Theory of Defect-Induced Crystal Field Perturbations in Rare-Earth Magnets.

We present a theory describing the single-ion anisotropy of rare-earth (RE) magnets in the presence of point defects. Taking the RE-lean 1∶12 magnet class as a prototype, we use first-principles calculations to show how the introduction of Ti substitutions into SmFe_{12} perturbs the crystal field, generating new coefficients due to the lower symmetry of the RE environment. We then demonstrate that these perturbations can be described extremely efficiently using a screened point charge model. We provide analytical expressions for the anisotropy energy that can be straightforwardly implemented in atomistic spin dynamics simulations, meaning that such simulations can be carried out for an arbitrary arrangement of point defects. The significant crystal field perturbations calculated here demonstrate that a sample that is single phase from a structural point of view can nonetheless have a dramatically varying anisotropy profile at the atomistic level if there is compositional disorder, which may influence localized magnetic objects like domain walls or skyrmions.

Enhancing Conductivity of Silver Nanowire Networks through Surface Engineering Using Bidentate Rigid Ligands.

Solution processable metallic nanomaterials present a convenient way to fabricate conductive structures, which are necessary in all electronic devices. However, they tend to require post-treatments to remove the bulky ligands around them to achieve high conductivity. In this work, we present a method to formulate a post-treatment free conductive silver nanowire ink by controlling the type of ligands around the silver nanowires. We found that bidentate ligands with a rigid molecular structure were effective in improving the conductivity of the silver nanowire networks as they could maximize the number of linkages between neighboring nanowires. In addition, DFT calculations also revealed that ligands with good LUMO to silver energy alignment were more effective. Because of these reasons, fumaric acid was found to be the most effective ligand and achieved a large reduction in sheet resistance of 70% or higher depending on the nanowire network density. The concepts elucidated from this study would also be applicable to other solution processable nanomaterials systems such as quantum dots for photovoltaics or LEDs which also require good charge transport being neighboring nanoparticles.

First-Principles Band Alignments at the Si:Anatase TiO2 Interface.

TiO2 has been identified as a promising electron transport layer in Si solar cells. Experiments have revealed that the Si:TiO2 interface undergoes structural changes depending on how it was fabricated. However, less is understood about the sensitivity of electronic properties, such as band alignments, to these changes. Here, we present first-principles calculations of band alignments between Si and anatase TiO2, investigating different surface orientations and terminations. By calculating vacuum-level alignments, we observe a large band offset reduction of 2.5 eV for the O-terminated Si slab compared to other terminations. Furthermore, a 0.5 eV increase is found for the anatase (101) surface compared to (001). We compare the band offsets obtained through vacuum alignment with four different heterostructure models. Even though the heterostructure models contain an excess of oxygen, their offsets agree well with vacuum-level alignments using stoichiometric or H-terminated slabs, and the reduction in band offsets seen for the O-terminated Si slab is not observed. Additionally, we have investigated different exchange-correlation treatments including PBE + U, postprocessing GW corrections, and the meta-GGA rSCAN functional. We find that rSCAN provides more accurate band offsets than PBE, but further corrections are still required to achieve <0.5 eV accuracy. Overall, our study quantifies the importance of surface termination and orientation for this interface.

Picoperovskites: The Smallest Conceivable Isolated Halide Perovskite Structures Formed within Carbon Nanotubes.

Halide perovskite structures are revolutionizing the design of optoelectronic materials, including solar cells, light-emitting diodes, and photovoltaics when formed at the quantum scale. Four isolated sub-nanometer, or picoscale, halide perovskite structures formed inside ≈1.2-1.6 nm single-walled carbon nanotubes (SWCNTs) by melt insertion from CsPbBr3 and lead-free CsSnI3 are reported. Three directly relate to the ABX3 perovskite archetype while a fourth is a perovskite-like lamellar structure with alternating Cs4 and polyhedral Sn4 Ix layers. In ≈1.4 nm-diameter SWCNTs, CsPbBr3 forms Cs3 PbII Br5 nanowires, one ABX3 unit cell in cross section with the Pb2+ oxidation state maintained by ordered Cs+ vacancies. Within ≈1.2 nm-diameter SWCNTs, CsPbBr3 and CsSnI3 form inorganic-polymer-like bilayer structures, one-fourth of an ABX3 unit cell in cross section with systematically reproduced ABX3 stoichiometry. Producing these smallest halide perovskite structures at their absolute synthetic cross-sectional limit enables quantum confinement effects with first-principles calculations demonstrating bandgap widening compared to corresponding bulk structural forms.

