of n i. The pressure-induced changes in electronic polarizability αі, refraction R, and the parameters of UV oscillators are studied for mechanically deformed Rb2ZnCl4 crystals. The contributions of the UV and IR oscillators to the changes in n i at different temperatures, in different spectral regions, and under different mechanical stresses are estimated. The points of paraelectric–incommensurate–commensurate phase transitions (PTs) are found to undergo a significant pressure-induced shift to different temperature regions, depending on the pressure-application direction.

Influence of misorientation on graphene Moiré patterns

In this work the influence of film-substrate misorientation on the strain-induced ordering of graphene films on various metallic surfaces is examined using a mesoscopic continuum model and first-principles atomistic calculations. The periodicity and free energy of the Moir\'e patterns that emerge are studied as a function of film-substrate adhesion strength for misfit strains far from and close to an incommensurate-commensurate phase transition. Interestingly the lowest energy states are found to be at small but finite misorientation even though these states have a higher domain wall density than the zero-misorientation states. First-principles density functional theory calculations are used to connect the results with experimental findings in graphene epitaxy. This combination of mesoscopic and atomistic approaches can be applied to the study of a wide range of strained 2D material systems including the III-nitride monolayer systems.

Birefringence Imaging Measurements on Various Structural Phase Transitions in (CnH2n+1NH3)2MnCl4 with n = 1, 2, and 3 Using Multiple Wavelengths

Birefringence imaging microscopy is well suited for comprehensively investigating various structural phase transitions but its weak point is that it imposes an inherent limit on the maximum retardance that can be detected. To detect retardance above this limit, we performed simultaneous birefringence measurements at multiple wavelengths on (CnH2n+1NH3)2MnCl4 with \(n = 1,2,3\). For n = 1, we successfully detected large jumps in retardance (over six times greater than the limit) in the first-order phase transitions at Tc1 \( \simeq \) 88 K and Tc2 \( \simeq \) 251 K. For n = 2, a gradual change in retardance appears in the second-order phase transition at Tc = 214 K. High-definition images of optical fast-axis azimuths provided information on the misorientation of the alkylammonium chains. For n = 3, a retardance kink appears at Tc4 \( \simeq \) 152–155 K, and a retardance jump appears in the commensurate-incommensurate phase transition at Tc5 \( \simeq \) 96–99 K.

Dislocations in stacking and commensurate-incommensurate phase transition in bilayer graphene and hexagonal boron nitride

Dislocations corresponding to a change of stacking in two-dimensional hexagonal bilayers, graphene and boron nitride, and associated with boundaries between commensurate domains are investigated using the two-chain Frenkel-Kontorova model on top of ab initio calculations. Structural transformations of bilayers in which the bottom layer is stretched and the upper one is left to relax freely are considered for gradually increased elongation of the bottom layer. Formation energies of dislocations, dislocation width and orientation of the boundary between commensurate domains are analyzed depending on the magnitude and direction of elongation. The second-order phase transition from the commensurate phase to the incommensurate one with multiple dislocations is predicted to take place at some critical elongation. The order parameter for this transition corresponds to the density of dislocations, which grows continuously upon increasing the elongation of the bottom layer above the critical value. In graphene and metastable boron nitride with the layers aligned in the same direction, where elementary dislocations are partial, this transition, however, is preceded by formation of the first dislocation at the elongation smaller than the critical one. The phase diagrams including this intermediate state are plotted in coordinates of the magnitude and direction of elongation of the bottom layer.

Phase Diagram of Modulated Structures in Ferroelectric Crystals Based on Quantum Ising Model with Third-Neighbor Interactions

Incommensurate–commensurate phase transitions are analyzed using a model derived from the normal coordinate Hamiltonian for a crystal lattice. The Hamiltonian consists of a local self-potential and effective third-neighbor interactions. Free energies of various modulated phases are calculated with a mean-field approximation under the condition that two quantum states within the local potential are important at low temperature. It is demonstrated that the quantum effect works to stabilize the incommensurate phase rather than the commensurate phase. Even at zero temperature, the incommensurate phase can occupy a finite region in the phase diagram. This situation is similar to quantum paraelectricity in some ferroelectrics, and can be expected as a general feature of modulated structures of dielectric crystals. The phase diagram for ferroic first- and third-neighbor interactions but antiferroic second-neighbor interactions is constructed theoretically and is discussed in detail to explain qualitatively the l...

