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In this paper, we introduce an efficient, linear algebra-based method for optimizing supercell selection to determine Heisenberg exchange parameters from DFT calculations. A widely used approach for deriving these parameters involves mapping DFT energies from various magnetic configurations within a supercell to the Heisenberg Hamiltonian. However, periodic boundary conditions in crystals limit the number of exchange parameters that can be extracted. To identify supercells that allow for more exchange parameters, we generate all possible supercell sizes within a specified range and apply null space analysis to the coefficient matrix derived from mapping DFT results to the Heisenberg Hamiltonian. By selecting optimal supercells, we significantly reduce computational time and resource consumption. This method, which involves generating and analyzing supercells before performing DFT calculations, has demonstrated a reduction in computational costs by 1-2 orders of magnitude in many cases.

Monolayer NiI$_2$ garners large research interest due to its multiferroic behavior stemming from the interplay between its non-collinear magnetic order and the spin-orbit coupling. This prompts an investigation into the stability of the magnetic order in NiI$_2$ and similar materials under external stimuli. In this work, we report the effect of biaxial and uniaxial strain on the magnetic ground state, the critical temperature, and the magnonic properties of the NiX$_2$ (X = I, Br, Cl) monolayers. For all three materials, we reveal intricate strain-dependent phase diagrams, including ferromagnetic, helimagnetic, and skyrmionic phases. Moreover, we discuss the necessity of considering the biquadratic exchange interaction in the latter analysis. We reveal that the biquadratic exchange significantly alters both the magnetic ground state and the critical temperature of the magnetic order, and we demonstrate that its importance becomes even more explicit when monolayer Ni-dihalides are strained. Finally, we calculate the magnonic dispersion for the predicted magnetic states, showing that the skyrmionic phase functions as a magnonic crystal, and demonstrate the presence of strain-tunable soft magnon modes at finite wavevectors in the helimagnetic phase.

In the pursuit of advancing solar energy technologies, this study presents 20 direct and quasi-direct band gap silicon crystalline semiconductors that satisfy the Shockley-Queisser limit, a benchmark for solar cell efficiency. Employing two evolutionary algorithm-based searches, we optimize structures and calculate fitness function using the DFTB method and Gaussian approximation potential. Following the preselection of structures based on energy considerations, we further optimize them using PBEsol DFT. Subsequently, we screen the structures based on their band gap, employing a DFTB method tailored for band gap calculation of silicon crystals. To ensure accurate band gap determination, we employ HSE and GW methods. To validate the structural stability, we employ phonon analysis via linear regression algorithm applied to PBEsol DFT data. Significantly, the structures unveiled in this study are of great importance due to their proven stability from both mechanical and dynamic perspectives. Furthermore, the ductility and low density of certain structures enhance their potential application. We examine the optical properties by studying the imaginary part of the dielectric function by solving the Bethe-Salpeter Equation on top of GW approximation. By calculating the SLME, we achieve an efficiency of 32.7% for Si$_{22}$ at a thickness of 500 nm. Moreover, the study harnesses various machine learning algorithms to develop a predictive model for the band gap energy of these silicon structures. Input data for machine learning models are derived from structural MBTR and SOAP descriptors, as well as DFT outputs. Notably, the results reveal that features extracted from DFT outperform the MBTR and SOAP descriptors., Comment: 14 pages, 8 figures, 5 tables

We use density functional theory to investigate effects of spin-orbit coupling and single-stripe-type antiferromagnetic (sAFM) ordering on the crystal structure and electronic properties of SmFeAsO. The results indicate that AFM ordering causes the crystal structure transition from tetragonal to orthorhombic, along with increase in the height of As atoms from Fe layer due to magnetostriction. It also leads to the opening of partial band gaps, the emergence of a prominent peak near Fermi energy (EF) in the density of states (DOS) and a reduction in Fermi surface nesting. The study finds a correlation between the calculated area under the DOS curve, spanning from EF to the first peak above it, and the optimal electron-doped concentration required for inducing superconductivity in SmFeAsO. The findings suggest that spin and charge density waves can play important roles in the superconducting mechanism of Fe-based superconductors. Our calculations demonstrate that spin-orbit coupling reduces electronic correlation., Comment: 29 pages, 8 figures, 1 table

