Sublattice-Dependent Antiferromagnetic Transitions in Rare Earth Nickelates
Y. Shi and L.-Q. Chen, Physical Review Letters 130, 186801 (2023) https://doi.org/10.1103/PhysRevLett.130.186801
Perovskite rare earth nickelates exhibit remarkably rich physics in their metal-insulator and antiferromagnetic transitions, and there has been a long-standing debate on whether their magnetic structures are collinear or noncollinear. Through symmetry consideration based on the Landau theory, we discover that the antiferromagnetic transitions on the two nonequivalent Ni sublattices occur separately at different Néel temperatures induced by the O breathing mode. It is manifested by two kinks on the temperature-dependent magnetic susceptibilities with the secondary kink being continuous in the collinear magnetic structure but discontinuous in the noncollinear one. The prediction on the secondary discontinuous kink is corroborated by an existing magnetic susceptibility measurement on bulk single-crystalline nickelates, thus strongly supporting the noncollinear nature of the magnetic structure in bulk nickelates, thereby shedding new light on the long-standing debate.
Phase-Field Model of Coupled Insulator-Metal Transitions and Oxygen Vacancy Redox Reactions
Y. Shi, V. Gopalan, and L.-Q. Chen, Physical Review B 107, L201110 (2023) https://doi.org/10.1103/PhysRevB.107.L201110
A predominant ubiquitous feature of strongly correlated oxides is the possible presence of oxygen vacancies, which has recently been shown to have profound effects on their electronic phase transitions. Here, we formulate a comprehensive phase-field model of intercoupled insulator-metal transitions and oxygen vacancy redox reactions, taking into account the valence electron state of oxygen vacancies. We use the model to study the voltage self-oscillation phenomenon in a prototypical strongly correlated oxide, VO2, and discover the mutual activation of the insulator-metal transition and oxygen vacancy redox reactions leading to systematic enhancement of the oscillation frequency. The established methodology and the mutual activation mechanism are generally applicable to understanding any insulator-metal transition dynamics in oxygen-deficient correlated oxides and improving the performance of voltage self-oscillation-based artificial neurons.
Integral Boundary Conditions in Phase Field Models
X. Xu, L. Zhang, Y. Shi, L.-Q. Chen, and J. Xu, Computers & Mathematics with Applications 135, 1 (2023) https://doi.org/10.1016/j.camwa.2022.11.025
Modeling the chemical, electric and thermal transport as well as phase transitions and the accompanying mesoscale microstructure evolutionwithin a material in an electronic device setting involves the solution of partial differential equations often with integral boundary conditions. Employing the familiar Poisson equation describing the electric potential evolution in a material exhibiting insulator to metal transitions, we exploit a special property of such an integral boundary condition, and we properly formulate the variational problem and establish its well-posedness. We then compare our method with the commonly-used Lagrange multiplier method that can also handle such boundary conditions. Numerical experiments demonstrate that our new method achieves optimal convergence rate in contrast to the conventional Lagrange multiplier method. Furthermore, the linear system derived from our method is symmetric positive definite, and can be efficiently solved by Conjugate Gradient method with algebraic multigrid preconditioning.
Landau-Ginzburg Theory of Charge Density Wave Formation Accompanying Lattice and Electronic Long-Range Ordering
We propose an analytical Landau-Ginzburg (LG) theory of the charge density waves coupled with lattice and electronic long-range order parameters. Examples of long-range order include the electronic wave function of superconducting Cooper pairs, structural distortions, electric polarization, and magnetization. We formulate the LG free energy density as a power expansion with respect to the charge density and other long-range order parameters as well as their spatial gradients and biquadratic coupling terms. We introduced a biquadratic coupling between the charge density gradient and long-range order parameters as well as nonlinear higher gradients of the long-range order parameters. The biquadratic gradient coupling is critical to the appearance of different spatially modulated phases in charge-ordered ferroics and high-temperature superconductors. We derived the thermodynamic conditions for the stability of the spatially modulated phases, which are the intertwined spatial waves of charge density and lattice/electronic long-range order. The analytical expressions for the energies of different phases, corresponding order parameters, charge density waves amplitudes, and modulation periods obtained in this paper can be employed to guide the comprehensive physical explanation, deconvolution, and Bayesian analysis of experimental data on quantum materials ranging from charge-ordered ferroics to high-temperature superconductors.
