Density functional perturbation theory within non-collinear magnetism

We extend the density functional perturbation theory formalism to the case of non-collinear magnetism. The main problem comes with the exchange-correlation (XC) potential derivatives, which are the only ones that are affected by the non-collinearity of the system. Most of the present XC functionals are constructed at the collinear level, such that the off-diagonal (containing magnetization densities along $x$ and $y$ directions) derivatives cannot be calculated simply in the non-collinear framework. To solve this problem, we consider here possibilities to transform the non-collinear XC derivatives to a local collinear basis, where the $z$ axis is aligned with the local magnetization at each point. The two methods we explore are i) expanding the spin rotation matrix as a Taylor series, ii) evaluating explicitly the XC for the local density approximation through an analytical expression of the expansion terms. We compare the two methods and describe their practical implementation. We show their application for atomic displacement and electric field perturbations at the second order, within the norm-conserving pseudopotential methods

Vibrational and dielectric properties of monolayer transition metal dichalcogenides

First-principles studies of two-dimensional transition metal dichalcogenides have contributed considerably to the understanding of their dielectric, optical, elastic, and vibrational properties. The majority of works to date focus on a single material or physical property. Here we use a single first-principles methodology on the whole family of systems, to investigate in depth the relationships between different physical properties, the underlying symmetry and the composition of these materials, and observe trends. We compare to bulk counterparts to show strong interlayer effects in triclinic compounds. Previously unobserved relationships between these monolayer compounds become apparent. These trends can then be exploited by the materials science, nanoscience, and chemistry communities to better design devices and heterostructures for specific functionalities.Comment: 4 figures, 11 page

Vibrational and dielectric properties of the bulk transition metal dichalcogenides

Interest in the bulk transition metal dichalcogenides for their electronic, photovoltaic, and optical properties has grown and led to their use in many technological applications. We present a systematic investigation of their interlinked vibrational and dielectric properties, using density functional theory and density functional perturbation theory, studying the effects of the spin-orbit interaction and of the long-range e$^-$- e$^-$ correlation as part of our investigation. This study confirms that the spin-orbit interaction plays a small role in these physical properties, while the direct contribution of dispersion corrections is of crucial importance in the description of the interatomic force constants. Here, our analysis of the structural and vibrational properties, including the Raman spectra, compare well to experimental measurement. Three materials with different point groups are showcased and data trends on the full set of fifteen existing hexagonal, trigonal, and triclinic materials are demonstrated. This overall picture will enable the modeling of devices composed of these materials for novel applications.Comment: 11 pages, 6 figure

Unravelling the role of Sm 4f electrons in the magnetism of SmFeO3_3

Magnetic rare-earth orthoferrites $R$FeO$_3$ host a variety of functional properties from multiferroicity and strong magnetostriction, to spin-reorientation transitions and ultrafast light-driven manipulation of magnetism, which can be exploited in spintronics and next-generation devices. Among these systems, SmFeO$_3$ is attracting a particular interest for its rich phase diagram and the high temperature Fe-spin magnetic transitions, which combines with a very low temperature and as yet unclear Sm-spin ordering. Various experiments suggest that the interaction between the Sm and Fe magnetic moments (further supported by the magnetic anisotropy), is at the origin of the complex cascade of transitions, but a conclusive and clear picture has not yet been reached. In this work, by means of comprehensive first-principles calculations, we unravel the role of the magnetic Sm ions in the Fe-spin reorientation transition and in the detected anomalies in the lattice vibrational spectrum, which are a signature of a relevant spin-phonon coupling. By including both Sm-$f$ electrons and non-collinear magnetism, we find frustrated and anisotropic Sm interactions, and a large magnetocrystalline anisotropy mediated by the SOC of the Sm-$4f$ electrons, which drive the complex magnetic properties and phase diagram of SmFeO$_3$

