Domain Wall Lattice Research Articles

Reduction of the lattice strain with increasing field amplitude in polycrystalline BiFeO3

As dynamic interfaces in piezoelectric materials, domain walls can greatly impact the functionality under applied external fields. Recently, conductive domain walls have been found to result in Maxwell-Wagner (M-W)-like dispersion of the lattice strain and ferroelastic domain wall motion as a function of field frequency in polycrystalline BiFeO3. Here, we reveal an anomalous field-dependent behavior of the ferroelastic domain wall motion and lattice strain during field cycling. This response is dominated by a common nonlinear increase of ferroelastic domain wall motion and an unusual nonlinear reduction of the lattice strain with increasing field amplitude. Using analytical modeling, this complex field-dependent behavior of polycrystalline BiFeO3 is interpreted by the generation of opposing fields accompanying domain wall motion. Two contributors to the opposing fields are charge accumulation and movement along conductive domain walls and elastic coupling between adjacent grains.

Proton momentum and angular momentum decompositions with overlap fermions

We present a calculation of the proton momentum and angular momentum decompositions using overlap fermions on a $2+1$-flavor RBC/UKQCD domain-wall lattice at 0.143 fm with a pion mass of 171 MeV which is close to the physical one. A complete determination of the momentum and angular momentum fractions carried by up, down, strange, and glue inside the proton has been done with valence pion masses varying from 171 to 391 MeV. We have utilized fast Fourier transform on the stochastic-sandwich method for connected-insertion parts and the cluster-decomposition error reduction technique technique for disconnected-insertion parts has been used to reduce statistical errors. The full nonperturbative renormalization and mixing between the quark and glue operators are carried out. The final results are normalized with the momentum and angular momentum sum rules and reported at the physical valence pion mass at $\overline{\mathrm{MS}}(\ensuremath{\mu}=2\text{ }\text{ }\mathrm{GeV})$. The renormalized momentum fractions for the quarks and glue are $⟨x{⟩}^{q}=0.491(20)(23)$ and $⟨x{⟩}^{g}=0.509(20)(23)$, respectively, and the renormalized total angular momentum fractions for quarks and glue are $2{J}^{q}=0.539(22)(44)$ and $2{J}^{g}=0.461(22)(44)$, respectively. The quark spin fraction is $\mathrm{\ensuremath{\Sigma}}=0.405(25)(37)$ from our previous work and the quark orbital angular momentum fraction is deduced from $2{L}^{q}=2{J}^{q}\ensuremath{-}\mathrm{\ensuremath{\Sigma}}$ to be 0.134(22)(44).

Direct observation of domain wall motion and lattice strain dynamics in ferroelectrics under high-power resonance

Domain wall motion and lattice strain dynamics of ferroelectrics at resonance were simultaneously measured by combining high-power burst excitation and in situ high-energy x-ray diffraction. The increased loss at high vibration velocity was directly related to the increased domain wall motion, driven by dynamic mechanical stress. A general relationship between the microstructural strain contributions and macroscopic electromechanical behavior was established, allowing the prediction of high-power stability of ferroelectric materials. The results indicate that the materials' stability during high-power drive is predominantly related to the basic chemical composition, while the piezoelectric hardening mechanisms mainly influence the small-signal behavior.

Strong Running Coupling from the Gauge Sector of Domain Wall Lattice QCD with Physical Quark Masses.

We report on the first computation of the strong running coupling at the physical point (physical pion mass) from the ghost-gluon vertex, computed from lattice simulations with three flavors of domain wall fermions. We find α_{MS[over ¯]}(m_{Z}^{2})=0.1172(11), in remarkably good agreement with the world-wide average. Our computational bridge to this value is the Taylor-scheme strong coupling, which has been revealed of great interest by itself because it can be directly related to the quark-gluon interaction kernel in continuum approaches to the QCD bound-state problem.

BSM Kaon Mixing at the Physical Point

We present a progress update on the RBC-UKQCD calculation of beyond the standard model (BSM) kaon mixing matrix elements at the physical point. Simulations are performed using 2+1 flavour domain wall lattice QCD with the Iwasaki gauge action at 3 lattice spacings and with pion masses ranging from 430 MeV to the physical pion mass.