Stoichiometric Control and Optical Properties of BaTiO3 Thin Films Grown by Hybrid MBE
R. Engel-Herbert et al., Advanced Materials Interfaces 10, 2300018 (2023) https://doi.org/10.1002/admi.202300018
BaTiO3 is a technologically relevant material in the perovskite oxide class with above-room-temperature ferroelectricity and a very large electro-optical coefficient, making it highly suitable for emerging electronic and photonic devices. An easy, robust, straightforward, and scalable growth method is required to synthesize epitaxial BaTiO3thin films with sufficient control over the film’s stoichiometry to achieve reproducible thin film properties. Here the growth of BaTiO3 thin films by hybrid molecular beam epitaxy is reported. A self-regulated growth window is identified using complementary information obtained from reflection high energy electron diffraction, the intrinsic film lattice parameter, film surface morphology, and scanning transmission electron microscopy. Subsequent optical characterization of the BaTiO3 films by spectroscopic ellipsometry revealed refractive index and extinction coefficient values closely resembling those of stoichiometric bulk BaTiO3 crystals for films grown inside the growth window. Even in the absence of a lattice parameter change of BaTiO3 thin films, degradation of optical properties is observed, accompanied by the appearance of a wide optical absorption peak in the IR spectrum, attributed to optical transitions involving defect states present. Therefore, the optical properties of BaTiO3 can be utilized as a much finer and more straightforward probe to determine the stoichiometry level present in BaTiO3 films.
Machine-Learning Enabled Construction of Temperature-Strain Phase Diagrams of Ferroelectric Thin Films
J. A. Zorn and L.-Q. Chen, Journal of Materials Research 38, 1644-1656 (2023) https://doi.org/10.1557/s43578-023-00916-y
Ferroelectric thin films have been explored for many applications such as microelectronics or system-on-a-chip prototypes. It is well established that stability of ferroelectric states of thin films are determined by both temperature and strain between the film and its underlying substrate and the chemical composition for solid solution thin films. A complexity associated with ferroelectric thin films constrained by a substrate is that often the multidomain states of multiple ferroelectric domain variants become stable. Using a combination of high-throughput calculations, classification machine-learning algorithms, and phase-field simulations, we systematically investigate the phase diagrams of (Bax, Ca1-x)TiO3 (BCTO) solid solution thin films. We examine several machine-learning techniques to understand the differences in their accuracies and capabilities for the construction of phase diagrams of ferroelectric thin films. We demonstrate that a computational scheme consisting of high-throughput calculations, machine-learning, and phase-field simulations, can be employed to obtain accurate phase-stability diagrams of ferroelectric films.
Thermodynamics of Light-Induced Nanoscale Polar Structures in Ferroelectric Superlattices
T. Yang, C. Dai, and L.-Q. Chen, Nano Letters 23, 2551-2556 (2023) https://doi.org/10.1021/acs.nanolett.2c04586
Thermodynamic and Electron Transport Properties of Ca3Ru2O7 from First-Principles Phonon Calculations and Boltzmann Transport Theory
Y. Wang et al., Physical Review B 107, 035118 (2023) https://doi.org/10.1103/PhysRevB.107.035118
Strong Electron-Phonon Coupling in a Correlated Polar Metal
V. Gopalan et al., Nature Communications 14, 1 (2023)
https://doi.org/10.1038/s41467-023-41460-x
There is tremendous interest in employing collective excitations of the lattice, spin, charge, and orbitals to tune strongly correlated electronic phenomena. We report such an effect in a ruthenate, Ca3Ru2O7, where two phonons with strong electron-phonon coupling modulate the electronic pseudogap as well as mediate charge and spin density wave fluctuations. Combining temperature-dependent Raman spectroscopy with density functional theory reveals two phonons, B2P and B2M, that are strongly coupled to electrons and whose scattering intensities respectively dominate in the pseudogap versus the metallic phases. The B2P squeezes the octahedra along the out of plane c-axis, while the B2M elongates it, thus modulating the Ru 4d orbital splitting and the bandwidth of the in-plane electron hopping; Thus, B2P opens the pseudogap, while B2M closes it. Moreover, the B2 phonons mediate incoherent charge and spin density wave fluctuations, as evidenced by changes in the background electronic Raman scattering that exhibit unique symmetry signatures. The polar order breaks inversion symmetry, enabling infrared activity of these phonons, paving the way for coherent light-driven control of electronic transport.
Electronic bandwidth modulation by static pressure has been explored in several material families. Wang et al. use temperature-dependent Raman spectroscopy and density functional theory to reveal phonon-driven modulation of electronic pseudogap and density wave fluctuations in a ruthenate Ca3Ru2O7.
