Uncertainty quantification in DFT caclulations
Density functional theory is one of the most widely used computation methods for the calculation of electronic and magnetic structure of materials from first principles, yet little is known about the uncertainty of its predictions. An understanding of uncertainty is the single most important aspect for computational high-throughput material discovery.
Highly Correlated Metal Oxides
The field of correlated transition metal oxides has a rich spread of interesting phenomena with materials including high temperature superconductors, magnetic and spintronic materials, Mott insulators and more. It just so happens that the leading Li ion battery cathodes are all transition metal oxides. Understanding and contributing to the huge body of work pertaining to these materials in the physics community may help not only characterize existing cathodes but design the cathodes of the future.
High Performance Computing
I recently played a central role in the setup of a new CPU/GPU cluster named Arjuna and lead in the continual maintenance of the cluster. With this cluster, we hope to port higher-order-theory electron stuctructure calculations such as the Random Phase Approximation (RPA) to GPUs to give a more accurate calulation than DFT alone. What was previously a intractable calculation due to compute time, will hopefully be readily used with the implementation of the many logical threads available in a GPU.
Uncertainty Quantification in Prediction of Magnetic States
Jan 2016 - Current
One of the most useful calculations that can be done with Density functional theory is the prediction of magnetic ground states. By simply comparing the calculated energy of two spin configurations, one can determine which is more energetically favorable. On the other hand, all density functional theory calculations must approximate the 'exchange-correlation' energy which accounts for the quantum effects. This is done within the generalized gradient approximation (GGA) using a functional of the electron density and it's gradient. Therefore, with every DFT calculation, one must pick which of the many exchange-correlation functionals available to use. This choice can largely effect the prediction made so a natural question arises: What would happens to a DFT prediction if another functional were used? Using the Bayesian Error Estimation Functional (BEEF), a systematic sampling of magnetic predictions over many exchange-correlation functionals as well as an estimation of uncertainty can be incorporated into DFT calculations. This prediction sampling and uncertainty, understood in the context of a calculated c-value, can point to disagreements in DFT functionals at the GGA level and cue the need for higher-order theories. link
Berry Curvature and Neutron Scattering of Magnons in Honeycomb Lattice
Jan 2016 - May 2016
Berrry curvature plays a role in the dynamics of particles with non-trivaial k-space toplogies. In this work, we considered a honeycomb lattice with nearest neighbor Heisenberg exchange interaction and second nearest neighbor Dzyaloshinskii-Moriya interaction (DMI), which causes non-collinear spin configurations. The spin excitations were then quantized (magnons) using ladder operators analogously to phonons and used to analyitically calculate Berry Curvature and band structure with and without DMI. The addition of DMI is well known to add non-trivial topological configurations such as skymions and domain walls and is therfore solely responsible for the Berry curvature. From this, with the use of thermal greens functions and basic scattering thoery, the magnon-neutron scattering intensities with and without DMI can be calculated. The goal of this work was to to relate Berry curvature due to DMI to the difference in neutron scattering intensities between with and without DMI in an attempt to directly detect the curvature of reciprical space.
Simulations of Magnetically Substituted Graphene
Sep 2014 - July 2015
We explored the theoretical possibility of using graphene nanoribbons (GNRs) with directly substituted chromium atoms as spintronic device. Using density functional theory, we simulated a voltage bias across a constructed GNR in a device setup, where a magnetic dimer has been substituted into the lattice. Through this first principles approach, we calculate the electronic and magnetic properties as a function of Hubbard U, voltage, and magnetic configuration. By calculating of the total energy of each magnetic configuration, we determine that initial antiferromagnetic ground state flips to a ferromagnetic state with applied bias. Mapping this transition point to the calculated conductance for the system reveals that there is a distinct change in conductance through the GNR, which indicates the possibility of a spin valve. This corresponds to a distinct change in the induced magnetization within the graphene. A more complete discussion of this work can be found here.
Calculation Neutron Scattering Intensities of Spin Dimer Excitations
May 2014 - May 2015
One of the most sucessful models for magnetic interaction is the Heisenberg Spin Hamiltonian. In the context of experiment, the spin structure can of materials can be measured using neutron scattering. We calculated the energy spectrum of dimer spin system using the Heisenberg Hamiltonian and calculated inelastic neutron scattering intensities for these systems by hand. We then generalized these results with an analytic formula to create a theoretical fingerprint for spin monomers based on spin structure that can be calculated on the back of an envelope. We then expanded this work to the anisotrpic case by adding a Dzyaloshinskii-Moriya interaction (DMI). The results of this work was presented at the 2015 APS March meeting and published in Physical Review B .