The decay constants fD and {f}_{D_s} in the continuum limit of Nf = 2 + 1 domain wall lattice QCD

We present results for the decay constants of the D and Ds mesons computed in lattice QCD with Nf = 2 + 1 dynamical flavours. The simulations are based on RBC/UKQCD’s domain wall ensembles with both physical and unphysical light-quark masses and lattice spacings in the range 0.11-0.07 fm. We employ the domain wall discretisation for all valence quarks.The results in the continuum limit are fD = 208.7(2.8)stat(− 1.8+ 2.1)sysMeV and {f}_{D_s}=246.4{(1.3)}_{mathrm{stat}}{left({}_{-1.9}^{+1.3}right)}_{mathrm{sys}}mathrm{M}mathrm{e}mathrm{V} and {f}_{D_s}={f}_D=1.667{(77)}_{mathrm{stat}}{left({}_{-43}^{+57}right)}_{mathrm{sys}} . Using these results in a Standard Model analysis we compute the predictions |Vcd| = 0.2185(50)exp(− 37+ 35)lat and |Vcs| = 1.011(16)exp(− 9+ 4)lat for the CKM matrix elements.

Extra-Dimensional “Metamaterials”: A Model of Inflation Due to a Metric Signature Transition

Lattices of topological defects, such as Abrikosov lattices and domain wall lattices often arise as metastable ground states in higher-dimensional field theoretical models. We demonstrate that such lattice states may be described as extra-dimensional metamaterials via higher-dimensional effective medium theory. A 4+1 dimensional extension of Maxwell electrodynamics with a compactified time-like dimension has been considered as an example. It is demonstrated that from the point of view of macroscopic electrodynamics an Abrikosov lattice state in such a 4+1 dimensional spacetime may be described as a uniaxial hyperbolic metamaterial. Extraordinary photons perceive this medium as a 3+1 dimensional Minkowski spacetime in which one of the original spatial dimensions (the optical axis of the metamaterial) plays the role of a new time-like coordinate. Since metric signature of this effective space-time depends on the Abrikosov lattice periodicity, the described model may be useful in studying metric signature transitions. A particular kind of metric signature transition understood as a macroscopic medium effect may emulate cosmological inflation.

Coupled domain wall motion, lattice strain and phase transformation in morphotropic phase boundary composition of PbTiO3-BiScO3 piezoelectric ceramic

High energy synchrotron X-ray diffraction, in situ with electric field, was carried out on the morphotropic phase boundary composition of the piezoelectric alloy PbTiO3-BiScO3. We demonstrate a strong correlation between ferroelectric-ferroelastic domain reorientation, lattice strain and phase transformation. We also show the occurrence of the three phenomena and persistence of their correlation in the weak field regime.

Domain wall QCD with physical quark masses

We present results for several light hadronic quantities ($f_\pi$, $f_K$, $B_K$, $m_{ud}$, $m_s$, $t_0^{1/2}$, $w_0$) obtained from simulations of 2+1 flavor domain wall lattice QCD with large physical volumes and nearly-physical pion masses at two lattice spacings. We perform a short, O(3)%, extrapolation in pion mass to the physical values by combining our new data in a simultaneous chiral/continuum `global fit' with a number of other ensembles with heavier pion masses. We use the physical values of $m_\pi$, $m_K$ and $m_\Omega$ to determine the two quark masses and the scale - all other quantities are outputs from our simulations. We obtain results with sub-percent statistical errors and negligible chiral and finite-volume systematics for these light hadronic quantities, including: $f_\pi$ = 130.2(9) MeV; $f_K$ = 155.5(8) MeV; the average up/down quark mass and strange quark mass in the $\bar {\rm MS}$ scheme at 3 GeV, 2.997(49) and 81.64(1.17) MeV respectively; and the neutral kaon mixing parameter, $B_K$, in the RGI scheme, 0.750(15) and the $\bar{\rm MS}$ scheme at 3 GeV, 0.530(11).

27aSM-6 Nucleon isovector form factors and structure functions in 2+1-falvor domain-wall lattice QCD at physical mass

27aSM-6 Nucleon isovector form factors and structure functions in 2+1-falvor domain-wall lattice QCD at physical mass

The kaon semileptonic form factor in N f = 2 + 1 domain wall lattice QCD with physical light quark masses

We present the first calculation of the kaon semileptonic form factor with sea and valence quark masses tuned to their physical values in the continuum limit of 2+1 flavour domain wall lattice QCD. We analyse a comprehensive set of simulations at the phenomenologically convenient point of zero momentum transfer in large physical volumes and for two different values of the lattice spacing. Our prediction for the form factor is f+(0)=0.9685(34)(14) where the first error is statistical and the second error systematic. This result can be combined with experimental measurements of K->pi decays for a determination of the CKM-matrix element for which we predict |Vus|=0.2233(5)(9) where the first error is from experiment and the second error from the lattice computation.

