Commensurate-incommensurate Transition Research Articles

Extreme sensitivity of a frustrated quantum magnet:Cs2CuCl4

We report a thorough theoretical study of the low temperature phase diagram of Cs_2CuCl_4, a spatially anisotropic spin S=1/2 triangular lattice antiferromagnet, in a magnetic field. Our results, obtained in a quasi-one-dimensional limit in which the system is regarded as a set of weakly coupled Heisenberg chains, are in excellent agreement with experiment. The analysis reveals some surprising physics. First, we find that, when the magnetic field is oriented within the triangular layer, spins are actually most strongly correlated within planes perpendicular to the triangular layers. This is despite the fact that the inter-layer exchange coupling in Cs_2CuCl_4 is about an order of magnitude smaller than the weakest (diagonal) exchange in the triangular planes themselves. Second, the phase diagram in such orientations is exquisitely sensitive to tiny interactions, heretofore neglected, of order a few percent or less of the largest exchange couplings. These interactions, which we describe in detail, induce entirely new phases, and a novel commensurate-incommensurate transition, the signatures of which are identified in NMR experiments. We discuss the differences between the behavior of Cs_2CuCl_4 and an ideal two-dimensional triangular model, and in particular the occurrence of magnetization plateaux in the latter. These and other related results are presented here along with a thorough exposition of the theoretical methods, and a discussion of broader experimental consequences to Cs_2CuCl_4 and other materials.

Pinning quantum phase transition for a Luttinger liquid of strongly interacting bosons

Quantum many-body systems can have phase transitions even at zero temperature; fluctuations arising from Heisenberg's uncertainty principle, as opposed to thermal effects, drive the system from one phase to another. Typically, during the transition the relative strength of two competing terms in the system's Hamiltonian changes across a finite critical value. A well-known example is the Mott-Hubbard quantum phase transition from a superfluid to an insulating phase, which has been observed for weakly interacting bosonic atomic gases. However, for strongly interacting quantum systems confined to lower-dimensional geometry, a novel type of quantum phase transition may be induced and driven by an arbitrarily weak perturbation to the Hamiltonian. Here we observe such an effect--the sine-Gordon quantum phase transition from a superfluid Luttinger liquid to a Mott insulator--in a one-dimensional quantum gas of bosonic caesium atoms with tunable interactions. For sufficiently strong interactions, the transition is induced by adding an arbitrarily weak optical lattice commensurate with the atomic granularity, which leads to immediate pinning of the atoms. We map out the phase diagram and find that our measurements in the strongly interacting regime agree well with a quantum field description based on the exactly solvable sine-Gordon model. We trace the phase boundary all the way to the weakly interacting regime, where we find good agreement with the predictions of the one-dimensional Bose-Hubbard model. Our results open up the experimental study of quantum phase transitions, criticality and transport phenomena beyond Hubbard-type models in the context of ultracold gases.

Transport between twisted graphene layers

Commensurate-incommensurate transitions are ubiquitous in physics and are often accompanied by intriguing phenomena. In few-layer graphene (FLG) systems, commensurability between honeycomb lattices on adjacent layers is regulated by their relative orientation angle $\ensuremath{\theta}$, which is in turn dependent on sample preparation procedures. Because incommensurability suppresses interlayer hybridization, it is often claimed that graphene layers can be electrically isolated by a relative twist, even though they are vertically separated by a fraction of a nanometer. We present a theory of interlayer transport in FLG systems which reveals a richer picture in which the specific conductance depends sensitively on $\ensuremath{\theta}$, single-layer Bloch-state lifetime, in-plane magnetic field, and bias voltage. We find that linear and differential conductances are generally large and negative near commensurate values of $\ensuremath{\theta}$, and small and positive otherwise. We show that accounting for interlayer coupling may be essential for describing transport in FLG despite its physically insignificant effect on the band structure of the system.

Multiferroic nanoregions and a memory effect in cupric oxide

We report the observation of multiferroic nanoregions in cupric oxide, CuO, by means of resonant soft x-ray magnetic scattering. There exists an anomalous memory effect for the direction of the electric polarization in the commensurate-incommensurate magnetic transition that coincides with the ferroelectric transition. Scattering results, incorporated with simulations of diffuse scattering, lead us to propose a scenario that preserved spin handedness in the multiferroic nanoregions is responsible for this memory effect in the magnetically induced ferroelectric properties of CuO.