Mode-coupling theory of lattice dynamics for classical and quantum crystals

The dynamical properties of nuclei, carried by the concept of phonon quasiparticles (QP), are central to the field of condensed matter. While the harmonic approximation can reproduce a number of properties observed in real crystals, the inclusion of anharmonicity in lattice dynamics is essential to accurately predict properties such as heat transport or thermal expansion. For highly anharmonic systems, non perturbative approaches are needed, which result in renormalized theories of lattice dynamics. In this article, we apply the Mori-Zwanzig projector formalism to derive an exact generalized Langevin equation describing the quantum dynamics of nuclei in a crystal. By projecting this equation on quasiparticles in reciprocal space, and with results from linear response theory, we obtain a formulation of vibrational spectra that fully accounts for the anharmonicity. Using a mode-coupling approach, we construct a systematic perturbative expansion in which each new order is built to minimize the following ones. With a truncation to the lowest order, we show how to obtain a set of self-consistent equations that can describe the lineshapes of quasiparticles. The only inputs needed for the resulting set of equations are the static Kubo correlation functions, which can be computed using (fully quantum) path-integral molecular dynamics or approximated with (classical or ab initio) molecular dynamics. We illustrate the theory with an application on fcc 4He, an archetypal quantum crystal with very strong anharmonicity

Low energy phases of bilayer Bi predicted by structure search in two dimensions

We employ an ab-initio structure search algorithm to explore the configurational space of Bi in quasi two dimensions. A confinement potential restricts the movement of atoms within a pre-defined thickness during structure search calculations within the minima hopping method to find the stable and metastable forms of bilayer Bi. In addition to recovering the two known low-energy structures (puckered monoclinic and buckled hexagonal), our calculations predict three new structures of bilayer Bi. We call these structures the $\alpha$, $\beta$, and $\gamma$ phases of bilayer Bi, which are, respectively, 63, 72, and 83 meV/atom higher in energy than that of the monoclinic ground state, and thus potentially synthesizable using appropriate substrates. We also compare the structural, electronic, and vibrational properties of the different phases. The puckered monoclinic, buckled hexagonal, and $\beta$ phases exhibit a semiconducting energy gap, whereas $\alpha$ and $\gamma$ phases are metallic. We notice an unusual Mexican-hat type band dispersion leading to a van Hove singularity in the buckled hexagonal bilayer Bi. Notably, we find symmetry-protected topological Dirac points in the electronic spectrum of the $\gamma$ phase. The new structures suggest that bilayer Bi provides a novel playground to study distortion-mediated metal-insulator phase transitions

Electron-Beam Manipulation of Silicon Dopants in Graphene

The direct manipulation of individual atoms in materials using scanning probe microscopy has been a seminal achievement of nanotechnology. Recent advances in imaging resolution and sample stability have made scanning transmission electron microscopy a promising alternative for single-atom manipulation of covalently bound materials. Pioneering experiments using an atomically focused electron beam have demonstrated the directed movement of silicon atoms over a handful of sites within the graphene lattice. Here, we achieve a much greater degree of control, allowing us to precisely move silicon impurities along an extended path, circulating a single hexagon, or back and forth between the two graphene sublattices. Even with manual operation, our manipulation rate is already comparable to the state-of-the-art in any atomically precise technique. We further explore the influence of electron energy on the manipulation rate, supported by improved theoretical modeling taking into account the vibrations of atoms near the impurities, and implement feedback to detect manipulation events in real time. In addition to atomic-level engineering of its structure and properties, graphene also provides an excellent platform for refining the accuracy of quantitative models and for the development of automated manipulation.Comment: 5 figures, 4 supporting figure

Non-monotonic anisotropy in charge conduction induced by antiferrodistortive transition in metallic SrTiO3_{3}

Cubic SrTiO$_{3}$ becomes tetragonal below 105 K. The antiferrodistortive (AFD) distortion leads to clockwise and counter-clockwise rotation of adjacent TiO$_{6}$ octahedra. This insulator becomes a metal upon the introduction of extremely low concentration of n-type dopants. However, signatures of the structural phase transition in charge conduction have remained elusive. Employing the Montgomery technique, we succeed in resolving the anisotropy of charge conductivity induced by the AFD transition, in the presence of different types of dopants. We find that the slight lattice distortion ($<6 \times 10^{-4}$) gives rise to a twenty percent anisotropy in charge conductivity, in agreement with the expectations of band calculations. Application of uniaxial strain amplifies the detectable anisotropy by disfavoring one of the three possible tetragonal domains. In contrast with all other known anisotropic Fermi liquids, the anisotropy has opposite signs for elastic and inelastic scattering. Increasing the concentration of dopants leads to a drastic shift in the temperature of the AFD transition either upward or downward. The latter result puts strong constraints on any hypothetical role played by the AFD soft mode in the formation of Cooper pairs and the emergence of superconductivity in SrTiO$_3$.Comment: 6 pages with 5 figure