Torque magnetometry study of the spin reorientation transition and temperature-dependent magnetocrystalline anisotropy in NdCo5.

We present the results of torque magnetometry and magnetic susceptibility measurements to study in detail the spin reorientation transition (SRT) and magnetic anisotropy in the permanent magnet NdCo5. We further show simulations of the measurements using first-principles calculations based on density-functional theory and the disordered local moment picture of magnetism at finite temperatures. The good agreement between theory and experimental data leads to a detailed description of the physics underpinning the SRT. In particular we are able to resolve the magnetization of, and to reveal a canting between, the Nd and Co sublattices. The torque measurements carried out in the ac and ab planes near the easy direction allow us to estimate the anisotropy constants, K 1, K 2 and K 4 and their temperature dependences. Torque curves, τ(γ) recorded by varying the direction of a constant magnetic field in the crystallographic ac plane show a reversal in the polarity as the temperature is changed across the SRT (240 < T < 285 K). Within this domain, τ(γ) exhibits unusual features different to those observed above and below the transition. The single crystals of NdCo5 were grown using the optical floating zone technique.

Crystal field coefficients for yttrium analogues of rare-earth/transition-metal magnets using density-functional theory in the projector-augmented wave formalism.

We present a method of calculating crystal field coefficients of rare-earth/transition-metal (RE-TM) magnets within density-functional theory (DFT). The principal idea of the method is to calculate the crystal field potential of the yttrium analogue ('Y-analogue') of the RE-TM magnet, i.e. the material where the lanthanide elements have been substituted with yttrium. The advantage of dealing with Y-analogues is that the methodological and conceptual difficulties associated with treating the highly-localized 4f  electrons in DFT are avoided, whilst the nominal valence electronic structure principally responsible for the crystal field is preserved. In order to correctly describe the crystal field potential in the core region of the atoms we use the projector-augmented wave formalism of DFT, which allows the reconstruction of the full charge density and electrostatic potential. The Y-analogue crystal field potentials are combined with radial 4f  charge densities obtained in self-interaction-corrected calculations on the lanthanides to obtain crystal field coefficients. We demonstrate our method on a test set of ten materials comprising nine RE-TM magnets and elemental Tb. We show that the calculated easy directions of magnetization agree with experimental observations, including a correct description of the anisotropy within the basal plane of Tb and NdCo5. We further show that the Y-analogue calculations generally agree quantitatively with previous calculations using the open-core approximation to treat the 4f  electrons, and argue that our simple approach may be useful for large-scale computational screening of new magnetic materials.

Field-induced canting of magnetic moments in GdCo5 at finite temperature: first-principles calculations and high-field measurements.

We present calculations and experimental measurements of the temperature-dependent magnetization of a single crystal of GdCo5 in magnetic fields of order 60 T. At zero temperature the calculations, based on density-functional theory in the disordered-local-moment picture, predict a field-induced transition from an antiferromagnetic to a canted alignment of Gd and Co moments at 46.1 T. At higher temperatures the calculations find this critical field to increase along with the zero-field magnetization. The experimental measurements observe this transition to occur between 44-48 T at 1.4 K. Up to temperatures of at least 100 K, the experiments continue to observe the transition; however, at variance with the calculations, no strong temperature dependence of the critical field is apparent. We assign this difference to the inaccurate description of the zero-field magnetization of the calculations at low temperatures, due to the use of classical statistical mechanics. Correcting for this effect, we recover a consistent description of the high-field magnetization of GdCo5 from theory and experiment.

Calculating the Magnetic Anisotropy of Rare-Earth-Transition-Metal Ferrimagnets.