Pressure-induced normal-incommensurate and incommensurate-commensurate phase transitions in CrOCl.

The high-pressure behavior of layered CrOCl is shown to be governed by non-bonded interactions between chlorine atoms in relation to a rigid framework composed of Cr and O atoms. The competition between optimizing intra- and interlayer Cl–Cl distances and the general trend towards denser packing defines a novel mechanism for high-pressure phase transitions of inorganic materials. CrOCl possesses an incommensurate phase for 16–51 GPa. Single-crystal x-ray diffraction in a diamond anvil cell provides an accurate description of the evolution of the incommensurate wave with pressure. It thus demonstrates a continuous increase of the amplitude up to 30 GPa, followed by a decrease of the wavelength until a lock-in transition occurs at 51 GPa.

Pressure effect on magnetism and multiferroicity inMn2GeO4

The effect of high pressure exceeding 6 GPa on magnetism and multiferroicity was investigated for the olivine ${\text{Mn}}_{2}$${\text{GeO}}_{4}$ that shows successive magnetic transitions at ambient pressure and a ferroelectric ground state driven by spin-spiral order. We measured heat capacity, dielectric constant, and electric polarization at various pressures using a diamond anvil cell. The pressure evolution of the magnetic structures was also investigated by powder neutron diffraction measurements using a Paris-Edinburgh press. We found that all of the magnetic transition temperatures are enhanced monotonically by applying pressure. Furthermore, the spin-driven ferroelectricity persists up to about 6 GPa but suddenly vanishes by 6.3 GPa. A consistent description of all data is achieved if an incommensurate-commensurate phase transition occurs with pressurization and causes the suppression of ferroelectricity. We discuss the origin of the observed pressure effects on the magnetism and multiferroicity in ${\text{Mn}}_{2}$${\text{GeO}}_{4}$ in terms of a pressure-induced change in the superexchange magnetic interactions.

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.

Interlayer Magnetoresistance due to Chiral Soliton Lattice Formation in Hexagonal Chiral MagnetCrNb3S6

We investigate the interlayer magnetoresistance (MR) along the chiral crystallographic axis in the hexagonal chiral magnet CrNb3S6. In a region below the incommensurate-commensurate phase transition between the chiral soliton lattice and the forced ferromagnetic state, a negative MR is obtained in a wide range of temperature, while a small positive MR is found very close to the Curie temperature. Normalized data of the negative MR almost falls into a single curve and is well fitted by a theoretical equation of the soliton density, meaning that the origin of the MR is ascribed to the magnetic scattering of conduction electrons by a nonlinear, periodic, and countable array of magnetic soliton kinks.

Commensurate-incommensurate magnetic phase transition induced in TbNi5 by an external magnetic field

Neutron-diffraction studies of a single crystal of TbNi5 have been performed. Temperature and field dependences of the intensities of the Bragg reflection (001) and magnetic satellites (001)− and (001)+ have been determined. In the temperature range of 7–10 K, sharp changes in the intensities of both the Bragg reflection and its satellites have been revealed. A conclusion is made that these changes are due to the existence of a magnetic transition from an incommensurate into a lock-in structure. It has been found that at 11 K an external magnetic field μ0H = 0.1 T oriented along the [100] axis induces the same magnetic state of the crystal as its cooling to 7 K in the absence of a field. In an external magnetic field μ0H = 0.4 T, there occurs a magnetic transition from the incommensurate phase with a wave vector k = 2π/c (0, 0, 0.18) into a commensurate ferromagnetic phase with k = 0. In the ferromagnetic phase, an increase in the field from 0.4 to 0.6 T is accompanied by an increase in the intensity of the ferromagnetic reflection (001) by a factor of 1.6. This indicates the existence of strong fluctuations of the magnetization at 0.4 T.

