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Prof. Aldo Humberto Romero
Department of Physics and Astronomy
Eberly College of Arts and Sciences
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Research

Material Crystal Design

As computational capabilities have advanced exponentially over recent decades, material scientists, including our research group, have leveraged these advancements to make groundbreaking discoveries. Utilizing First Principles calculations based on Density Functional Theory, we can predict stable crystal structure phases under varying stoichiometry, temperature, and pressure conditions. But our work doesn't stop there; we go beyond mere prediction to characterize and unveil novel properties of these materials.Our research encompasses various material properties, from electronic and phonon band structures to elastic, mechanical, thermoelectric, and thermodynamic attributes. We also delve into the complexities of magnetic and orbital ordering, spin-orbit interactions, electron-phonon interactions, and topological features in electronic and phononic band structures. Our analyses extend to topological surface states and various transport properties.We employ cutting-edge algorithms like Firefly and Minima Hopping to facilitate our material search, mainly when prior knowledge about the material is limited.


Our research group has recently broken new ground by developing an innovative methodology rooted in symmetry arguments. This versatile approach applies to 3D, 2D, and even 1D configuration systems. In 2D materials, we've achieved a nuanced search for layered materials by synergistically integrating Density Functional Theory (DFT) with machine learning techniques. Collaborating with Miguel Marques' research group, we've expanded the concept of a "universal potential"—a classical potential applicable across a wide range of materials—into the two-dimensional domain. Utilizing transfer learning techniques, we've retrained neural networks to achieve energy calculations with an accuracy surpassing ten meV/atom compared to traditional DFT calculations.We're extending this methodology to 1D systems, where the absence of periodicity in two dimensions allows for unique structural relaxation patterns distinct from their 3D counterparts. Additionally, we are exploring the diverse properties of the more than 120,000 materials we have successfully cataloged in our 2D materials database.

This innovative approach has led to the prediction of multiple materials with exotic properties, detailed in our publications section.

Machine Learning in Materials Design

Markov Chain Monte Carlo in parameter optimization in strongly correlated materials

Markov Chain Monte Carlo (MCMC) is a powerful tool for sampling various parameter spaces based on underlying probability distributions. Particularly useful for tackling problems characterized by intricate functional dependencies on external parameters, MCMC enables a more nuanced exploration of complex systems. In our research, we employ a diverse array of algorithms to sample the Coulomb (U) and exchange (J) parameters in the Hubbard Model, integrated within the framework of Density Functional Theory (DFT).We aim to generalize this methodology, allowing us to determine the (J, U) values for materials featuring the same correlated species, irrespective of their oxidation states. We have successfully demonstrated the feasibility of this approach, although it comes with a significant computational overhead.

Dynamical Learning of the Exchange correlation parameters in the SCAN functional

Density Functional Theory (DFT) has evolved significantly since its inception in the mid-20th century. One of the most critical aspects of DFT is the exchange-correlation term, which has undergone substantial development over the years. This summary provides an overview of essential milestones and current challenges in the field based on seminal papers.

    Milestones in DFT

  • Kohn-Sham Density-Functional Theory (KS-DFT): Introduced in the 1960s, KS-DFT laid the foundation for modern DFT. The theory gained traction in the mid-1980s when advancements in the exchange-correlation term made it competitive with wave-function methods. Thanks to that, it is now the most used method to describe materials properties.

    Addressing Electron Over-Delocalization

  • DFT+U Method: This technique emerged to tackle the problem of electron over-delocalization in DFT. It uses ideas from model Hamiltonians and acts as an "elevator" to systematically tune relative energetics, particularly for d or f electrons. Though this theory has been used for many years to describe strongly correlated materials, we must remember that determining the (J, U) parameters is still an unresolved problem. Several methods are:
  • Linear Response Theory: This method calculates U and J by perturbing the system and observing how the electron density responds. It's one of the most commonly used methods for obtaining Hubbard parameters.
          Constrained Random Phase Approximation (cRPA): This extension of the Random Phase Approximation is used to calculate U and J from the first principles.
         Constrained Density Functional Theory (cDFT): In this method, the Hubbard U is calculated by denying the number of electrons in a particular region and computing the corresponding change in total energy.
         Fitting to Experimental Data: U and J are sometimes determined by fitting DFT+U calculations to experimental observations, such as X-ray absorption spectra or magnetic moments.
         Iterative Methods: Some approaches iteratively adjust U and J during the DFT+U calculations until a specific criterion is met, such as minimizing the total energy or the best match to experimental data.
         Machine Learning Approaches: Recent advancements have seen the use of machine learning algorithms to predict the Hubbard parameters based on a dataset of known materials.
        Spectral Functions: In some cases, U and J are extracted from the features of the spectral functions obtained from photoemission experiments.
        Quantum Monte Carlo Methods: These are high-accuracy methods used to benchmark U and J values, although they are computationally expensive.