The kaon semileptonic form factor with near physical domain wall quarks

We present a new calculation of the K->pi semileptonic form factor at zero momentum transfer in domain wall lattice QCD with Nf=2+1 dynamical quark flavours. By using partially twisted boundary conditions we simulate directly at the phenomenologically relevant point of zero momentum transfer. We perform a joint analysis for all available ensembles which include three different lattice spacings (a=0.09-0.14fm), large physical volumes (m_pi*L>3.9) and pion masses as low as 171 MeV. The comprehensive set of simulation points allows for a detailed study of systematic effects leading to the prediction f+(0)=0.9670(20)(+18/-46), where the first error is statistical and the second error systematic. The result allows us to extract the CKM-matrix element |Vus|=0.2237(+13/-8) and confirm first-row CKM-unitarity in the Standard Model at the sub per mille level.

WWscattering parameters via pseudoscalar phase shifts

Using domain-wall lattice simulations, we study pseudoscalar-pseudoscalar scattering in the maximal isospin channel for an $SU(3)$ gauge theory with two and six fermion flavors in the fundamental representation. This calculation of the $S$-wave scattering length is related to the next-to-leading order corrections to $WW$ scattering in technicolor models through the low-energy coefficients of the chiral Lagrangian. While two- and six-flavor scattering lengths are similar for a fixed ratio of the pseudoscalar mass to its decay constant, six-flavor scattering shows a somewhat less repulsive next-to-leading order interaction than its two-flavor counterpart. Estimates are made for the $WW$ scattering parameters and the plausibility of detection is discussed.

Chiral magnetization configurations in magnetic nanostructures in the presence of Dzyaloshinskii-Moriya interactions

Many low-dimensional systems, such as nanoscale islands, thin films, and multilayers, as well as bulk systems, such as multiferroics, are characterized by the lack of inversion symmetry, a fact that may give rise to a Dzyaloshinskii-Moriya (DM) interaction. For sufficient strength, the DM interaction will favor spiral spin configurations of definite chirality. In order to harness such systems for applications, it is important to understand the conditions under which these spiral spin configurations form and how they can be controlled via an external field. Here, we present exact solutions of the 1D magnetization profiles in such systems for arbitrary material parameters in closed form. Determining the energy per unit length exactly, we are able to present the critical strength of the DM interaction, at which spiral solutions are energetically favorable. These magnetization profiles, in general, take the form of a domain wall or soliton lattice, with all solitons having the same chirality, whose sign is dictated by DM interaction. Conversely, given an energetically favorable spiral solution, we determine quantitatively how the magnetization profile changes as a function of the applied field.

Soliton theory of incommensurate phases in LiCsSO4 crystals

An extended version of the soliton theory is derived and used to explain the observed low-temperature phase transitions in LiCsSO4 which are assumed to be driven by the planar orientation of SO4 tetrahedrons. Two possible states of this orientation are expressed as S=1/2 spin states. Within the framework of the hcp Ising model, the phase transitions are described in terms of two order parameters representing spin-density wave along two mutually orthogonal directions in the basic hcp plane. The first order parameter describes the modulated phase below the temperature, T1. The ground-state configuration of the incommmensurate phase is a soliton lattice of domain walls which get narrower as the temperature decreases till the lock-in point, T2. The second order parameter describes the Curie second-order phase transition at T* and represents a collinear coherence of the planar turns of the tetrahedrons SO4 in each of the single magnetic planes, being the building units of the domain walls.

Nucleon electromagnetic form factors from lattice QCD using2+1flavor domain wall fermions on fine lattices and chiral perturbation theory

We present a high-statistics calculation of nucleon electromagnetic form factors in $N_f=2+1$ lattice QCD using domain wall quarks on fine lattices, to attain a new level of precision in systematic and statistical errors. Our calculations use $32^3 \times 64$ lattices with lattice spacing a=0.084 fm for pion masses of 297, 355, and 403 MeV, and we perform an overdetermined analysis using on the order of 3600 to 7000 measurements to calculate nucleon electric and magnetic form factors up to $Q^2 \approx$ 1.05 GeV$^2$. Results are shown to be consistent with those obtained using valence domain wall quarks with improved staggered sea quarks, and using coarse domain wall lattices. We determine the isovector Dirac radius $r_1^v$, Pauli radius $r_2^v$ and anomalous magnetic moment $\kappa_v$. We also determine connected contributions to the corresponding isoscalar observables. We extrapolate these observables to the physical pion mass using two different formulations of two-flavor chiral effective field theory at one loop: the heavy baryon Small Scale Expansion (SSE) and covariant baryon chiral perturbation theory. The isovector results and the connected contributions to the isoscalar results are compared with experiment, and the need for calculations at smaller pion masses is discussed.