Spin state of Mn3O4investigated by55Mn nuclear magnetic resonance

The ${}^{55}$Mn nuclear magnetic resonance spectrum for the spinel oxide Mn${}_{3}$O${}_{4}$ was measured at low temperature to investigate the spin structure in the ground state. The spectrum consists of three peaks in the frequency range of 250--265 MHz, which corresponds to the hyperfine field range of 24--25 T. The temperature dependence of the spectrum and the rf enhancement factor show that Mn${}^{3+}$ ions have two different magnetic moments, one of which is strongly related to the commensurate-incommensurate phase transition. This is consistent with the picture of two magnetic moments $R$ and $S$ claimed from the results of a neutron experiment. Comparison with a heat-treated sample suggests a relation between the two different magnetic moments and the occupation sites of manganese ions, the tetrahedral and octahedral sites. Theoretical estimations of the dipolar hyperfine field and the observed peak splitting predict that the magnetic moments of $R$ and $S$ differ by 5$%$ at maximum. The spin-spin relaxation time has a frequency dependence that induces spectrum broadening and further splitting of the peak coming from $S$, indicating that the Suhl-Nakamura interaction is the major relaxation mechanism in Mn${}_{3}$O${}_{4}$.

Commensurate-incommensurate phase transition in chlorine monolayer chemisorbed on Ag(111): Direct observation of crowdion condensation into a domain-wall fluid

The commensurate-incommensurate phase transition in chlorine monolayer on Ag(111) has been studied with low-temperature scanning tunneling microscopy and low-energy electron diffraction. We report the observation of self-interstitial defects: two-dimensional (2D) crowdions formed at the initial stage of the ($\sqrt{3}\ifmmode\times\else\texttimes\fi{}\sqrt{3}$)R30${}^{\ensuremath{\circ}}$ lattice compression. After critical coverage of 0.34 monolayer (ML) the crowdions condense into a domain-wall fluid. As coverage further increases, the domain-wall crystal solidifies with average wall separation of 23 \AA{}.

Double-kphase of the Dzyaloshinskii-Moriya helimagnet Ba2CuGe2O7

Neutron diffraction is used to reinvestigate the magnetic phase diagram of the noncentrosymmetric tetragonal antiferromagnet Ba${}_{2}$CuGe${}_{2}$O${}_{7}$. An incommensurate double-$k$ magnetic phase is detected near the commensurate-incommensurate phase transition. This phase is stable only for field closely aligned with the fourfold symmetry axis. The results emphasize the inadequacy of existing theoretical models for this unique material, and points to additional terms in the Hamiltonian or lattice effects.

Temperature‐dependent thermo‐mechanical and Raman spectroscopy study of the SRS‐active melilite‐type crystal Ca2ZnSi2O7 (hardystonite) at its incommensurate–commensurate phase transition

AbstractStimulated Raman scattering (SRS) active crystals of Ca2ZnSi2O7 (hardystonite) adopt a melilite‐type structure at temperatures above ca. 402 K, while at ambient conditions they show a two‐dimensionally incommensurate structure modulation. To study the influence of the incommensurability of the structure on SRS‐based χ(3)‐nonlinear lasing of the crystals temperature‐dependent Raman spectroscopy investigations at the commensurate–incommensurate phase‐transition and comparative SRS measurements in the high‐temperature and in the low‐temperature phase of Ca2ZnSi2O7 are reported. In addition, the commensurate–incommensurate phase transition is characterised by caloric and dilatometric measurements, and linear optical properties of the crystals are given.

