Lattice Fluctuations Research Articles

Observation of lattice spacing fluctuation and strain undulation around through-Si vias in wafer-on-wafer structures using X-ray microbeam diffraction

Spatial fluctuations of the Si 004 lattice spacing, strain, and lattice tilt around through-Si vias (TSVs) in wafer-on-wafer (WOW) structures annealed at different temperatures were quantitatively investigated using X-ray microbeam diffraction. The TSVs were found to induce spatial fluctuations in the base and bonded wafers, and a strain of approximately 0.1% and lattice tilt with a long undulation period of 40 µm were clearly observed. Furthermore, annealing at approximately 100 °C effectively reduced the spatial fluctuation, strain, and lattice tilt in the WOW structure.

Manifestation of percolation in high temperature superconductivity

Emergent advanced electronic and magnetic functionalities in novel materials appear in systems with a complex lattice structure. The key point is understanding the intrinsic effect of lattice fluctuations on the relevant electronic features in the range of 10–100meV near the Fermi level in new materials which is needed to develop advanced quantum nano-devices. This requires the control of structural inhomogeneity at multiple scales. Here we report some of the known advances in the field of percolative superconductivity. The necessity of the review is based on the growing consensus that the lack of an understanding of high temperature superconductivity is due to the few information on lattice fluctuations. In particular they could control the pseudo-gap phase, the electronic duality of holes in Fermi arcs and electrons in small Fermi pockets, multiple condensates in different points of the k-space. Moreover the emerging lattice granularity in cuprates shifts the search for the superconducting mechanism from a homogeneous superconductivity to a percolative superconductivity, therefore it is the scope of this review to provide further data to this kind of research.

Quantum hexatic order in two-dimensional dipolar and charged fluids

Recent advances in cold atom experimentation suggest that studies of quantum two-dimensional melting of dipolar molecules, with dipoles aligned perpendicular to ordering plane, may be on the horizon. An intriguing aspect of this problem is that two-dimensional classical aligned dipoles (already studied in great detail in soft matter experiments on magnetic colloids) are known to melt via a two-stage process, with an intermediate hexatic phase separating the usual crystal and isotropic fluid phases. We estimate here the effect of quantum fluctuations on this hexatic phase, for both dipolar systems and charged Wigner crystals. Our approximate phase diagrams rely on a pair of Lindemann criteria, suitably adapted to deal with the effects of thermal fluctuations in two dimensions. As part of our analysis, we determine the phonon spectra of quantum particles on a triangular lattice interacting with repulsive $1/{r}^{3}$ and $1/r$ potentials. A large softening of the transverse and longitudinal phonon frequencies, due to both lattice effects and quantum fluctuations, plays a significant role in our analysis. The hexatic phase is predicted to survive down to very low temperatures.

Direct observation of dynamic charge stripes in La2–xSrxNiO4

The insulator-to-metal transition continues to be a challenging subject, especially when electronic correlations are strong. In layered compounds, such as La2-xSrxNiO4 and La2-xBaxCuO4, the doped charge carriers can segregate into periodically spaced charge stripes separating narrow domains of antiferromagnetic order. Although there have been theoretical proposals of dynamically fluctuating stripes, direct spectroscopic evidence of charge-stripe fluctuations has been lacking. Here we report the detection of critical lattice fluctuations, driven by charge-stripe correlations, in La2-xSrxNiO4 using inelastic neutron scattering. This scattering is detected at large momentum transfers where the magnetic form factor suppresses the spin fluctuation signal. The lattice fluctuations associated with the dynamic charge stripes are narrow in q and broad in energy. They are strongest near the charge-stripe melting temperature. Our results open the way towards the quantitative theory of dynamic stripes and for directly detecting dynamical charge stripes in other strongly correlated systems, including high-temperature superconductors such as La2-xSrxCuO4.