Subcoercive Cyclic Electrical Loading of Lead Zirconate Titanate Ceramics II: Time‐Resolved X‐Ray Diffraction

Structural changes such as non‐180° domain wall motion and lattice strains in Pb(Zr,Ti)O3 ceramics are measured during the application of subcoercive cyclic electric fields using time‐resolved high‐energy X‐ray diffraction with a stroboscopic data collection technique. The contributions to the electric‐field‐induced strains from non‐180° domain wall motion and lattice distortions are determined as a function of material composition and type of dopant. For the different compositions studied, the largest strains due to non‐180° domain wall motion are measured for La‐doped tetragonal ceramics with a composition close to the morphotropic phase boundary. It is further observed that strain contributions from both non‐180° domain wall motion and lattice distortions can be nonlinear with respect to the applied electric field. The correlation between the electric‐field‐induced structural changes and the macroscopic piezoelectric properties is discussed.

Imbalanced superfluid state in an annular disk

The imbalanced superfluid state of spin-1/2 fermions with s-wave pairing is numerically studied by solving the Bogoliubov–de Gennesequation at zero temperature in an annular disk geometry with narrow radial width. Twodistinct types of systems are considered. The first case may be relevant to heavy fermionsuperconductors, where magnetic field causes spin imbalance via Zeeman interactionand the system is studied in a grand canonical ensemble. As the magnetic fieldincreases, the system is transformed from the uniform superfluid state to theFulde–Ferrell–Larkin–Ovchinnikov state, and finally to the spin polarized normal state.The second case may be relevant to cold fermionic systems, where the number offermions of each species is fixed as in a canonical ensemble. In this case, the groundstate depends on the pairing strength. For weak pairing, the order parameterexhibits a periodic domain wall lattice pattern with a localized spin distribution atlow spin imbalance, and a sinusoidally modulated pattern with extended spindistribution at high spin imbalance. For strong pairing, the phase separationbetween the superfluid state and polarized normal state is found to be preferable,while the increase of spin imbalance simply changes the ratio between them.

Stability of winding cosmic wall lattices with X type junctions

This work confirms the stability of a class of domain wall lattice models that can produce accelerated cosmological expansion, with pressure to density ratio w = −1/3 at early times, and with w = −2/3 at late times when the lattice scale becomes large compared to the wall thickness. For walls of tension TI, the relevant X type junctions could be unstable (for a sufficiently acute intersection angle α) against separation into a pair of Y type junctions joined by a compound wall, only if the tension of the latter were less than 2TI (and for an approximately right-angled intersection if it were less than ) which cannot occur in the class considered here. In an extensive category of multicomponent scalar field models of forced harmonic (linear or nonlinear) type it is shown how the relevant tension—which is the same as the surface energy density U of the wall—can be calculated as the minimum (geodesic) distance between the relevant vacuum states as measured on the space of field values Φi using a positive definite (Riemannian) energy metric that is obtained from the usual kinetic metric (which is flat for a model with an ordinary linear kinetic part) by application of a conformal factor proportional to the relevant potential function V. For suitably periodic potential functions there will be corresponding periodic configurations—with parallel walls characterized by incrementation of a winding number—in which the condition for stability of large scale bunching modes is shown to be satisfied automatically. It is suggested that such a configuration—with a lattice lengthscale comparable to intergalactic separation distances—might have been produced by a late stage of cosmological inflation.

Lattice calculation of SU(3) flavor breaking ratios inB0−B¯0mixing

We present an unquenched lattice calculation for the SU(3) flavor breaking ratios of the heavy-light decay constants and the {delta}B=2 matrix elements. The calculation was performed on 16{sup 3}x32 lattices with two dynamical flavors of domain-wall quarks and inverse lattice spacing 1/a=1.69(5) GeV. Heavy quarks were implemented using an improved lattice formulation of the static approximation. In the infinite heavy-quark mass limit we obtain f{sub B{sub s}}/f{sub B{sub d}}=1.29(4)(6), B{sub B{sub s}}/B{sub B{sub d}}=1.06(6)(4), {xi}=1.33(8)(8) where the first error is statistical and the second systematic.