Single magnetic chirality in the magnetoelectricNdFe3(B11O3)4

We have performed an extensive study of single crystals of the magnetoelectric ${\text{NdFe}}_{3}{({^{11}\text{B}\text{O}}_{3})}_{4}$ by means of a combination of single-crystal neutron diffraction and spherical neutron polarimetry. Our investigation did not detect significant deviations at low temperatures from space group $R32$ concerning the chemical structure. With respect to magnetic ordering our combined results demonstrate that in the commensurate magnetic phase below ${T}_{N}\ensuremath{\approx}30\text{ }\text{K}$ all three magnetic Fe moments and the magnetic Nd moment are aligned ferromagnetically in the basal hexagonal plane but align antiferromagnetically between adjacent planes. The phase transition to the low-temperature incommensurate (IC) magnetic structure observed at ${T}_{\text{IC}}\ensuremath{\approx}13.5\text{ }\text{K}$ appears to be continuous. By means of polarized neutron studies it could be shown that in the incommensurate magnetic phase the magnetic structure of ${\text{NdFe}}_{3}{({^{11}\text{B}\text{O}}_{3})}_{4}$ is transformed into a long-period antiferromagnetic helix with single chirality. Close to the commensurate-incommensurate phase transition third-order harmonics were observed, which in addition indicate the formation of magnetic solitons.

Pokrovsky-Talapov model at finite temperature: A renormalization-group analysis

We calculate the finite-temperature shift of the critical wavevector $Q_{c}$ of the Pokrovsky-Talapov model using a renormalization-group analysis. Separating the Hamiltonian into a part that is renormalized and one that is not, we obtain the flow equations for the stiffness and an arbitrary potential. We then specialize to the case of a cosine potential, and compare our results to well-known results for the sine-Gordon model, to which our model reduces in the limit of vanishing driving wavevector Q=0. Our results may be applied to describe the commensurate-incommensurate phase transition in several physical systems and allow for a more realistic comparison with experiments, which are always carried out at a finite temperature.

Low-temperature specific heat of one-dimensional multicomponent systems at the commensurate-incommensurate phase transition point

Low-temperature dependence of specific heat of one-dimensional multicomponent systems at the commensurate-incommensurate phase transition point is studied. It is found that for canonical systems, with a fixed total number of particles, low-temperature specific heat linearly depends on temperature with a diverging prefactor.

Study of SF6 adsorption on graphite using infrared spectroscopy

We report an experimental study of adsorbed monolayers of SF(6) on graphite using infrared reflection absorption spectroscopy supplemented by ellipsometry. The asymmetric S-F stretch mode nu(3) near 948 cm(-1) in the gas is strongly blueshifted in the film by dynamic dipole coupling. This blueshift is very sensitive to the intermolecular spacing in the SF(6) layer. We convert the measured frequency nu(3) to a lattice spacing a, using a self-consistent field calculation, calibrated by the frequency in the commensurate phase. The resolution in lattice spacing is 0.002 A, although there is a larger systematic uncertainty associated with nondynamic-dipole contributions to the frequency shift. We map the commensurate-incommensurate transition, a transition between two incommensurate phases, and the melting transition. These results are compared to previous x-ray data. We provide a new determination of the layer critical point (156 K), the layer condensation line down to 110 K, and the spreading pressure at saturation in this temperature range.

Anomalous spin waves and the commensurate-incommensurate magnetic phase transition inLiNiPO4

Detailed spin-wave spectra of magnetoelectric ${\text{LiNiPO}}_{4}$ have been measured by neutron scattering at low temperatures in the commensurate (C) antiferromagnetic (AF) phase below ${T}_{N}=20.8\text{ }\text{K}$. An anomalous shallow minimum is observed at the modulation vector of the incommensurate (IC) AF phase appearing above ${T}_{N}$. A linear spin-wave model based on Heisenberg exchange couplings and single-ion anisotropies accounts for all the observed spin-wave dispersions and intensities. Along the $b$ axis an unusually strong next-nearest-neighbor AF coupling competes with the dominant nearest-neighbor AF exchange interaction and causes the IC structure.

Spin-Orbital Singlet and Quantum Critical Point on the Diamond Lattice:FeSc2S4

We present a theory of spin and orbital physics in the A-site spinel compound FeSc2S4, which experimentally exhibits a broad "spin-orbital liquid" regime. A spin-orbital Hamiltonian is derived from a combination of microscopic consideration and symmetry analysis. We demonstrate a keen competition between spin-orbit interactions, which favor formation of a local "spin-orbital singlet," and exchange, which favors magnetic and orbital ordering. Separating the spin-orbital singlet from the ordered state is a quantum critical point. We argue that FeSc2S4 is close to this quantum critical point on the spin-orbital singlet side. The full phase diagram includes a commensurate-incommensurate transition within the ordered phase. A variety of comparisons to and suggestions for experiments are discussed.

