UC Santa Barbara

Density functional theory (DFT) is undergoing a shift from a descriptive to a predictive tool in the field of solid state physics, with undertakings like the Materials Project, OQMD, and AFLOW leading the way in utilizing high-throughput data to predict and seek novel materials properties. However, methods to rigorously evaluate the \textit{validity} and \textit{accuracy} of these studies is lacking in both the availability and utilization of techniques. The natural disconnect between simulated and experimental length-scales and temperatures, combined with this lack of validation, raises serious questions when simulation and experiment disagree. In this thesis, we analyze several transition metal systems where simulations and experiments present unusual disagreements, and develop a new formalism for comparing high-temperature measurements to \textit{ab-initio} calculations. Our work aims to broaden the understanding not only of the specific systems discussed, but of how presently available \textit{ab-initio} methods perform for transition metal alloys across \textit{all} systems.

Recent high-throughput ab-initio studies of transition metal binaries have suggested a great number of undiscovered stable phases present in well-studied systems. Co-Pt alloys, especially, have a long experimental history demonstrating three stable mixed phases: L1$_0$ CoPt and L1$_2$ Co$_3$Pt and CoPt$_3$, but density functional theory suggests a set of yet-unobserved long-period $\beta_2$-like superstructures at Pt-rich compositions. We analyze the Co-Pt system in-depth, calculating the energy of over 1,400 structures to thoroughly explore the series of unusual superstructures suggested by DFT\@. Simulated diffraction patterns, analysis of magnetic behavior, and investigation of the density-of-states emphasize the stark differences between measured behaviors and \textit{ab-initio} predictions. By moving up the Jacob's Ladder of functionals, we show that we only replace one set of discrepancies for another, and even the introduction of vibrational degrees of freedom fails to solve the massive differences in predicted phase stability. By fitting the \textit{ab-initio} results to a cluster expansion Hamiltonian and performing Monte Carlo calculations, we show that the resulting high-temperature phase diagram is wholly incompatible with experimental results.

Like Co-Pt, Heusler compounds have unique magnetic properties, resulting in interest for their potential applications as spintronic materials. The pseudo-binary (Mn,Fe)Ru$_2$Sn, formed as a solid solution of the full Heuslers (Mn, Fe)Ru$_2$Sn, has been recently shown to exhibit exchange-hardening implicative of two \textit{magnetic} phases, despite the presence of only one \textit{chemical} phase. Using \textit{ab-initio} calculations we show that the magnetic behavior of this alloy arises from a competition between AFM-favoring Sn-mediated superexchange and FM-favoring RKKY exchange mediated by spin-polarized conduction electrons. Changes in valency upon replacement of Mn with Fe shifts the balance from superexchange-dominated interactions to RKKY-dominated interactions. Using our electronic structure calculations, we parameterize a mixed-basis chemical-and-magnetic cluster expansion, and use Monte Carlo simulations to demonstrate a ferromagnetic (FM) to antiferromagnetic (AFM) behavior dependent on composition with the experimental study. By examining the low-temperature ensemble averages of magnetic and chemical correlations, we identify the mechanism behind magnetic hardening in the solid solution.

Our multiple successes in utilizing cluster expansions, both to deeply analyze failures and successfully describe complex chemical-magnetic interactions, motivates an experiments-driven approach to lattice Hamiltonians. For alloys, cluster expansion Hamiltonians reduce the complex, many-body electron problem of density functional theory to a series of simple site-wise basis functions (e.g., products of site occupancy variables) on an atomic scale. The resulting energy polynomial is computationally inexpensive, and hence suitable for the (tens of) thousands of calculations of large systems required by stochastic methods. We present a new method to run the statistical mechanics problem ``in reverse'', using high-temperature observations and thermodynamic connections to construct an effective Hamiltonian and thereby predict the 0 Kelvin energy spectrum and associated ground states. By re-examining the cluster expansion coefficients as thermodynamic state variables and utilizing entropy-maximization approaches, we develop an algorithm to select clusters and determine cluster interactions using only a few, high-temperature experiments on disordered phases. We demonstrate that our approach can recover not only the stable ground states at 0 Kelvin, but also the full phase behavior for three realistic two-dimensional and three-dimensional alloy test-cases.