Hello, A new project on the LCRC cluster has been requested. Please forward the information on to the LCRC Allocation sub-committee. Applicant's name: James Rondinelli Applicant's institution: ANL Applicant's division: X-Ray Science Division (XSD) Project Name: IMPROPER11 Project title: Chemical-activated hidden lattice couplings in ultra short perovskite superlattices Associated funding: None; this research project is part of a collaboration with Prof. Craig Fennie at Cornell University (Ithaca, NY) Other Systems: The PI has access to the Center for Nanoscale Materials (CNM) computational facilities. A 100,000 hour allocation for the current year at that facility is dedicated to the investigation of isosymmetric phase transitions in perovskite oxides from first-principles. Science: Complex oxide heteroepitaxy of ultra-short period superlattices provides an elegant route to access latent correlated functionalities derived from artificial elastic, structural, and electronic boundary conditions that are restricted from bulk equilibrium phase diagrams. Such artificially structured ABO3 perovskite materials are amenable to chemical and electrostatic doping for tuning exotic phase diagrams and are suggested to be digital analogues of more complex, and often incompletely, ordered quaternary, oxides. A crucial aspect often overlooked in digitally ordered ultra-short superlattices is that the superlattice geometry and cation ordering leads to a reduction in the atomic site symmetry of the functional atoms. The consequences of such changes in point symmetry are naturally described within a Ginzburg-Landau free energy functional framework. This methodology allows one to identify new symmetry allowed free energy invariants activated by the additional boundary conditions. Motivated by the recent observation of a potentially useful and emergent trilinear coupling in ferroelectric/paraelectric perovskite superlattices, this research project aims to establish a generic framework and set of design rules that guide the choice of materials which show “improper" transitions among three active modes [1]. Manipulating trilinear order parameter couplings or mutually coupled phase transitions in perovskite oxide superlattices are a practical route to achieve control of the non-polar BO6 corner-connected octahedral blocks—which are intimately linked to the magnetic superexchange interactions, orbital bandwidths, and critical superconducting temperatures—through alternative external fields [2,3]. Our goals are to: 1. Identify and understand the trilinear lattice couplings available in ultra-short superlattices from first-principles calculations; 2. Use Ginzburg-Landau theory to identify the symmetry allowed order parameter invariants; 3. Perform first principles calculations (with this allocation) to identify the microscopic mechanism responsible for the activated lattice coupling; and 4. Explore the strength of this coupling with these calculations for a series of material systems; our aim is to suggest which artificially layered heterostructure is the most promising to explore experimentally. This computational research project offers to shed light on an unexplored route that directly activates structurally-driven electronic phase transitions forbidden in the bulk phase diagram of the constituent materials because of symmetry restrictions that prohibit orbital mixing. The work stands to have substantial impact in the field of rational materials design. References: [1] E. Bousquet, M. Dawber, N. Stucki, C. Lichtensteiger, P. Hermet, S. Gariglio, J.-M. Triscone, and P. Ghosez, Nature 452, 732 (2008). [2] M. Rini, R. Tobey, N. Dean, J. Itatani, Y. Tomioka, Y. Tokura, R.W. Schoenlein, and A. Cavalleri, Nature 449, 72 (2007) [3] J.M. Rondinelli and N.A. Spaldin, Phys. Rev. B. 81, 085109 (2010) Project description: All of our investigations employ plane-wave density-functional theory (DFT) to explore and characterize the allowed free energy invariants from first principles [1,2] with recent developments in materials theory understanding of structural phase transitions in perovskite oxides. This investigation combines calculations of materials exhibiting different order parameters (electric polarization, non-polar structural distortions, and magnetization) and their subsequent response to different perturbations on those order parameters (strain, magnetic field, and electric field) to exploit emergent functionalities in artificially structured oxides. Our ultimate goal is to combine multiple functionalities for the design of practical devices based on these couplings. Ab initio theory plays a central role in