An Efficient Iterative Method for Dynamical Ginzburg-Landau Equations
Q. Hong et al., Journal of Computational Physics 474, 111794 (2023)
https://doi.org/10.1016/j.jcp.2022.111794
We propose a new finite element approach to simulate the time-dependent Ginzburg-Landau equations under the temporal gauge, and design an efficient precon- ditioner for the Newton iteration of the resulting discrete system. The new approach solves the magnetic potential in H(curl) space by the lowest order of the second kind Nédélec element. This approach offers a simple way to deal with the boundary condition, and leads to a stable and reliable performance when dealing with the superconductor with reentrant corners. The comparison in numerical simulations verifies the efficiency of the proposed preconditioner, which can significantly speed up the simulation in large-scale computations.
Computing Diffraction Patterns of Microstructures from Phase-field Simulations
T. Yang, et al., Acta Materialia 239, 118258 (2022)
https://doi.org/10.1016/j.actamat.2022.118258
The diffraction pattern of a material contains information not only on the crystal structures of its constituting phases, but also on its mesoscale spatial distributions of phases, grains, and ferroelastic, ferroelectric, and ferromagnetic domains. While diffraction patterns from experiments such as x-ray diffraction are presented in the reciprocal or Fourier space, mesoscale microstructure models such as the phase-field method naturally produce real-space images of spatial distribution of chemical composition, structural, and ferroic domains. Although one could rather readily compute the Fourier amplitudes of chemical and structural domain distributions generated by mesoscale simulations, they only contain information about the length scale and alignment of the real-space chemical and structure domains. Therefore, a direct comparison between diffraction experiments and mesoscale microstructure simulations is not possible. Here, we develop a theoretical approach to directly compute the crystal diffraction patterns of microstructures predicted by phase-field simulations. In particular, we consider five representative examples of microstructure patterns involving purely compositional domains, a single pair of tetragonal twin structures, multiple twin variants in a hexagonal system, ferroelectric polar vortices, and polycrystalline grains. The results are compared with previous experimental observations as well as X-ray diffraction experiments performed in the present study. The theoretical framework allows one to directly connect material microstructures and diffraction patterns predicted from phase-field simulations and the corresponding diffraction patterns from experiments, and thus providing guidance to experimental diffraction characterization and interpretation of microstructures.
Analytical and Numerical Modeling of Optical Second Harmonic Generation in Anisotropic Crystals Using ♯SHAARP Package
R. Zu, et al., npj Computational Materials 8, 246 (2022)
https://doi.org/10.1038/s41524-022-00930-4
Electric-dipole optical second harmonic generation (SHG) is a second-order nonlinear process that is widely used as a sensitive probe to detect broken inversion symmetry and local polar order. Analytical modeling of the SHG polarimetry of a nonlinear optical material is essential to extract its point group symmetry and the absolute nonlinear susceptibilities. Current literature on SHG analysis involves numerous approximations and a wide range of (in)accuracies. We have developed an open-source package called the Second Harmonic Analysis of Anisotropic Rotational Polarimetry (♯SHAARP.si) which derives analytical and numerical solutions of reflection SHG polarimetry from a single interface (.si) for bulk homogeneous crystals with arbitrary symmetry group, arbitrary crystal orientation, complex and anisotropic linear dielectric tensor with frequency dispersion, a general SHG tensor and arbitrary light polarization. ♯SHAARP.si enables accurate modeling of polarimetry measurements in reflection geometry from highly absorbing crystals or wedge-shaped transparent crystals. The package is extendable to multiple interfaces.
Intrinsic Insulator-Metal Phase Oscillations
Y. Shi, L.-Q. Chen, Physical Review Applied 17, 014042 (2022)
https://doi.org/10.1103/PhysRevApplied.17.014042
Insulator-metal phase oscillations driven by direct voltages in strongly correlated materials, which can naturally emulate nonlinear neural behavior, have hitherto been realized largely as extrinsic charging and discharging cycles of capacitors with limited frequencies. Here, based on an experimentally validated physical phase-field description of the insulator-metal transition, we demonstrate an intrinsic noncapacitive insulator-metal phase oscillation in a prototypical strongly correlated material, VO2, near room temperature, which can be generic in Mott insulators. Such intrinsic phase oscillations exhibit frequencies 1–2 orders of magnitude higher than the typical frequencies of the extrinsic capacitive phase oscillations. They manifest themselves as electronically driven automatic growth and shrinkage of conduction filaments in contrast to the usual suggestion of thermally driven growth. The discovery of intrinsic phase oscillations has important implications for exploring the intrinsic nonlinear electronic dynamics in strongly correlated materials and advances the realization of high-frequency Mott electronic oscillators for neuromorphic computing.
