Higher dimensional Wannier functions of multi-parameter Hamiltonians

Abstract

When using Wannier functions to study the electronic structure of multi-parameter Hamiltonians $H^{(\mathbf{k},\lambda )}$ carrying a dependence on crystal momentum $\mathbf{k}$ and an additional periodic parameter $\lambda$, one usually constructs several sets of Wannier functions for a set of values of $\lambda$. We present the concept of higher dimensional Wannier functions (HDWFs), which provide a minimal and accurate description of the electronic structure of multi-parameter Hamiltonians based on a single set of HDWFs. The obstacle of non-orthogonality of Bloch functions at different $\lambda$ is overcome by introducing an auxiliary real space, which is reciprocal to the parameter $\lambda$. We derive a generalized interpolation scheme and emphasize the essential conceptual and computational simplifications in using the formalism, for instance, in the evaluation of linear response coefficients. We further implement the necessary machinery to construct HDWFs from ab initio within the full-potential linearized augmented plane-wave method (FLAPW). We apply our implementation to accurately interpolate the Hamiltonian of a one-dimensional magnetic chain of Mn atoms in two important cases of $\lambda$: (i) the spin-spiral vector $\mathbf{q}$, and (ii) the direction of the ferromagnetic magnetization $\hat{\mathbf{m}}$. Using the generalized interpolation of the energy, we extract the corresponding values of magneto-crystalline anisotropy energy, Heisenberg exchange constants, and spin stiffness, which compare very well with the values obtained from direct first principles calculations. For toy models we demonstrate that the method of HDWFs can also be used in applications such as the virtual crystal approximation, ferroelectric polarization and spin torques.

arXiv comment23 pages, 11 figures

References in corpus (29)

• Maximally-localized generalized Wannier functions for composite energy bands
• Wannier90: A Tool for Obtaining Maximally-Localised Wannier Functions
• Maximally localized Wannier functions: Theory and applications
• Maximally-localized Wannier functions for entangled energy bands
• Symmetry and magnitude of spin-orbit torques in ferromagnetic heterostructures
• First Principles Calculation of Anomalous Hall Conductivity in Ferromagnetic bcc Fe
• The virtual crystal approximation revisited: Application to dielectric and piezoelectric properties of perovskites
• Ab initio calculation of the anomalous Hall conductivity by Wannier interpolation
• Evidence for reversible control of magnetization in a ferromagnetic material via spin-orbit magnetic field
• Spectral and Fermi surface properties from Wannier interpolation
• Maximally-localized Wannier functions for disordered systems: application to amorphous silicon
• Full orbital calculation scheme for materials with strongly correlated electrons
• Spin-orbit torques in Co/Pt(111) and Mn/W(001) magnetic bilayers from first principles
• Dynamical mean-field theory using Wannier functions: a flexible route to electronic structure calculations of strongly correlated materials
• Band Structure and Quantum Conductance of Nanostructures from Maximally-Localized Wannier Functions: The Case of Functionalized Carbon Nanotubes
• Exponential decay properties of Wannier functions and related quantities
• Maximally Localized Wannier Functions within the FLAPW formalism
• Berry phase theory of Dzyaloshinskii-Moriya interaction and spin-orbit torques
• Systematic {\it ab initio} study of the magnetic and electronic properties of all 3d transition metal linear and zigzag nanowires
• LDA+DMFT computation of the electronic spectrum of NiO
• Phase-Space Berry Phases in Chiral Magnets: Dzyaloshinskii-Moriya Interaction and the Charge of Skyrmions
• Orientation Dependence of the Intrinsic Anomalous Hall Effect in hcp Cobalt
• Exchange interactions and local moment fluctuation corrections in ferromagnets at finite temperatures based on non-collinear density-functional calculations
• Maximally-localized Wannier Functions in Antiferromagnetic MnO within the FLAPW Formalism
• Prediction of high zT in thermoelectric silicon nanowires with axial germanium heterostructures
• How disorder affects the Berry-phase anomalous Hall conductivity: the view from k space
• Non-collinear magnetism in freestanding and supported monatomic Mn chains
• First-principles study on the origin of large thermopower in hole-doped LaRhO3 and CuRhO2
• Conductance fingerprints of non-collinear magnetic states in single atom contacts: a first-principles Wannier functions study

Cited by in corpus (8)

• Crystal Hall and crystal magneto-optical effect in thin films of SrRuO${}_3$
• Mixed topological semimetals driven by orbital complexity in two-dimensional ferromagnets
• Electric-field control of spin-orbit torques in perpendicularly magnetized W/CoFeB/MgO films
• Mixed Weyl semimetals and dissipationless magnetization control in insulators by spin-orbit torques
• Ab initio analysis of magnetic properties of prototype B20 chiral magnet FeGe
• Higher-dimensional Wannier interpolation for the modern theory of the Dzyaloshinskii-Moriya interaction: Application to Co-based trilayers
• Engineering the dynamics of topological spin textures by anisotropic spin-orbit torques
• Tailoring the anomalous Hall effect of SrRuO${}_3$ thin films by strain: a first principles study