Superconductivity is a remarkable phenomenon in condensed matter physics, which comprises a fascinating array of properties expected to revolutionize energy-related technologies and pertinent fundamental research. However, the field faces the challenge of achieving superconductivity at room temperature. In recent years, Artificial Intelligence (AI) approaches have emerged as a promising tool for predicting such properties as transition temperature (Tc) to enable the rapid screening of large databases to discover new superconducting materials. This study employs the SuperCon dataset as the largest superconducting materials dataset. Then, we perform various data pre-processing steps to derive the clean DataG dataset, containing 13022 compounds. In another stage of the study, we apply the novel CatBoost algorithm to predict the transition temperatures of novel superconducting materials. In addition, we developed a package called Jabir, which generates 322 atomic descriptors. We also designed an innovative hybrid method called Soraya package to select the most critical features from the feature space. These yield R2 and RMSE values (0.952 and 6.45 K, respectively) superior to those previously reported in the literature. Finally, as a novel contribution to the field, a web application was designed for predicting and determining the Tc values of superconducting materials., Comment: 21 pages, 8 figures, 6 Tables

This study investigates the predictive capabilities of common DFT methods (GGA, GGA+$U$, and GGA+$U$+$V$) for determining the transition temperature of antiferromagnetic insulators. We utilize a dataset of 29 compounds and derive Heisenberg exchanges based on DFT total energies of different magnetic configurations. To obtain exchange parameters within a supercell, we have devised an innovative method that utilizes null space analysis to identify and address the limitations imposed by the supercell on these exchange parameters. With obtained exchanges, we construct Heisenberg Hamiltonian to compute Transition temperatures using classical Monte Carlo simulations. To refine the calculations, we apply linear response theory to compute on-site ($U$) and intersite ($V$) corrections through a self-consistent process. Our findings reveal that GGA significantly overestimates the transition temperature (by ~113%), while GGA+$U$ underestimates it (by ~53%). To improve GGA+$U$ results, we propose adjusting the DFT results with the $(S+1)/S$ coefficient to compensate for quantum effects in Monte Carlo simulation, resulting in a reduced error of 44%. Additionally, we discover a high Pearson correlation coefficient of approximately 0.92 between the transition temperatures calculated using the GGA+$U$ method and the experimentally determined transition temperatures. Furthermore, we explore the impact of geometry optimization on a subset of samples. Using consistent structures with GGA+U and GGA+U+V theories reduced the error.

In this study, we use Hubbard-Corrected density functional theory (DFT+$U$) to derive spin model Hamiltonians consisting of Heisenberg exchange interactions up to the fourth nearest neighbors and bi-quadratic interactions. We map the DFT+$U$ results of several magnetic configurations to the Heisenberg spin model Hamiltonian to estimate Heisenberg exchanges. We demonstrate that the number of magnetic configurations should be at least twice the number of exchange parameters to estimate exchange parameters correctly. To calculate biquadratic interaction, we propose specific non-collinear magnetic configurations that do not change the energy of the Heisenberg spin model. We use classical Monte Carlo (MC) simulations to evaluate DFT+$U$ results. We obtain the temperature dependence of magnetic susceptibility and specific heat to determine the Curie-Weiss and N\'eel temperatures. The MC simulations reveal that although the biquadratic interaction can not change the N\'eel temperature, it modifies the order parameter. We indicate that for a fair comparison between classical MC simulations and experiments, we need to consider the quantum effect by applying $(S+1)/S$ correction in classical MC simulations.

Compositional disorder is common in crystal compounds. In these compounds, some atoms are randomly distributed at some crystallographic sites. For such compounds, randomness forms many non-identical independent structures. Thus, calculating the energy of all structures using ordinary quantum ab initio methods can be significantly time-consuming. Machine learning can be a reliable alternative to ab initio methods. We calculate the energy of these compounds with an accuracy close to that of density functional theory calculations in a considerably shorter time using machine learning. In this study, we use kernel ridge regression and neural network to predict energy. In the KRR, we employ sine matrix, Ewald sum matrix, SOAP, ACSF, and MBTR. To implement the neural network, we use two important classes of application of the neural network in material science, including high-dimensional neural network and convolutional neural network based on crystal graph representation. We show that kernel ridge regression using MBTR and neural network using ACSF can provide better accuracy than other methods., Comment: 15pages,3figures,1table