Anisotropic crystalline morphology of epitaxial thick AlN films grown on triangular‐striped AlN/sapphire template

We have investigated crystalline morphology such as wafer curvature, mosaicity, and lattice tilting of an AlN film grown on a triangular‐striped AlN/α‐Al2O3 template by X‐ray rocking curve (XRC) and reciprocal space map (RSM) measurements. The result of XRC for the AlN (0002) plane showed the difference of the value in the wafer curvature between the [11–20] and [1–100] directions. This indicates the anisotropic strain relaxation preferentially along [11–20] direction due to the triangular‐striped structure and the voids in the AlN film. From the results of asymmetric RSMs for AlN 11–24 and 1–104 diffractions, the broadening of the reciprocal lattice spots in elliptical shape was observed. These results reflect anisotropic crystalline morphology in the AlN film. The elliptical diffraction spot for AlN 11–24 predominantly indicates the lattice tilting fluctuation around the [1–100] axes while that for AlN 1–104 indicates the lattice spacing fluctuation. Anisotropic crystalline morphology in the AlN film grown on the triangular‐striped template has been clarified in combination with XRC and asymmetric RSMs.

Lattice and orbital fluctuations in TiPO4

In the $s=1/2$ antiferromagnetic spin chain material TiPO${}_{4}$, the formation of a spin gap takes place in a two-step process with two characteristic temperatures, ${T}^{*}=111$ K and ${T}_{\mathrm{SP}}=74$ K. We observe an unusual lattice dynamics over a large temperature regime as well as evidence for an orbital instability preceding the spin-Peierls transition. We relate different intrachain exchange interactions of the high temperature compared to the spin-Peierls phase to a modification of the orbital ordering pattern. In particular, our observation of a high-energy excitation of mixed electronic and lattice origin suggests an exotic dimerization process different from other spin-Peierls materials.

Large-amplitude superexchange of high-spin fermions in optical lattices

We show that fermionic high-spin systems with spin-changing collisions allow one to monitor superexchange processes in optical superlattices with large amplitudes and strong spin fluctuations. By investigating the non-equilibrium dynamics, we find a superexchange dominated regime at weak interactions. The underlying mechanism is driven by an emerging tunneling-energy gap in shallow few-well potentials. As a consequence, the interaction-energy gap that is expected to occur only for strong interactions in deep lattices is re-established. By tuning the optical lattice depth, a crossover between two regimes with negligible particle number fluctuations is found: firstly, the common regime with vanishing spin-fluctuations in deep lattices and, secondly, a novel regime with strong spin fluctuations in shallow lattices. We discuss the possible experimental realization with ultracold 40K atoms and observable quantities in double wells and two-dimensional plaquettes.

Scaling between Magnetic and Lattice Fluctuations in Iron Pnictide Superconductors

The phase diagram of the iron arsenides is dominated by a magnetic and a structural phase transition, which need to be suppressed in order for superconductivity to appear. The proximity between the two transition temperature lines indicates correlation between these two phases, whose nature remains unsettled. Here, we find a scaling relation between nuclear magnetic resonance and shear modulus data in the tetragonal phase of electron-doped Ba(Fe1-xCox)2As2 compounds. Because the former probes the strength of magnetic fluctuations while the latter is sensitive to orthorhombic fluctuations, our results provide strong evidence for a magnetically driven structural transition.

Thermal Effects on Charge Transport in Conjugated Polymers

Field dependent polaron transport in a conjugated polymer chain is studied numerically with local thermal fluctuations taken into account. Within a dynamical evolution method, a polaron moves from the left to the right side of the polymer chain in the presence of an applied electric field. Local lattice fluctuations are assumed to occur in a random way. The local thermal fluctuations are found to be equivalent to a potential barrier for the polaron. The range of the thermally disturbed region in the molecule and the effective temperature difference resulted from asymmetric thermal absorptions determine the height of the barrier. The intra-molecule polaron mobility obeys a logarithmic law in low electric field range provided that there exist asymmetric thermal absorptions within the molecule.

Effects of energetic ion irradiation on the magnetism of Fe–Ni Invar alloy

The magnetic properties of Fe–Ni Invar alloys are significantly affected by ion irradiation. Au3+ with the energy of 16MeV irradiation effects on the magnetism of Fe66Ni34 have been reported in this paper. Considering from the temperature variations of AC susceptibility of irradiated Fe66Ni34, Curie temperature of a part of sample increase with increasing incident ion fluence, and the magnetization of irradiated Fe66Ni34 is also increase. The FCC structure of Fe66Ni34 is not changed by ion irradiation; however peaks become broader with increasing ion fluence. It means that lattice fluctuations are generated owing to ion irradiation. However it cannot be considered that lattice fluctuations observed X-ray diffraction measurements are enough to increase the Curie temperature observed in AC susceptibility measurements. Then, we suggest as the considerable origin of increasing TC, atomic mixing effects owing to the ion irradiation. It might change the chemical ordering reported in the diffused scattering, such as Fe–Fe coupling.

