Accelerating the discovery of novel magnetic materials using machine learning-guided adaptive feedback.

Magnetic materials are essential for energy generation and information devices, and they play an important role in advanced technologies and green energy economies. Currently, the most widely used magnets contain rare earth (RE) elements. An outstanding challenge of notable scientific interest is the discovery and synthesis of novel magnetic materials without RE elements that meet the performance and cost goals for advanced electromagnetic devices. Here, we report our discovery and synthesis of an RE-free magnetic compound, Fe3CoB2, through an efficient feedback framework by integrating machine learning (ML), an adaptive genetic algorithm, first-principles calculations, and experimental synthesis. Magnetic measurements show that Fe3CoB2 exhibits a high magnetic anisotropy (K1 = 1.2 MJ/m3) and saturation magnetic polarization (Js = 1.39 T), which is suitable for RE-free permanent-magnet applications. Our ML-guided approach presents a promising paradigm for efficient materials design and discovery and can also be applied to the search for other functional materials.

Efficient Full-Frequency GW Calculations Using a Lanczos Method.

The GW approximation is widely used for reliable and accurate modeling of single-particle excitations. It also serves as a starting point for many theoretical methods, such as its use in the Bethe-Salpeter equation (BSE) and dynamical mean-field theory. However, full-frequency GW calculations for large systems with hundreds of atoms remain computationally challenging, even after years of efforts to reduce the prefactor and improve scaling. We propose a method that reformulates the correlation part of the GW self-energy as a resolvent of a Hermitian matrix, which can be efficiently and accurately computed using the standard Lanczos method. This method enables full-frequency GW calculations of material systems with a few hundred atoms on a single computing workstation. We further demonstrate the efficiency of the method by calculating the defect-state energies of silicon quantum dots with diameters up to 4 nm and nearly 2,000 silicon atoms using only 20 computational nodes.

Real-space solution to the electronic structure problem for nearly a million electrons.

We report a Kohn-Sham density functional theory calculation of a system with more than 200 000 atoms and 800 000 electrons using a real-space high-order finite-difference method to investigate the electronic structure of large spherical silicon nanoclusters. Our system of choice was a 20 nm large spherical nanocluster with 202 617 silicon atoms and 13 836 hydrogen atoms used to passivate the dangling surface bonds. To speed up the convergence of the eigenspace, we utilized Chebyshev-filtered subspace iteration, and for sparse matrix-vector multiplications, we used blockwise Hilbert space-filling curves, implemented in the PARSEC code. For this calculation, we also replaced our orthonormalization + Rayleigh-Ritz step with a generalized eigenvalue problem step. We utilized all of the 8192 nodes (458 752 processors) on the Frontera machine at the Texas Advanced Computing Center. We achieved two Chebyshev-filtered subspace iterations, yielding a good approximation of the electronic density of states. Our work pushes the limits on the capabilities of the current electronic structure solvers to nearly 106 electrons and demonstrates the potential of the real-space approach to efficiently parallelize large calculations on modern high-performance computing platforms.

Atomic Fingerprinting of Heteroatoms Using Noncontact Atomic Force Microscopy.

Immense strides have been made in increasing the resolution of scanning probe microscopy. Noncontact atomic force microscopy (nc-AFM) now offers one the ability to characterize and visualize single molecules with subatomic resolution. Specifically, nc-AFM with a carbon monoxide (CO) functionalized tip has the ability to discriminate functional groups (-CC-, -CH2 , -CO, …), although discriminating atomic species often remains as an ongoing challenge. Here, real-space pseudopotentials constructed within density functional theory are employed to accurately simulate nc-AFM images of molecules containing heteroatoms (S, I, and N) within dibenzothiophene (DBT), 2-iodotriphenylene (ITP), acridine (ACR) and ferrous phthalocyanine (FePc). It is found that S and I atoms can be easily identified from C based on their unique features. For N atoms, a use of tip functionalization is proposed to effectively discriminate them from C atoms.

Prediction of Intrinsic Ferroelectricity and Large Piezoelectricity in Monolayer Arsenic Chalcogenides.