Compare with all these methods, we are taking a different approach, which is based on the nature of the functional, which depends on parameters that can be optimized by using Machine Learning methods. Our method has proven to be useful in 3D materials but also in 2D materials.

Dynamical Mean Field Theory

The overarching goal of contemporary materials science is to pioneer methodologies that pave the way for creating cutting-edge materials with exceptional properties. The rapid advancements in computational resources, encompassing both software and hardware, have propelled us closer to this objective. Our research is centered on the computational modeling of Strongly Correlated Materials (SCM) through an integrated approach that combines Density Functional Theory (DFT) and Dynamical Mean Field Theory (DMFT).SCMs present unique challenges for study under conventional mean field approximations due to the significant impact of correlated electrons, particularly in the spatially confined d and f electron shells. These materials necessitate a more nuanced approach to independent treatment. The intricate electron correlations give rise to many fascinating material phenomena, such as magnetism, high-temperature superconductivity, colossal magnetoresistance, heavy fermion systems, metal-to-insulator transitions (Mott insulators), and thermomagnetism. These phenomena have far-reaching implications for a host of novel applications.Given the complexity and potential impact of SCMs, it is crucial to establish a comprehensive research program that seamlessly integrates the design, synthesis, and characterization of these materials.

Magnetic Parameters and 2D magnetic materials

The Heisenberg Hamiltonian is a simplified model used to describe magnetic systems, and it primarily focuses on the exchange interactions between spins. In its most basic form, the Heisenberg Hamiltonian for a system of spins S⃗i is given by:

Heisenberg model

Here, the Hamiltonian have three important components. The first term is the Isotropic Heisenberg Term and describes the isotropic exchange interaction between spins S⃗i and S⃗j. Here, Jij​ is the isotropic exchange coupling constant. The second term is the Dzyaloshinskii–Moriya Term and represents the antisymmetric exchange interaction, which is significant in systems lacking inversion symmetry. The last term is the Anisotropic Exchange Term and accounts for the anisotropic exchange interactions. The anisotropic tensor Jijaniso describes the strength and directionality of the anisotropic exchange. In a large number of systems, this model Hamiltonian is able to capture most of the magnetic properties and by knowing then, we would be able to compute the magnetic susceptibility, the Curie or the Neil temperature, the saturation magnetization and coercivity, the magnetic domains and domain walls, the damping parameter and the magnetic permeability and more importantly, the spin waves and magnons.

In this project, we have developed a methodology that interfaced with TB2J and SIESTA, we are able to find the lowest energy magnetic configuration and with it, we can compute the magnon spectra and any other parameter. We are now using this methodology to search for 2D materials with optimal magnetic properties. 

Software Development

  • PyProcar. A python script used to perform spin band structure analysis from the PROCAR file. This is an output file obtained from an electronic structure VASP ( https://www.vasp.at). In general this file contains the energy eigenstates of each band and Kohn-Sham orbital per spin.  This script can be accessed from the following link. 
      https://github.com/uthpalah/PyProcar
  • PyChemia. A general python package to perform structural search. The code is able to use different methodologies to search over optimal structures such as genetic algorithms and firefly. Forces, stresses and energies are obtained from different electronic structure codes such as Abinit, Vasp, Octupus, Elk, Siesta, Fireball and DFTB+. In the focus of the fluorides project, an implementation to create unit cells of surfaces under any Miller indeces orientation has been created. The only necessary input is the input unit cell and the Miller indices, where the orientation is desired. See documentation for that specific part of PyChemia.  This script can be accessed from the following link.
      https://github.com/MaterialsDiscovery/PyChemia

  • DMFTwDFT.  Thi
  • MechElastic
  • ABINIT

Complex Fluorides

There is significant interest in multifunctional materials, such as multiferroics. Those that combine simultaneous responses to electric, magnetic, and strain fields. Potential applications include new power efficient electronics and ultra-fast information processing devices. To date, most of the multiferroics that have been studied are complex oxide materials. Despite the exciting fundamental discoveries emanating from research on these materials, their multiferroic performance is not yet adequate for use in practical applications. In this project, the investigators propose to systematically study complex fluoride materials as alternatives to complex oxides because the different physical origins of the multiferroic effects in fluorides can potentially enhance the multiferroic response. The research consists of a synergistic collaboration between computational and experimental researchers. The computational effort predicts the most likely materials to have desired multiferroic properties, and the experimental counterpart synthesizes and characterizes the suggested materials. In turn, the experimental results will be used to improve the accuracy of the calculations, which ultimately will lead to an efficient optimization of the design of the new materials.