Dynamical Phase-field Model of Coupled Electronic and Structural Processes
T. Yang, L.-Q. Chen, npj Computational Materials 8, 130 (2022)
https://doi.org/10.1038/s41524-022-00820-9
Many functional and quantum materials derive their functionality from the responses of both their electronic and lattice subsystems to thermal, electric, and mechanical stimuli or light. Here we propose a dynamical phase-field model for predicting and modeling the dynamics of simultaneous electronic and structural processes and the accompanying mesoscale pattern evolution under static or ultrafast external stimuli. As an illustrative example of application, we study the transient dynamic response of ferroelectric domain walls excited by an ultrafast above-bandgap light pulse. We discover a two-stage relaxational electronic carrier evolution and a structural evolution containing multiple oscillational and relaxational components across picosecond to nanosecond timescales. The phase-field model offers a general theoretical framework which can be applied to a wide range of functional and quantum materials with interactive electronic and lattice orders and phase transitions to understand, predict, and manipulate their ultrafast dynamics and rich mesoscale evolution dynamics of domains, domain walls, and charges. Read more in news report.
Q-Pop-Thermo: A General-purpose Thermodynamics Solver for Ferroelectric Materials
J. Zorn, et al., Computer Physics Communications [275]108302 (2022)
Q-POP-Thermo is a program designed to compute thermodynamic monodomain equilibrium states and their properties for ferroelectric single crystals and thin films based on the Landau-Ginzburg-Devonshire (LGD) Theory. Utilizing symbolic manipulation with the SymPy Library, the governing equations along with appropriate boundary conditions are solved for speedy minimization of the free energy of a crystal. Utilizing the popular Differential Evolution algorithm, with appropriate hybridization, multiple phase diagrams, such as the pressure-temperature phase diagram for bulk single crystals and the common strain-temperature phase diagram for monodomain thin-film systems can be readily generated. Furthermore, a variety of material properties of stable ferroelectric phases, including dielectric, piezoelectric, and electrocaloric properties, can simultaneously be calculated. Validation studies are presented for both thin-film and single crystal systems to test the effectiveness and capability of the open-source program.
Condensation of Collective Polar Vortex Modes
T. Yang, et al., Physical Review B 103, L220303 (2021)
https://doi.org/10.1103/PhysRevB.103.L220303
The dynamics of extended objects such as domain walls, domain bubbles, vortex structures, etc., can be described by their equations of motion associated with their effective mass and spring constant. Here we analytically derive the equations of motion for the polarization dynamics and elastodynamics for the structural responses of ferroelectric polar vortices, and theoretically extract their effective mass, spring constant, and mode frequencies. We demonstrate two sub-terahertz phonon modes and predicted their frequencies, both consistent with our recent experimental measurements and phase-field simulations. We show that elastic modulation of the energy function and spring constants leads to a condensation of a collective mode upon a second-order structural transition from symmetric to asymmetric vortices at a critical strain, analogous to the ferroelectric soft phonon mode at a ferroelectric transition. The present work offers a theoretical framework for predicting and manipulating the ultrafast collective dynamics of polar nanostructures.
Dynamics of Voltage-driven Oscillating Insulator-metal Transitions
Y. Shi, et al., Physical Review B 104, 064308 (2021)
https://journals.aps.org/prb/abstract/10.1103/PhysRevB.104.064308
Recent experiments demonstrated emerging alternating insulator and metal phases in Mott insulators actuated by a direct bias voltage, leading to oscillating voltage outputs with characteristic frequencies. Here, we develop a physics-based nonequilibrium model to describe the dynamics of oscillating insulator-metal phase transitions and experimentally validate it using a VO2 device as a prototype. The oscillation frequency is shown to scale monotonically with the bias voltage and series resistance and terminate abruptly at lower and upper device-dependent limits, which are dictated by the nonequilibrium carrier dynamics. We derive an approximate analytical expression for the dependence of the frequency on the device operating parameters, which yields a fundamental limit to the frequency and may be utilized to provide guidance to potential applications of insulator-metal transition materials as building blocks of brain-inspired non-von Neumann computers.
Universal Phase Dynamics in VO2 Switches Revealed by Ultrafast Operando Diffraction
A. Sood, et al., Science 373, 352-355 (2021)
https://www.science.org/doi/10.1126/science.abc0652
Understanding the pathways and time scales underlying electrically driven insulator-metal transitions is crucial for uncovering the fundamental limits of device operation. Using stroboscopic electron diffraction, we perform synchronized time-resolved measurements of atomic motions and electronic transport in operating vanadium dioxide (VO2) switches. We discover an electrically triggered, isostructural state that forms transiently on microsecond time scales, which is shown by phase-field simulations to be stabilized by local heterogeneities and interfacial interactions between the equilibrium phases. This metastable phase is similar to that formed under photoexcitation within picoseconds, suggesting a universal transformation pathway. Our results establish electrical excitation as a route for uncovering nonequilibrium and metastable phases in correlated materials, opening avenues for engineering dynamical behavior in nanoelectronics.