Two-dimensional materials that exhibit spontaneous electric polarization are of notable interest for functional materials. However, despite the prediction of many two-dimensional polar materials, the number of experimentally confirmed two-dimensional ferroelectrics is far less than bulk ferroelectrics. We provide strong evidence that the Pmn21 phase of arsenic chalcogenides As2X3 (X = S, Se, and Te), which include the recently isolated monolayer orpiment, are intrinsic ferroelectrics and demonstrate strong in-plane piezoelectricity. We found the calculated energy barriers for collectively reversing the electric polarization or moving a 180° domain wall are reasonable compared to previously reported ferroelectrics. We propose a high-symmetry structure (with Pmmn space group) that transforms into the ferroelectric Pmn21 phase by a soft B2u phonon mode. By studying other soft modes of the high-symmetry Pmmn structure, we identify several undiscovered metastable polymorphs, including a polar phase (with a P21 space group) with sizable piezoelectricity.

Discrimination of Bond Order in Organic Molecules Using Noncontact Atomic Force Microscopy.

Noncontact atomic force microscopy (nc-AFM) with a CO-functionalized tip can image submolecular structures through high-resolution images with the possibility of discriminating bond order. We employ real-space pseudopotential calculations to simulate nc-AFM images of molecules containing double (dibenzo(cd,n)naphtho(3,2,1,8-pqra)perylene (DBNP), hexabenzo(bc,ef,hi,kl,no,qr)coronene (HBC)) and triple (1,2-bis[2-(2-ethynylphenyl)ethynyl]-benzene (BEEB), 6-phenylhexa-1,3,5-triynylbenzene (PHTB)) bonds. We find (1) triple bonds can be unambiguously distinguished from other interatomic interactions based on a characteristic image and (2) the degree of double bond character can be directly determined from the image. We propose that large lateral forces acting on the tip may induce specific image distortions in the cases of DBNP and BEEB.

Optically Driven Magnetic Phase Transition of Monolayer RuCl3.

Strong light-matter interactions within nanoscale structures offer the possibility of optically controlling material properties. Motivated by the recent discovery of intrinsic long-range magnetic order in two-dimensional materials, which allow for the creation of novel magnetic devices of unprecedented small size, we predict that light can couple with magnetism and efficiently tune magnetic orders of monolayer ruthenium trichloride (RuCl3). First-principles calculations show that both free carriers and optically excited electron-hole pairs can switch monolayer RuCl3 from a proximate spin-liquid phase to a stable ferromagnetic phase. Specifically, a moderate electron-hole pair density (on the order of 1 × 1013 cm-2) can significantly stabilize the ferromagnetic phase by 10 meV/f.u. in comparison to the competing zigzag phase, so that the predicted ferromagnetism can be driven by optical pumping experiments. Analysis shows that this magnetic phase transition is driven by a combined effect of doping-induced lattice strain and itinerant ferromagnetism. According to Ising-model calculations, we find that the Curie temperature of the ferromagnetic phase can be increased significantly by raising carrier or electron-hole pair density. This enhanced optomagnetic effect opens new opportunities to manipulate two-dimensional magnetism through noncontact, optical approaches.

The stability, electronic structure, and optical absorption of boron-nitride diamondoids predicted with first-principles calculations.

Although diamondoids are broadly studied for their fundamental properties and applications, boron-nitride-based diamondoids are scarcely explored. Here we predict the stability, electronic structure, and optical absorption spectra of six boron-nitride (BN) diamondoids with first-principles methods based on pseudopotential density functional theory and many-body perturbation methods implemented with a real-space formalism. We find that four of them are thermodynamically stable at room temperature, while B10N8H24 and B6N4H16 show thermodynamic instability in molecular dynamics simulations. With the GW approximation, we predicted the ionization energies and electron affinities of BN-diamondoids and find that the evolution of the electronic structure with size does not follow the same trend as diamondoids, owing to the unbalanced numbers of boron and nitrogen atoms. We show strong photoabsorption of BN-triamantane and BN-adamantane in the infrared and visible ranges and analyze the features of low-energy absorption by examining the characteristics of related orbitals.

Orientation dependence of the work function for metal nanocrystals.

Work function values measured at different surfaces of a metal are usually different. This raises an interesting question: What is the work function of a nano-size crystal, where differently oriented facets can be adjacent? Work functions of metallic nanocrystals are also of significant practical interest, especially in catalytic applications. Using real space pseudopotentials constructed within density functional theory, we compute the local work function of large aluminum and gold nanocrystals. We investigate how the local work function follows the change of the surface plane orientation around multifaceted nanocrystals, and we establish the importance of the orbital character near the Fermi level in determining work function differences between facets.