Competing lattice fluctuations and magnetic excitations in CuO

Lattice vibrations as well as magnetic excitations are investigated using Raman scattering to understand the high-${T}_{c}$ multiferroic properties of CuO. We observe a flat, broad spinon continuum extending to 2800 cm${}^{\ensuremath{-}1}$, being superimposed by magnon excitations with energies below 1350 cm${}^{\ensuremath{-}1}$. This allows us to estimate an exchange coupling constant of $J=108$ meV. Three Raman-active phonon modes predicted by lattice dynamical calculations are assigned and analyzed. We find a crossover temperature ${T}^{*}=140--150$ K through which new phonon modes are activated and phonon parameters show appreciable anomalies. This feature is discussed in terms of a competition of polar and nonpolar lattice distortions. Our study suggests the importance of competing lattice fluctuations for multiferroic compounds, which possess an intermediate multiferroic phase.

Proposal to use neutron scattering to access scalar spin chirality fluctuations in kagome lattices

In the theory of quantum spin liquids, gauge fluctuations are emergent excitations at low energy. The gauge magnetic field is proportional to the scalar spin chirality, S1.(S2xS3). It is therefore highly desirable to measure the fluctuation spectrum of the scalar spin chirality. We show that in the Kagome lattice with a Dzyaloshinskii-Moriya term, the fluctuation in Sz which is readily measured by neutron scattering contains a piece which is proportional to the chirality fluctuation.

Structure of phase-separated athermal colloid-polymer systems in the protein limit

Structural features of phase-separated athermal colloid-polymer mixtures in the so-called "protein limit," where polymer chain dimensions exceed those of the colloid, are investigated using grand canonical Monte Carlo simulations on a fine lattice. Previous work [N. A. Mahynski et al., Phys. Rev. E 85, 051402 (2012)] has shown that this model accurately captures the phase behavior of experimental systems, and that colloids with sufficiently small diameters, σ(c), relative to that of the monomeric segments, σ(s), phase separate more readily than their large-diameter counterparts. In the present study, we directly connect colloid and polymer structure with their phase behavior by investigating these solutions along their binodal curves; we also explore the role of colloid surface curvature in destabilizing such solutions. Our findings suggest that simple consideration of an additional depletion radius, on the order of the σ(s), leads to a quantitatively accurate prediction of the division between stable and unstable ranges of d=σ(s)/σ(c). We compare these results to continuum models with different bonding potentials between monomer segments in order to elucidate the significance of the lattice model's bond fluctuations and inherently coarse colloid surface. In a number of cases, the continuum models deviate both qualitatively and quantitatively from the lattice results, but the binodals of the continuum models are presently not known, making a strong conclusion about these differences impossible.

Nonadiabatic Fluctuations and the Charge-Density-Wave Transition in One-Dimensional Electron–Phonon Systems: A Dynamic Self-Consistent Theory

The Peierls instability in one-dimensional electron-phonon systems is known to be qualitatively well described by the Mean-Field theory, however the related self-consistent problem so far has only been able to predict a partial suppression of the transition even with proper account of classical lattice fluctuations. Here the Hartree-Fock approximation scheme is extended to the full quantum regime, by mapping the momentum-frequency spectrum of order-parameter fluctuations onto a continuous two-parameter space. For the one-dimensional half-filled Su-Schrieffer-Heeger model the ratio $d=\Omega/2\pi T_c^0$, where $\Omega$ is the characteristic phonon frequency and $2\pi T_c^0$ the lowest finite phonon Matsubara frequency at the mean-field critical point $T_c^0$, provides a natural measure of the adiabaticity of lattice fluctuations. By integrating out finite-frequency phonons, it is found that a variation of $d$ from the classical regime $d=0$ continuously connects $T_c^0$ to a zero-temperature charge-density-wave transition setting up at a finite crossover $d=d_c$. This finite crossover decreases within the range $0\leq d \approx 1$ as the electron-phonon coupling strength increases but remaining small enough for weak-coupling considerations to still hold. Implications of $T_c$ supression on the Ginzburg criterion is discussed, and evidence is given of a possible coherent description of the charge-density-wave problem within the framework of a renormalized Mean-Field theory encompassing several aspects of the transition including its thermodynamics close to the quantum critical point.