the research effort aimed at the rational design of materials with multiple functionalities. In particular, first-principles (parameter-free) calculations are excellent compliments to experimental discovery efforts because of their ability to study ideal, defect-free films; additionally, unlike experimental studies, our calculations can treat bi-axial strain present in heteroepitaxial films as a continuous variable since we do not rely on the availability of suitable and chemically compatible substrates. Furthermore, with first-principles calculations we can, with relative ease, decouple the effects of strain from those of interface chemistry, to isolate the microscopic origin for changes in functionality. We plan to employ two codes for our investigations: (1) the commercially available VASP code [3-5], which tends to be most useful for studying materials with complex magnetic structures and their responses, due to the ability to simultaneously use spin-orbit coupling, non-collinear magnetism and LDA+U, and (2) the open-source Abinit package [6,7], which we use primarily to characterize structures, ferroelectricity and responses of materials within a perturbation theory framework. Both codes are based on the plane-wave formalism with PAW potentials for efficient separation of the core and valence electrons. Code Scalability and Efficiency: The scaling of these codes on clusters at national computation facilities is well documented. The PI has not used the LCRC (FUSION) facility before, but all approximate timings and computation hours used to estimate the current allocation size are from benchmarks obtained with a highly-optimized VASP code at the National Center for Supercomputing Applications (NCSA) on the COBALT machine. Similar optimization should be readily achieved on the FUSION machine. Benchmarks for the efficiency and parallelization of the VASP code for the CARBON machine at the CNM (Argonne) are available at https://wiki.anl.gov/cnm/HPC/Benchmarks/Generation_1_vs_2. All available data indicate that the codes scales linearly up to 132 processors. Both codes also have a range of parallelization strategies that can be selected for efficiency based on the size of the calculation and the machine architecture. Minimal communications and near-perfect scaling can be achieved by parallelizing over k-points and electron bands. However, calculations of very large systems, which tend to be memory intensive, are best parallelized over the FFT (plane wave) mesh, at the expense of increased communications. In VASP, the strategy can be readily tuned between two extremes with a single parameter [8]. The LCRC system (FUSION cluster) is ideally suited for our first-principles calculations for two reasons: (i) the nodes are both individually efficient and are linked by high-speed interconnects, which enables us to make use of the excellent scalability and optimization of the MPI-based density-functional codes to be used for these projects, and (ii) the short queue times enable enable efficient completion of our project goals, which typically require running a large number of small 8-32 processor (1-4 node) calculations. Software requirements: Both codes require a FORTRAN 90 Compiler and MPI software for parallel execution. System optimized BLAS and LaPACK libraries (such as MKL or GoTo) are also needed for execution. Experiments planned: The computational portion of this research project address items (3) and (4) described in the Scientific Section of the proposal. The first-principles calculations will be performed to understand the fundamental origin for our predicted trilinear lattice couplings. We will focus on the trilinear invariant of the form P(z)Phi(z+)Phi(z-), which couples a ferroelectric polarization P(z) along the superlattice direction with structural phonon modes [Phi(z+) and Phi(z-)]that describe different BO6 octahedral rotation patterns about the same axis. By systematically changing the chemical composition of the superlattice, we will attempt to disentangle the competing interactions and microscopic origins for the trilinear term which is forbidden in the bulk systems. For this study we will examine ultra-short period superlattices composed of the following ABO3 perovskites: • (LaGaO3)1/(BiGaO3)1 -- (SL1 = LGO/BGO) • (BiFeO3)/(BiGaO3)1 -- (SL2 = BFO/BGO) We will first examine if our computational methods can accurately reproduce the known structural phases of each material that comprise the superlattice. To do so, we will calculate the phonon modes for each material using density functional perturbation theory in the high symmetry cubic phase; we will then systematically “freeze in” each mode to obtain the ground state structures (see the next portion for an example of such an experiment). The initial first step is critical to verifying the predicative power of our computational models. Once we have successfully obtained the correct ground state structures, we will then evaluate if the trilinear coupling term is active in SL1 and SL2. To do so, we will evaluate the change in the free energy equation of state as a function of the soft (and unstable) phonon modes obtained for the individual components of the superlattice. We will calculate specifically how the polarization arises from a coupling to the Phi(z+)Phi(z-) order parameter by increasing the strength of the interaction—practically this is accomplished by increasing the amplitude of the Phi(z+)Phi(z-) structural distortion. Each oxide is anticipated to exhibit certain allowed invariants in the 1/1 period superlattices based on our phenomological studies. The intellectual challenge in these calculations is that each subsequent system (and therefore superlattice) is more complex than the previous due to additional spin degrees of freedom and the fact that DFT studies of multiple order parameters are not routine: • LaGaO3 : non-magnetic dielectric with large octahedral rotations • BiGaO3 : ferroelectric with an anomalously large tetragonality • BiFeO3 : antiferromagnetic-ferroelectric; the quintessential room temperature multiferroic. Upon completion of the first portion of the project, we will then study how strain can be used to tune the energy barrier between different structural phases so as to enhance the coupling strength of the trilinear invariant. Technical details: We outline below how our calculations will proceed to investigate the presence and magnitude of the trilinear coupling term in the chemically different superlattices outlined above. First we will examine how the energetics of of the ideal high-symmetry tetragonal superlattices evolve by ``freezing-in'' linear combinations of the soft phonon modes obtained from our structural study on each component. Based on the know structural phase diagrams, we anticipate most of the eigendisplacments obtained from the calculations will be octahedral rotations that are associated with a symmetry-adapted mode that transforms according to the 3-dimensional irreducible representation R4+ of the parent cubic phase. This is highly desirable since these symmetry modes provide an effective order parameter to map onto our phenomenologically obtained Ginzburg-Landau free energy functional. In order to get an idea of how the calculations will proceed, we describe in more detail the general procedure: the calculations are started by freezing-in the R4+ distortions [9] with amplitudes ranging from 0 to 25% at 5% intervals (5 calculations per mode direction). Each structural distortion requires an integer multiple increase in the primitive unit cell so as to accommodate the atomic displacement pattern associated with the phonon mode and the periodic boundary conditions used in the calculations. Since the computational cost of each calculation approximately scales as (N2)Ln(N), where N is the number of atoms, we have used approximate timings done on the NCSA COBALT machine to estimate the number of CPU hours needed to study the three perovskite materials. Since the PI has not used the FUSION cluster, the timings are only approximately accurate since the machines are of comparable speed. Using these estimated timings we request 7,560 CPU hours for this portion of th e project. LaGaO3 and BiGaO3 will each require approximately 1,890 hours and BiFeO3 will require 3,780 to properly treat the material’s antiferromagnetic order. [The magnetic order in the BFO compound doubles the CPU time due to the fact that two (spin “up” and spin “down”) independent electronic wavefunction manifolds need to be calculated.] Next, starting from the lowest energy configurations we relax the internal coordinates through a conjugate-gradient algorithm which requires a line minimization and proceeds based on calculated forces and total energies. For example, relaxing a monoclinic structure C2/c structure requires the optimization of 15 free internal parameters. We have performed a test of this calculation on the COBALT machine (NCSA) and find that on average 245 CPU hours are necessary to reach a converged structure. On average these calculations require 230 electronic steps, with a computational cost of 465 s/step. Once we have the ionic ground state, we plan to calculate the Born-effective-charges (BECs) to evaluate the complete polarization of each superlattice. This type of