Magnetocrystalline anisotropy, the microscopic origin of permanent magnetism, is often explained in terms of ferromagnets. However, the best performing permanent magnets based on rare earths and transition metals (RE-TM) are in fact ferrimagnets, consisting of a number of magnetic sublattices. Here we show how a naive calculation of the magnetocrystalline anisotropy of the classic RE-TM ferrimagnet GdCo_{5} gives numbers that are too large at 0 K and exhibit the wrong temperature dependence. We solve this problem by introducing a first-principles approach to calculate temperature-dependent magnetization versus field (FPMVB) curves, mirroring the experiments actually used to determine the anisotropy. We pair our calculations with measurements on a recently grown single crystal of GdCo_{5}, and find excellent agreement. The FPMVB approach demonstrates a new level of sophistication in the use of first-principles calculations to understand RE-TM magnets.

Stochastic Approach to Phonon-Assisted Optical Absorption.

We develop a first-principles theory of phonon-assisted optical absorption in semiconductors and insulators which incorporates the temperature dependence of the electronic structure. We show that the Hall-Bardeen-Blatt theory of indirect optical absorption and the Allen-Heine theory of temperature-dependent band structures can be derived from the present formalism by retaining only one-phonon processes. We demonstrate this method by calculating the optical absorption coefficient of silicon using an importance sampling Monte Carlo scheme, and we obtain temperature-dependent line shapes and band gaps in good agreement with experiment. The present approach opens the way to predictive calculations of the optical properties of solids at finite temperature.

Adiabatic-connection fluctuation-dissipation DFT for the structural properties of solids-The renormalized ALDA and electron gas kernels.

We present calculations of the correlation energies of crystalline solids and isolated systems within the adiabatic-connection fluctuation-dissipation formulation of density-functional theory. We perform a quantitative comparison of a set of model exchange-correlation kernels originally derived for the homogeneous electron gas (HEG), including the recently introduced renormalized adiabatic local-density approximation (rALDA) and also kernels which (a) satisfy known exact limits of the HEG, (b) carry a frequency dependence, or (c) display a 1/k(2) divergence for small wavevectors. After generalizing the kernels to inhomogeneous systems through a reciprocal-space averaging procedure, we calculate the lattice constants and bulk moduli of a test set of 10 solids consisting of tetrahedrally bonded semiconductors (C, Si, SiC), ionic compounds (MgO, LiCl, LiF), and metals (Al, Na, Cu, Pd). We also consider the atomization energy of the H2 molecule. We compare the results calculated with different kernels to those obtained from the random-phase approximation (RPA) and to experimental measurements. We demonstrate that the model kernels correct the RPA's tendency to overestimate the magnitude of the correlation energy whilst maintaining a high-accuracy description of structural properties.

TiO2 anatase with a bandgap in the visible region.

TiO2 anatase plays a central role in energy and environmental research. A major bottleneck toward developing artificial photosynthesis with TiO2 is that it only absorbs ultraviolet light, owing to its large bandgap of 3.2 eV. If one could reduce the bandgap of anatase to the visible region, TiO2-based photocatalysis could become a competitive clean energy source. Here, using scanning tunneling microscopy and spectroscopy in conjunction with density functional theory calculations, we report the discovery of a highly reactive titanium-terminated anatase surface with a reduced bandgap of less than 2 eV, stretching into the red portion of the solar spectrum. By tuning the surface preparation conditions, we can reversibly switch between the standard anatase surface and the newly discovered low bandgap surface phase. The identification of a TiO2 anatase surface phase with a bandgap in the visible and high chemical reactivity has important implications for solar energy conversion, photocatalysis, and artificial photosynthesis.

Unified theory of electron-phonon renormalization and phonon-assisted optical absorption.