The quantum compass chain in a transverse magnetic field

We study the magnetic behaviors of a spin-1/2 quantum compass chain (QCC) in a transverse magnetic field, by means of the analytical spinless fermion approach and numerical Lanczos method. In the absence of the magnetic field, the phase diagram is divided into four gapped regions. To determine what happens by applying a transverse magnetic field, using the spinless fermion approach, critical fields are obtained as a function of exchanges. Our analytical results show, the field-induced effects depend on in which one of the four regions the system is. In two regions of the phase diagram, the Ising-type phase transition happens in a finite field. In another region, we have identified two quantum phase transitions in the ground state magnetic phase diagram. These quantum phase transitions belong to the universality class of the commensurate-incommensurate phase transition. We also present a detailed numerical analysis of the low energy spectrum and the ground state magnetic phase diagram. In particular, we show that the intermediate state ($h_{c_{1}}<h<h_{c_{2}}$) is gapful, describing the spin-flop phase.

Commensurate-incommensurate phase transition in bilayer graphene

A commensurate-incommensurate phase transition in bilayer graphene is investigated in the framework of the Frenkel-Kontorova model extended to the case of two interacting chains of particles. Analytic expressions are derived to estimate the critical unit elongation of one of the graphene layers at which the transition to the incommensurate phase takes place, the length and formation energy of incommensurability defects (IDs) and the threshold force required to start relative motion of the layers on the basis of dispersion-corrected density functional theory calculations of the interlayer interaction energy as a function of the relative position of the layers. These estimates are confirmed by atomistic calculations using the DFT-D based classical potential. The possibility to measure the barriers for relative motion of graphene layers by the study of formation of IDs in bilayer graphene is discussed.

Antiferromagnetic resonance in ferroborate NdFe 3(BO 3) 4

The AFMR spectra of the NdFe 3(BO 3) 4 crystal are measured in a wide range of frequencies and temperatures. It is found that by the type of its magnetic anisotropy the compound is an “easy-plane” antiferromagnet with a weak anisotropy in the basal plane. The effective magnetic parameters are determined: anisotropy fields H a1 =1.14 kOe and H a2 =60 kOe and magnetic excitation gaps Δ ν 1 =101.9 GHz and Δ ν 2 =23.8 GHz. It is shown that commensurate–incommensurate phase transition causes a shift in resonance field and a considerable change in absorption line width. At temperatures below 4.2 K nonlinear regimes of AFMR excitation at low microwave power levels are observed.

CW one-micron (4F3/2-4I11/2) laser oscillation of Nd3+ ions in the melilite-type crystal Ca2MgSi2O7:Nd3+(Na+) at its incommensurate–commensurate phase transition

The spectroscopic and stimulated-emission (4F3/2→4I11/2) properties of the novel melilite-type laser crystal Ca2MgSi2O7:Nd3+(Na+) were studied in a temperature range that covers its incommensurate–commensurate (IC↔N) phase transition. The phase transition temperatures of both undoped Ca2MgSi2O7 and the doped crystal were ascertained at 346.6 K (undoped) and 341.3 K (doped) by means of differential scanning calorimetry (DSC). The temperature-dependent spectroscopic and laser experiments showed a significant decrease in CW output power and a strong distortion of the generated lasing beam in the region of the phase transition. The observed crystal field disorder of Nd3+ lasants in Ca2MgSi2O7:Nd3+(Na+) is dominantly due to occupation of the position of Ca2+ by cations of different valency, while the influence of incommensurability is of minor importance.

Piezo-optic properties of incommensurately modulated K2ZnCl4 crystals

The effect that uniaxial pressures along the principal crystallophysical directions have on the dispersion and temperature dependences of the birefringence in incommensurate K2ZnCl4 crystals has been investigated in a wide temperature range. This parameter has been established to be fairly sensitive to uniaxial pressures. The spectral and temperature dependences of combined piezo-optic coefficients are analyzed. Significant anomalies of these coefficients are found at the incommensurate-commensurate phase transition. They are due to the change in the induced birefringence that results from spontaneous polarization and to the significant effect of uniaxial stress on the soliton structure of the crystal. The contributions that the electrooptic effect, the elasto-optic effect, and the order parameter make to the spontaneous changes in the piezooptic coefficients are separated.