Visualization of quantum electronic and lattice fluctuations by using the resonating Hartree-Fock method

Large quantum fluctuations in the strongly correlated electron systems as well as electron-phonon coupled systems are visualized by the resonating Hartree-Fock (HF) method). We show that, in the two-dimensional Hubbard model, doped holes form topological defects called polarons. It is also shown that the quantum fluctuations drastically change the lattice structures in the Su-Schrieffer-Heeger model.

Critical adsorption of a flexible polymer confined between two parallel interacting surfaces

Critical adsorption of a lattice self-avoiding bond fluctuation polymer chain confined between two parallel impenetrable surfaces is studied using the Monte Carlo method. The dependence of the mean contact number <M> on the temperature T and on the chain length N is simulated for a polymer-surface interaction E=-1. A critical adsorption of the polymer is found at T(c)=1.65 for large surface separation distance D>N(ν)b, whereas no critical adsorption is observed for small distance D<N(ν)b, where ν ≈ 0.58 is the Flory exponent and b is the mean bond length. The critical adsorption point T(c)=1.65 is the same as that of a grafted polymer. Normal diffusion is observed for the confined polymer; however, the diffusion rate is dependent on the temperature and surface separation distance.

Time-resolved Bragg coherent X-ray diffraction revealing ultrafast lattice dynamics in nano-thickness crystal layer using X-ray free electron laser

Ultrafast time-resolved Bragg coherent X-ray diffraction (CXD) has been performed to investigate lattice dynamics in a thin crystal layer with a nanoscale thickness by using a SASE (Self-Amplified Spontaneous Emission)–XFEL (X-ray Free Electron Laser) facility, SACLA. Single-shot Bragg coherent diffraction patterns of a 100 nm-thick silicon crystal were measured in the asymmetric configuration with a grazing exit using an area detector. The measured coherent diffraction patterns showed fringes extending in the surface normal direction. By using an optical femtosecond laser-pump and the XFEL-probe, a transient broadening of coherent diffraction pattern profile was observed at a delay time of around a few tens of picosecond, indicating transient crystal lattice fluctuation induced by the optical laser. A perspective application of the time-resolved Bragg CXD method to investigate small sized grains composing ceramic materials is discussed.

Direct Observation of a Pressure-Induced Precursor Lattice in Silicon

Detailed knowledge of atomic-scale structural change is essential for understanding the process and mechanism of phase transitions in solids. We present the direct experimental evidence of a precursor lattice in silicon at high pressures. The precursor lattice may appear to coexist dynamically with the host lattice over a large pressure range through rapid lattice fluctuations. The first-principles calculations are used to elucidate a dynamic lattice-fluctuation mechanism that accounts for the experimental observations. This precursor lattice-fluctuation mechanism for the phase transition goes beyond previously considered reconstructive or displacive processes and provides a novel picture of the underlying dynamics.

Current-dependent electrode lattice fluctuations and anode phase evolution in a lithium-ion battery investigated by in situ neutron diffraction

This work uses real-time in situ neutron powder diffraction to study the electrode lattice response and anode phase evolution in a commercial lithium-ion battery. We show that the time-resolved lattice response of the LixCoO2 cathode and LixC6 anode under non-equilibrium conditions varies proportionally with the applied current, where higher current results in faster structural change. Higher current also reduces the LixCoO2 cathode c lattice parameter and the LiC6 quantity that forms at the charged state of the battery, both of which are related to lower battery capacity. At the anode, we find that the LixC6 phase evolution is current-dependent.

Shaking the entropy out of a lattice: Atomic filtering by vibrational excitations

We present a simple and efficient scheme to reduce atom-number fluctuations in optical lattices. The interaction-energy difference for atoms in different vibrational states is used to remove excess atomic occupation. The remaining vacant sites are then filled with atoms by merging adjacent wells, for which we implement a protocol that circumvents the constraints of unitarity. The preparation of large regions with precisely one atom per lattice site is discussed for both bosons and fermions. The resulting low-entropy Mott-insulating states may serve as high-fidelity register states for quantum computing and as a starting point for investigations of many-body physics.