Exploiting machine learning in multiscale modelling of materials

Recent developments in efficient machine learning algorithms have spurred significant interest in the materials community. The inherently complex and multiscale problems in Materials Science and Engineering pose a formidable challenge. The present scenario of machine learning research in Materials Science has a clear lacunae, where efficient algorithms are being developed as a separate endeavour, while such methods are being applied as ‘black-box’ models by others. The present article aims to discuss pertinent issues related to the development and application of machine learning algorithms for various aspects of multiscale materials modelling. The authors present an overview of machine learning of equivariant properties, machine learning-aided statistical mechanics, the incorporation of ab initio approaches in multiscale models of materials processing and application of machine learning in uncertainty quantification. In addition to the above, the applicability of Bayesian approach for multiscale modelling will be discussed. Critical issues related to the multiscale materials modelling are also discussed

Atomistic Simulation of Surface Effects on Magnetic Properties of Alloy Nanomaterials

In the magnetic recording industry, L10 ordered CoPt and FePt nanoparticles have been considered as promising material candidates to advance the recording density beyond 1Tbit/in2. Compared with their bulk form, these alloy nanoparticles exhibit inferior magnetic properties. Surface effects, which are much more pronounced in nanometer scale, have been suggested to contribute to the deteriorated properties. In this work, surface related phenomena in these alloys are explored using atomistic simulation method. Density Functional Theory (DFT) calculations on the surface segregation effect have been performed in cuboidal, cuboctahedral nanoparticles and the related low index surfaces of L10 ordered CoPt alloy. Pt surface segregation to the outermost surface is found thermodynamically favorable in both nanoparticles and crystallographic surfaces. This segregation causes directly the break in structural, chemical ordering and accordingly the reduction in magnetic moment and change in magnetic anisotropy. Under 2nd order perturbation theory, the magnetic anisotropy energy on surface slabs has been associated with the change in d_(z^2 ) state density of surface Co atoms in the minority spin channel. Moreover, the magnetic properties of CoPt and FePt nanoparticles are demonstrated to be affected by particle shape using DFT calculations. This shape dependent magnetism is found correlated with the contraction in atomic spacing and local chemical composition. In addition, the surface spin canting mechanisms are identified for CoPt and FePt cuboctahedral nanoparticles. The different spin canting fashions for these two materials have been reproduced by micromagnetic simulation using Néel’s surface anisotropy model. The relationship between magnetoelastic coupling and Néel’s anisotropy constant in tetragonal lattice has been established. Through the calculation of Néel’s anisotropy constant from first principles, the different spin canting mechanisms have been explained. Finally, the effect of doping Cu, Ag and Au atoms on CoPt and FePt surfaces has been investigated. The Pt surface segregation has been found suppressed by the impurity atoms and the magnetic moment of surface Co/Fe atoms is restored up to the value of corresponding bulk-terminated surface. These additive atoms are proved to be beneficial for the improvement of magnetic properties on CoPt (001) surface and FePt (100) surface