calculation allows us to access not only the ionic displacement contribution to the cell polarization but also the electronic term which originates from a redistribution of charge (or hybridization) among the electronic orbitals. Calculation of the BECs along the superlattice growth direction requires one self-consistent electronic calculation (120 CPU hour per calculation per ionic degree of freedom) and three non-self-consistent Berry-phase calculations leading to 640 CPU hours for a prototypical 40-atom simulation cell. For each non magnetic bulk system we require 4,890 CPU hours: 1,890 for the structural study, and 1,000 * (3 atoms for the BECs). The magnetic BiFeO3 material will require twice as much time (9,780). The 3 different bulk systems therefore require a total of ~20,000 CPU hours. For the two superlattices, we will need an additional 30,000 CPU hours in total to study the free energy evolution and electric polarization dependence with respect to the octahedral mode amplitudes. For the non-magnetic and magnetic superlattices we require approximately 10,000 CPU hours and 20,000 CPU hours, respectively. These numbers are based on the estimated described above. Next the in-plane lattice parameters of the superlattices will be varied to simulate growth on various substrate materials which are experimentally available. We propose investigating 5 different strain states: -3, -1.5, 0, +1.5, and +3% to map out a complete phase diagram. (Negative values indicate compression of the lattice, while positive values indicate a tensile strain state.) We then will re-compute the change in free energy with strain and the octahedral modes for each bulk material and superlattice: this gives 4 strain states times five systems (2 superlattices + 3 bulk phases). This gives a total of 20 additional calculations requiring approximately 80,000 CPU hours. We obtain this number based on the PI’s prior experience that only two modes will be of interest in the strained superlattices rather than the 5 modes considered in more exploratory zero strain study. Once we have optimized the internal degrees of freedom and the forces are converged to within an accur acy of 1meV Å-1, we then relax the out-of-plane lattice constant since it will typically decrease due to volume conservation (Poisson effects). Such calculations will also require further relaxations (~80 steps per lattice constant) until the equilibrium length is determined. Based on our estimates with 20 different structures requiring minimization, we request in additional 16,750 CPU hours. We also desire 1,000 CPU hours for optimization and testing of the VASP and Abinit codes (2,000 CPU hours total). The total requested allocation is then divided as follows: 20,000 (Bulk systems) + 30,000 (superlattices at zero strain) + 96,750 [(80,000) superlattices under strain(16,750)] + 2,000 (testing) = 148,750 CPU hours. Project Members: All calculations will be performed by the PI (Rondinelli), while exchange of ideas and data analysis will be done in collaboration with Fennie at Cornell University. References: [1] P. Hohenberg and W. Kohn. Phys. Rev., 136:B864–B871, 1964; W. Kohn and L. J. Sham. Phys. Rev., 140:A1133–A1138, 1965. [2] S. R. Phillpot and S. B. Sinnott. Science, 325, 1634 (2009). [3] G. Kresse and J. Furthmuller, Phys. Rev. B 54, 11169 (1996). [4] G. Kresse and D. Joubert, Phys. Rev. B 59, 1758 (1999). [5] The PI holds a license for this software and can be compiled and optimized for the FUSION architecture. [6] The ABINIT code is a common project of the Université Catholique de Louvain, Corning Incorporated, and other contributors (http://www.abinit.org.) [7] X. Gonze, Phys. Rev. B 55, 10337 (1997); X. Gonze and C. Lee, Phys. Rev. B 55, 10355(1997); X. Gonze et al., Comput. Mater. Sci. 25, 478 (2002). [8] The parallelization tags are described in detail at http://cms.mpi.univie.ac.at/vasp/vasp/Parallelisation_NPAR_tag_LPLANE_tag.ht.... [9] A supplemental table of the R4+ modes is available upon request. It includes an estimate of the number of CPU hours required to obtain a self-consistent charge density. Project URL: Requested allocation: 148750 Justification: The requester has used 0 hours of their initial startup project. In addition to approving an initial amount, please specify a Category and Subcategory for this project. For a list of the current selection of approved categories, please see: https://wiki.lcrc.anl.gov/wiki/Processes/Categories Once the Allocation committee has approved the project, please go to the Project Management page to create it: https://accounts.lcrc.anl.gov/projects.php Thank You, The LCRC Accounts System