We present a theory of electronic excitation energies and optical absorption spectra which incorporates energy-level renormalization and phonon-assisted optical absorption within a unified framework. Using time-independent perturbation theory we show how the standard approaches for studying vibronic effects in molecules and those for addressing electron-phonon interactions in solids correspond to slightly different choices for the non-interacting Hamiltonian. Our present approach naturally leads to the Allen-Heine theory of temperature-dependent energy levels, the Franck-Condon principle, the Herzberg-Teller effect and to phonon-assisted optical absorption in indirect band gap materials. In addition, our theory predicts sub-gap phonon-assisted optical absorption in direct gap materials, as well as an exponential edge which we tentatively assign to the Urbach tail. We also consider a semiclassical approach to the calculation of optical absorption spectra which simultaneously captures energy-level renormalization and phonon-assisted transitions and is especially suited to first-principles electronic structure calculations. We demonstrate this approach by calculating the phonon-assisted optical absorption spectrum of bulk silicon.

Atomic-scale observation of multiconformational binding and energy level alignment of ruthenium-based photosensitizers on TiO2 anatase.

Dye-sensitized solar cells constitute a promising approach to sustainable and low-cost solar energy conversion. Their overall efficiency crucially depends on the effective coupling of the photosensitizers to the photoelectrode and the details of the dye's energy levels at the interface. Despite great efforts, the specific binding of prototypical ruthenium-based dyes to TiO2, their potential supramolecular interaction, and the interrelation between adsorption geometry and electron injection efficiency lack experimental evidence. Here we demonstrate multiconformational adsorption and energy level alignment of single N3 dyes on TiO2 anatase (101) revealed by scanning tunnelling microscopy and spectroscopy. The distinctly bound molecules show significant variations of their excited state levels associated with different driving forces for photoelectron injection. These findings emphasize the critical role of the interfacial coupling and suggest that further designs of dye-sensitized solar cells should target a higher selectivity in the dye-substrate binding conformations in order to ensure efficient electron injection from all photosensitizers.

Quantum nuclear dynamics in the photophysics of diamondoids.

The unusual electronic properties of diamondoids, the nanoscale relatives of diamond, make them attractive for applications ranging from drug delivery to field emission displays. Identifying the fundamental origin of these properties has proven highly challenging, with even the most advanced quantum many-body calculations unable to reproduce measurements of a quantity as ubiquitous as the optical gap. Here, by combining first-principles calculations and Importance Sampling Monte Carlo methods, we show that the quantum dynamics of carbon nuclei is key to understanding the electronic and optical properties of diamondoids. Quantum nuclear effects dramatically modify the absorption lineshapes and renormalize the optical gaps. These findings allow us to formulate a complete theory of optical absorption in diamondoids, and establish the universal role of quantum nuclear dynamics in nanodiamond across the length scales.

Quantitative analysis of valence photoemission spectra and quasiparticle excitations at chromophore-semiconductor interfaces.

Investigating quasiparticle excitations of molecules on surfaces through photoemission spectroscopy forms a major part of nanotechnology research. Resolving spectral features at these interfaces requires a comprehensive theory of electron removal and addition processes in molecules and solids which captures the complex interplay of image charges, thermal effects, and configurational disorder. Here, we develop such a theory and calculate the quasiparticle energy-level alignment and the valence photoemission spectrum for the prototype biomimetic solar cell interface between anatase TiO(2) and the N3 chromophore. By directly matching our calculated photoemission spectrum to experimental data, we clarify the atomistic origin of the chromophore peak at low binding energy. This case study sets a new standard in the interpretation of photoemission spectroscopy at complex chromophore-semiconductor interfaces.

GW quasiparticle bandgaps of anatase TiO2 starting from DFT + U.

We investigate the quasiparticle band structure of anatase TiO(2), a wide gap semiconductor widely employed in photovoltaics and photocatalysis. We obtain GW quasiparticle energies starting from density-functional theory (DFT) calculations including Hubbard U corrections. Using a simple iterative procedure we determine the value of the Hubbard parameter yielding a vanishing quasiparticle correction to the fundamental bandgap of anatase TiO(2). The bandgap (3.3 eV) calculated using this optimal Hubbard parameter is smaller than the value obtained by applying many-body perturbation theory to standard DFT eigenstates and eigenvalues (3.7 eV). We extend our analysis to the rutile polymorph of TiO(2) and reach similar conclusions. Our work highlights the role of the starting non-interacting Hamiltonian in the calculation of GW quasiparticle energies in TiO(2) and suggests an optimal Hubbard parameter for future calculations.