First-Principles Atomic Force Microscopy Image Simulations with Density Embedding Theory.

We present an efficient first-principles method for simulating noncontact atomic force microscopy (nc-AFM) images using a "frozen density" embedding theory. Frozen density embedding theory enables one to efficiently compute the tip-sample interaction by considering a sample as a frozen external field. This method reduces the extensive computational load of first-principles AFM simulations by avoiding consideration of the entire tip-sample system and focusing on the tip alone. We demonstrate that our simulation with frozen density embedding theory accurately reproduces full density functional theory simulations of freestanding hydrocarbon molecules while the computational time is significantly reduced. Our method also captures the electronic effect of a Cu(111) substrate on the AFM image of pentacene and reproduces the experimental AFM image of Cu2N on a Cu(100) surface. This approach is applicable for theoretical imaging applications on large molecules, two-dimensional materials, and materials surfaces.

Real-space pseudopotential study of vibrational properties and Raman spectra in Si-Ge core-shell nanocrystals.

We examine the vibrational properties and Raman spectra of Si-Ge core-shell nanostructures using real-space pseudopotentials constructed within density functional theory. Our method uses no empirical parameters, unlike many popular methods for predicting Raman spectra for nanocrystals. We find the dominant features of the Raman spectrum for the Si-Ge core-shell structure to be a superposition of the Raman spectra of the Ge and Si nanocrystals with optical peaks around 300 and 500 cm(-1), respectively. We also find a Si-Ge "interface" peak at 400 cm(-1). The Ge shell causes the Si core to expand from the equilibrium structure. This strain induces significant redshift in the Si contribution to the vibrational and Raman spectra, while the Ge shell is largely unstrained and does not exhibit this shift. We find that the ratio of peak heights is strongly related to the relative size of the core and shell regions. This finding suggests that Raman spectroscopy may be used to characterize the size of the core and shell in these structures.

Real-space pseudopotential method for computing the vibrational Stark effect.

The vibrational Stark shift is an important effect in determining the electrostatic environment for molecular or condensed matter systems. However, accurate ab initio calculations of the vibrational Stark effect are a technically demanding challenge. We make use of density functional theory constructed on a real-space grid to expedite the computation of this effect. Our format is especially advantageous for the investigation of small molecules in finite fields as cluster boundary conditions eliminate spurious supercell interactions and allow for charged systems, while convergence is controlled by a single parameter, the grid spacing. The Stark tuning rate is highly sensitive to the interaction between anharmonicity in a vibrational mode and the applied field. To ensure this subtle interaction is fully captured, we apply three parallel approaches: a direct finite field, a perturbative method, and a molecular dynamics method. We illustrate this method by applying it to several small molecules containing C-O and C-N bonds and show that a consistent result can be obtained.

High order forces and nonlocal operators in a Kohn-Sham Hamiltonian.

Real space pseudopotentials have a number of advantages in solving for the electronic structure of materials. These advantages include ease of implementation, implementation on highly parallel systems, and great flexibility for describing partially periodic systems. One limitation of this approach, shared by other electronic structure methods, is the slow convergence of interatomic forces when compared to total energies. For real space methods, this requires a fine grid to converge a solution of the Kohn-Sham problem, which is accompanied by concurrent increase in memory and additional matrix-vector multiplications. Here we introduce a method to expedite the computation of interatomic forces by employing a high order integration technique. We demonstrate the usefulness of this technique by calculating accurate bond lengths and vibrational frequencies for molecules and nanocrystals without using fine real space grids.

A first-principles study of the electronic and structural properties of Sb and F doped SnO2 nanocrystals.

We examine the electronic properties of Sb and F doped SnO2 nanocrystals up to 2.4 nm in diameter. A real-space pseudopotential implementation of density functional theory is employed within the local density approximation. We calculate electron binding energies and dopant formation energies as function of nanocrystal size, dopant concentration, and dopant species. Structural changes for different dopant species are also investigated. Our study should provide useful information for the design of transparent conducting oxides at the nanoscale.

Interaction range of P-dopants in Si[110] nanowires: determining the nondegenerate limit.