Magnetic phase diagram of the dimerized spin S = 1/2 ladder

The ground-state magnetic phase diagram of a spin $S=1/2$ two-leg ladder with alternating rung exchange $J_{\perp}(n)=J_{\perp}[1 + (-1)^{n} \delta]$ is studied using the analytical and numerical approaches. In the limit where the rung exchange is dominant, we have mapped the model onto the effective quantum sine-Gordon model with topological term and identified two quantum phase transitions at magnetization equal to the half of saturation value from a gapped to the gapless regime. These quantum transitions belong to the universality class of the commensurate-incommensurate phase transition. We have also shown that the magnetization curve of the system exhibits a plateau at magnetization equal to the half of the saturation value. We also present a detailed numerical analysis of the low energy excitation spectrum and the ground state magnetic phase diagram of the ladder with rung-exchange alternation using Lanczos method of numerical diagonalizations for ladders with number of sites up to N=28. We have calculated numerically the magnetic field dependence of the low-energy excitation spectrum, magnetization and the on-rung spin-spin correlation function. We have also calculated the width of the magnetization plateau and show that it scales as $\delta^{\nu}$, where critical exponent varies from $\nu =0.87\pm0.01$ in the case of a ladder with isotropic antiferromagnetic legs to $\nu =1.82\pm0.01 $ in the case of ladder with ferromagnetic legs. Obtained numerical results are in an complete agreement with estimations made within the continuum-limit approach.

Effects of compressive epitaxial strain in the b-axis on the magnetization response of orthorhombic HoMnO3 thin films

The orthorhombic phase HoMnO3 (o-HMO in Pbnm symmetry setting) thin films were prepared on LaAlO3(110) (LAO(110)) substrates by pulsed laser deposition. While for films grown on LAO(110) substrates, the compressive strain along the b-axis was resulted from the tensile strain in the a-c plane. The films provide the opportunity of investigating the effects of strain, hence lattice elasticity, on the physical properties of this material. For o-HMO films an antiferromagnetic ordering with TN∼42 K, irrespective to the direction of applied field was clearly observed. However, an additional magnetic ordering occurring around 26.4 K was observed when the field was applied along the c-axis of o-HMO. This transition, however, was absent when the field was applied along a- and b-axis. These results indicate that the second magnetic ordering observed along the c-axis could be more relevant to the Mn moments lying along the partially strained b direction of the o-HMO which has been theoretically expected to result in incommensurate-commensurate lock-in transition.

Synchrotron X-ray study of charge density waves in o-TaS3

We report a synchrotron X-ray study of charge density waves (CDW) in an o-TaS3 crystal. CDW of o-TaS3 has been known to undergo a commensurate-incommensurate transition at 100 K, below which the wavevector locks in with the pristine lattice. We exploited the beamline BL02B1 of SPring-8. Temperature dependence of the Bragg peak (002) and satellite peak (1 -1 2)+q⃗ was measured from 7 K to 180 K. We found that a new phase in a temperature range of 130--50 K, where two independent CDWs coexist. These waves are incommensurate and commensurate CDWs with longitudinal wave vectors qc=0.252c* and 0.250c*, respectively. By lowering the temperature, intensity of the incommensurate CDW was decreased, while that of the commensurate CDW was increased. At 50 K, the incommensurate CDW was completely diminished. Based on the concept of discommensuration, we determined the dislocation configuration from the intensity of the two CDWs.

An investigation on magnetism, spin–phonon coupling, and ferroelectricity in multiferroic GdMn2O5

The magnetization, Raman spectroscopy, and ferroelectricity of multiferroic GdMn2O5 as a function of temperature and magnetic field are investigated. The complicated magnetic transitions at low temperatures are featured with anomalous Raman mode shifts, dielectric response, and ferroelectricity generation, indicating the significant spin–phonon coupling. It is argued that this coupling is possibly responsible for the electrical polarization generation associated with the incommensurate–commensurate transition.

Activation study of the pseudospin soliton in the v = 1 bilayer quantum Hall effect

We study thermal excitations of the pseudospin soliton phase in the bilayer quantum Hall (QH) state at total Landau level filling factor v = 1. Near the commensurate-incommensurate phase transition point in the bilayer v = 1 QH state, we have found anomalous magnetotransport phenomena, such as the magnetoresistance peak and its anisotropic transport, which are ascribed to the formation of the pseudospin soliton phase (A. Fukuda et al., Phys. Rev. Lett. 100, 016801 (2008)). In this work, we elaborately measured activation energy gap Δ of the bilayer v = 1 QH state. Δ shows a broad minimum in the pseudospin soliton phase between the commensurate and incommensurate phase. We suggest that the minimum in Δ is due to collective modes of the pseudospin solitons forming a lattice.