Growth and magnetism of 2D bimetallic nanostructures

This thesis addresses the growth and magnetic characterization of 2D bimetallic nanostructures deposited by atomic beam epitaxy (ABE) on Pt(111). These structures possess both tunable high perpendicular magnetic anisotropy (PMA) and magnetic moment. These properties make them appealing as model systems in order to learn how to control the properties of the futures media used in magnetic data storage. Our study combined two in situ measurements techniques : variable-temperature scanning tunneling microscopy (VT-STM) as a local probe allows insight on the morphology of nanostructures, while magneto-optic Kerr effect (MOKE) is a spatially integrating technique giving access to the variation of the overall magnetization of a sample. The first part of this work focuses on the growth of iron on the Pt(111) surface. Growth was investigated on the atomic scale as a function of the substrate temperature in the case of low coverages. We have fitted the mean cluster size as a function of the annealing temperature with mean field rate equations for diffusion-controlled growth. The activation parameters for monomer, dimer and trimer diffusion could be inferred from this procedure. The formation of monatomic Fe wires has also been evidenced on the temperature range 160 K–260 K. The origin of their formation was discussed. In a second part, we have made use of our knowledge on the growth of cobalt and iron on Pt(111) in order to fabricate "core-shell" Co nanostructures of which density, size and shape were controlled. Therefore, we could realized both compact and ramified structures within the size range 800–1800 atoms. The study of the mechanism of magnetization reversal of these model structures has revealed a strong size and shape dependence. This is due to the shape-induced non-uniformity of the local magnetization and the number of pinning centers. The conclusions are that ramified structures with arms longer than 150 Å reverse their magnetization by nucleation and domain-wall motion while compact structures reverse coherently their magnetization. The third part deals with the magnetic properties of one monolayer thick bimetallic "Co core-shell" nanostructures on Pt(111). The blocking temperature TB marks the transition between superparamagnetic and blocked states and is inferred from the magnetic anisotropy. Here, we performed magnetic zero-field susceptibility measurements so as to determine TB in our samples. From our experiments, we show the possibility to make up a fine tuning of the nanostructure magnetic anisotropy and overall magnetization. In the case of the FexCo1-x alloy, TB adopt a bell-shape with x and exhibit a maximum at x = 0:5. The various lateral and vertical interfaces between Co from one side and Fe, Pt or Pd from the other side are at the origin of substantial TB variation. Those variations are inferred from the symmetry breaking and the strong hybridization between the d orbitals of these elements

Simulation and Modeling of Nanomaterials

This Special Issue focuses on computational detailed studies (simulation, modeling, and calculations) of the structures, main properties, and peculiarities of the various nanomaterials (nanocrystals, nanoparticles, nanolayers, nanofibers, nanotubes, etc.) based on various elements, including organic and biological components, such as amino acids and peptides. For many practical applications in nanoelectronics., such materials as ferroelectrics and ferromagnetics, having switching parameters (polarization, magnetization), are highly requested, and simulation of dynamics and kinetics of their switching are a very important task. An important task for these studies is computer modeling and computational research of the properties on the various composites of the other nanostructures with polymeric ferroelectrics and with different graphene-like 2-dimensional structures. A wide range of contemporary computational methods and software are used in all these studies

Multireference approaches for excited states of molecules

Understanding the properties of electronically excited states is a challenging task that becomes increasingly important for numerous applications in chemistry, molecular physics, molecular biology, and materials science. A substantial impact is exerted by the fascinating progress in time-resolved spectroscopy, which leads to a strongly growing demand for theoretical methods to describe the characteristic features of excited states accurately. Whereas for electronic ground state problems of stable molecules the quantum chemical methodology is now so well developed that informed nonexperts can use it efficiently, the situation is entirely different concerning the investigation of excited states. This review is devoted to a specific class of approaches, usually denoted as multireference (MR) methods, the generality of which is needed for solving many spectroscopic or photodynamical problems. However, the understanding and proper application of these MR methods is often found to be difficult due to their complexity and their computational cost. The purpose of this review is to provide an overview of the most important facts about the different theoretical approaches available and to present by means of a collection of characteristic examples useful information, which can guide the reader in performing their own applications

Spin Dynamics Simulations of Iridium Manganese Alloys

Until the late 1980's, anti-ferromagnets were thought of as theoretically interesting but with no practical application. Since then, this idea has been completely altered, and they are a key element in nearly all magnetic recording devices such as read heads in magnetic hard drives. More recently, the development of antiferromagnetic spintronics has enabled the use of the anti-ferromagnet as the active element and could lead to storage devices with THz speeds, much higher storage densities and a lower power consumption. A current problem in the development of such devices is a lack of understanding of the magnetic properties of antiferromagnets. Atomistic modelling is a powerful tool in understanding these properties as it has the ability to model the materials in atomistic detail on a scale comparable to realistic device sizes. In this thesis, I present an atomistic model of the Iridium Manganese (IrMn) that was created to model the static and dynamic magnetic properties of this complex material. The ground state magnetic structure and thermal stability are calculated including composition effects, disorder effects and finite-size effects. The magnitude and symmetry of the anisotropy in IrMn is calculated, solving a long standing debate between theory and experiment, where the calculations differ orders of magnitude. Finally, an IrMn layer is coupled to a ferromagnet to study the origin of the exchange bias effect, with realistic device sizes, including multiple grains, temperature and interface disorder. The results presented in this thesis determine the properties of IrMn in extraordinary detail, paving the way for a full understanding of this complex and interesting material and its interaction with natural magnets. The work in this thesis has been published in four peer reviewed papers in world leading journals