It is well known that the activation energy of dopants in semiconducting nanomaterials is higher than in bulk materials owing to dielectric mismatch and quantum confinement. This quenches the number of free charge carriers in nanomaterials. Though higher doping concentration can compensate for this effect, there is no clear criterion on what the doping concentration should be. Using P-doped Si[110] nanowires as the prototypical system, we address this issue by establishing a doping limit by first-principles electronic structure calculations. We examine how the doped nanowires respond to charging using an effective capacitance approach. As the nanowire gets thinner, the interaction range of the P dopants shortens and the doping concentration can increase concurrently. Hence, heavier doping can remain nondegenerate for thin nanowires.

Real space pseudopotential calculations for size trends in Ga- and Al-doped zinc oxide nanocrystals with wurtzite and zincblende structures.

Zinc oxide is often used as a popular inexpensive transparent conducting oxide. Here, we employ density functional theory and local density approximation to examine the effects of quantum confinement in doped nanocrystals of this material. Specifically, we examine the addition of Ga and Al dopants to ZnO nanocrystals on the order of 1.0 nm. We find that the inclusion of these dopants is energetically less favorable in smaller particles and that the electron binding energy, which is associated with the dopant activation, decreases with the nanocrystal size. We find that the introduction of impurities does not alter significantly the Kohn-Sham eigenspectrum for small nanocrystals of ZnO. The added electron occupies the lowest existing state, i.e., no new bound state is introduced in the gap. We verify this assertion with hybrid functional calculations.

Anisotropy and isotope effect in superconducting solid hydrogen.

Elucidating the phase diagram of solid hydrogen is a key objective in condensed matter physics. Several decades ago, it was proposed that at low temperatures and high pressures, solid hydrogen would be a metal with a high superconducting transition temperature. This transition to a metallic state can happen through the closing of the energy gap in the molecular solid or through a transition to an atomic solid. Recent experiments have managed to reach pressures in the range of 400-500 GPa, providing valuable insights. There is strong evidence suggesting that metallization via either of these mechanisms occurs within this pressure range. Computational and experimental studies have identified multiple promising crystal phases, but the limited accuracy of calculations and the limited capabilities of experiments prevent us from determining unequivocally the observed phase or phases. Therefore, it is crucial to investigate the superconducting properties of all the candidate phases. Recently, we reported the superconducting properties of theC2/c-24,Cmca-12,Cmca-4 andI41/amd-2 phases, including anharmonic effects. Here, we report the effects of anisotropy on superconducting properties using Eliashberg theory. Then, we investigate the superconducting properties of deuterium and estimate the size of the isotope effect for each phase. We find that the isotope effect on superconductivity is diminished by anharmonicity in theC2/c-24 andCmca-12 phases and enlarged in theCmca-4 andI41/amd-2 phases. Our anharmonic calculations of theC2/c-24 phase of deuterium agree closely with the most recent experiment by Loubeyreet al(2022Phys. Rev. Lett.29035501), indicating that theC2/c-24 phase remains the leading candidate in this pressure range, and has a strong anharmonic character. These characteristics can serve to distinguish among crystal phases in experiment. Furthermore, expanding our understanding of superconductivity in pure hydrogen holds significance in the study of high-Tchydrides.

Observation of electron orbital signatures of single atoms within metal-phthalocyanines using atomic force microscopy.

Resolving the electronic structure of a single atom within a molecule is of fundamental importance for understanding and predicting chemical and physical properties of functional molecules such as molecular catalysts. However, the observation of the orbital signature of an individual atom is challenging. We report here the direct identification of two adjacent transition-metal atoms, Fe and Co, within phthalocyanine molecules using high-resolution noncontact atomic force microscopy (HR-AFM). HR-AFM imaging reveals that the Co atom is brighter and presents four distinct lobes on the horizontal plane whereas the Fe atom displays a "square" morphology. Pico-force spectroscopy measurements show a larger repulsion force of about 5 pN on the tip exerted by Co in comparison to Fe. Our combined experimental and theoretical results demonstrate that both the distinguishable features in AFM images and the variation in the measured forces arise from Co's higher electron orbital occupation above the molecular plane. The ability to directly observe orbital signatures using HR-AFM should provide a promising approach to characterizing the electronic structure of an individual atom in a molecular species and to understand mechanisms of certain chemical reactions.