Commensurate–incommensurate transition of charge density waves in o-

Abstract We report a synchrotron X-ray study of charge density waves (CDWs) in an o- TaS 3 crystal. CDW of o- TaS 3 has been known to undergo a commensurate–incommensurate transition at 100 K, below which the wavevector locks in with the pristine lattice. However, the details of the commensurate–incommensurate transition remain open problems, the example being whether the discommensuration exists or not in the neighborhood of the transition. We exploited the beamline BL02B1 of SPring-8. A two-dimensional detector was placed at a distance of 1300 mm from the sample, providing an angle resolution of 0.0076°. Temperature dependence of the Bragg peak (0 0 2) and satellite peak ( 1 - 1 2 ) + q was measured from 7 to 180 K. We found that a new phase in the temperature range of 130–50 K, where two independent CDWs coexist. These waves are incommensurate and commensurate CDWs with longitudinal wave vectors q c = 0.252 c * and 0.250 c * , respectively. By lowering the temperature, intensity of the incommensurate CDW was decreased, while that of the commensurate CDW was increased. Below 50 K, the incommensurate CDW was completely diminished. Based on the concept of discommensuration, we suggested the dislocation configuration from the intensity of the two CDWs.

Infrared-active excitations related toHo3+ligand-field splitting at the commensurate-incommensurate magnetic phase transition inHoMn2O5

Linearly polarized spectra of far-infrared (IR) transmission in HoMn2O5 multiferroic single crystals have been studied in the frequency range between 8.5 and 105 cm-1 and for temperatures between 5 K and 300 K. Polarization of IR-active excitations depends on the crystallographic directions in HoMn2O5 and is sensitive to the magnetic phase transitions. We attribute some of the infrared-active excitations to electric-dipole transitions between ligand-field split states of Ho3+ ions. For light polarization along crystalline b-axis, the oscillator strength of electric dipoles at low frequencies (10.5, 13, and 18 cm-1) changes significantly at the commensurate-incommensurate antiferromagnetic phase transition at T3 = 19 K. This effect shows a strong correlation with the pronounced steps of the b-directional static dielectric function. We propose that the ligand field (LF) on Ho3+ connects the magnetism and dielectric properties of this compound through coupling with the Mn spin structure. We comment on the possibility for composite excitations of magnons and excited LF states.

Domain fluctuations near the field-induced incommensurate-commensurate phase transition ofTbMnO3

We present temperature- and field-dependent inelastic light-scattering studies of multiferroic ${\text{TbMnO}}_{3}$. By carefully examining the evolution of magneto-elastic modes in various phases of ${\text{TbMnO}}_{3}$, our study reveals several features of the field-induced incommensurate-commensurate (IC-C) transition in ${\text{TbMnO}}_{3}$. We find that, for fields applied along the $b$ axis, there is a coexistence of distinct structural phases in the intermediate field regime $(H=4--7\text{ }\text{T})$ around the IC-C-phase transition. We present evidence for the existence of dynamical fluctuations of the C phase for fields lower than the critical field for $\mathbf{H}$ along the $b$ axis, $H<{H}_{c}^{b}$. Furthermore, we present evidence for strong spin-lattice coupling effects in ${\text{TbMnO}}_{3}$ in the form of zone-boundary phonon modes that strongly couple to the spins by modulating the exchange interaction in this material.

Commensurate-incommensurate phase transition in muthmannite, AuAgTe2: first evidence of a modulated structure at low temperature

To study the temperature-dependent structural changes and to analyze the crystal chemical behavior of silver as a function of temperature, a crystal of muthmannite, AuAgTe2, has been investigated by X-ray single-crystal diffraction methods at 300 K and 110 K. At room temperature, muthmannite was confirmed as belonging to the space group P2/m, while at low temperature (110 K) it undergoes a reversible commensurate–incommensurate phase transition with a modulation wave vector q = 0.215(1)a* + 0.379(2)c*. Muthmannite reconverts to the commensurate type upon returning to room temperature, thus indicating that the phase transition is completely reversible in character. The average structure of the low-temperature muthmannite remains monoclinic, space group P2/m, and shows only normal thermal compression over the entire temperature range investigated. Crystal-chemical characteristics are compared with published data on the other members of the system Au–Ag–Te. Speculations on the possible origin of the modulated structure at low temperature are also given.

Dynamical transitions of a driven Ising interface

We study the structure of an interface in a three-dimensional Ising system created by an external nonuniform field H(r,t) . H changes sign over a two-dimensional plane of arbitrary orientation. When the field is pulled with velocity v(e) , [i.e., H(r,t)=H(r-v(e)t) ], the interface undergoes several dynamical transitions. For low velocities it is pinned by the field profile and moves along with it, the distribution of local slopes undergoing a series of commensurate-incommensurate transitions. For large v(e) the interface depins and grows with Kardar-Parisi-Zhang exponents.