Coupling of crystal, electronic, and magnetic structures in quantum materials

The focus of this thesis is to understand a variety of emergent materials properties that are driven by quantum phenomena. A range of materials are investigated where the crystal, electronic and magnetic structures are delicately coupled to give rise to intriguing macroscopic properties. Computational methods are the primary tool for tackling these problems. This is largely centred around quantum mechanical, ab initio calculations using density functional theory (DFT), but also includes mean-field analyses and stochastic simulations of a model Hamiltonian. Tin telluride, SnTe, is a crystalline topological insulator with potential applications in a new generation of spintronics devices. In practice, SnTe shows a low temperature ferroelectric distortion and contains a large number of bulk carriers from Sn vacancies, so stands as a rare example of coexistence between metallicity and ferroelectricity. The implications of these effects for topological and transport properties require accurate modelling of the electronic structure. Here, in close collaboration with experiment, the evolution of the Fermi surface across this structural transition is probed by calculating quantum oscillation frequencies. The image analysis tools of Mathematica were exploited to develop a code for computing these frequencies from DFT electronic structure calculations. Agreement between experiment and theory is crucially dependent on the crystal structure. Calcium ruthenate, Ca2RuO4, is a layered perovskite compound with a rich phase diagram, which can be traced back to its strongly correlated electronic structure. Hydrostatic pressure can be used as a means to manipulate its crystal structure, which encourages several interesting effects. In particular, Ca2RuO4 undergoes anomalous expansion of the c axis, and a first-order structural transition coupled with a Mott insulator-metal transition. Here, this pressure response is investigated with DFT+U calculations, which account for the importance of electron correlation by adding an on-site Hubbard-like repulsion term. This work presents the first fully self-consistent electronic structure for Ca2RuO4, obtained from optimised crystal structures along a sequence of pressures. This appreciation of the coupling between lattice and electronic degrees of freedom sheds some light on its unusual phase diagram. The insulator-metal transition is reproduced and naturally coincides with a structural transition and associated orbital order. For the metallic phase, a complex energetic landscape with several competing phases emerges. Uranium gold, UAu2, is a heavy fermion metal with a complex spin-density-wave (SDW) phase at low temperature. This phase consists of frustrated, incommensurate ordering that is very robust in external fields, but suppressed by pressure to reveal unconventional superconductivity. The origin of this exotic magnetic ordering is of interest here, which is explored by several different approaches with DFT+U. Both itinerant and local-moment pictures of the magnetism are entertained. Fermi surface nesting is shown to be ineffective, but mapping the system to a Heisenberg model and computing effective exchange interactions identifies an instability towards modulated order. In addition to these material-specific investigations, the treatment of longitudinal magnetic fluctuations in computational methods is studied. Magnetic fluctuations are important for understanding materials on the border between itinerant and local-moment magnetism. The continuous-spin Ising (CSI) model is investigated here as a phenomenological model of these fluctuations. Using a bespoke simulation technique this model is extensively explored, firstly on a cubic ferromagnet and secondly on a highly frustrated, stacked triangular lattice with a variety of interaction topologies. The introduction of fluctuations is shown to alter the ground state of the prototypical frustrated triangular lattice, and to enhance the transition temperature of more severely frustrated systems. In all of these cases, different degrees of freedom in the system couple to one another, either to make an accurate theoretical description difficult, or to give rise to unexpected emergent properties. Both SnTe and Ca2RuO4 represent examples of delicately coupled crystal and electronic structures. In SnTe, the tuning of the crystal structure is vital to correctly describe the Fermi surface, while in Ca2RuO4 the Ru orbital structure very directly determines the structural properties, and drives the unusual pressure response. UAu2 introduces a non-trivial magnetic structure, which requires careful treatment of electron-electron interactions to locate. In the study of the CSI model, altering the interaction topology, which acts as a proxy for manipulating the underlying electronic structure, has drastic implications for the role of magnetic fluctuations in the system