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Ivo Souza

Publications and source records attributed to Ivo Souza.

At least 55 records · Page 3Linked to original sources
arXiv2014

How disorder affects the Berry-phase anomalous Hall conductivity: the view from k space

The anomalous Hall conductivity of "dirty" ferromagnetic metals is dominated by a Berry-phase contribution which is usually interpreted as an intrinsic property of the Bloch electrons in the pristine crystal. In this work we evaluate the geometric Hall current directly from the electronic ground state with disorder, and then recast it as an integral over the crystalline Brillouin zone. The integrand is a generalized k-space Berry curvature, obtained by unfolding the Berry curvature from the small Brillouin zone of a large supercell. Therein, disorder yields a net extrinsic Hall contribution, which we argue is related to the elusive side-jump effect. As an example, we unfold the first-principles Berry curvature of an Fe3Co ordered alloy from the original fcc-lattice Brillouin zone onto a bcc-lattice zone with four times the volume. Comparison with the virtual-crystal Berry curvature clearly reveals the symmetry-breaking effects of the substitutional Co atoms.

cond-mat.mtrl-sci↗
arXiv2013

Natural optical activity and its control by electric field in electrotoroidic systems

We propose the existence, via analytical derivations, novel phenomenologies, and first-principles-based simulations, of a new class of materials that are not only spontaneously optically active, but also for which the sense of rotation can be switched by an electric field applied to them-- via an induced transition between the dextrorotatory and laevorotatory forms. Such systems possess electric vortices that are coupled to a spontaneous electrical polarization. Furthermore, our atomistic simulations provide a deep microscopic insight into, and understanding of, this class of naturally optically active materials.

cond-mat.mtrl-sci↗
arXiv2012

Full magnetoelectric response of Cr2O3 from first principles

The linear magnetoelectric response of Cr2O3 at zero temperature is calculated from first principles by tracking the change in magnetization under a macroscopic electric field. Both the spin and the orbital contributions to the induced magnetization are computed, and in each case the response is decomposed into lattice and electronic parts. We find that the transverse response is dominated by the spin-lattice and spin-electronic contributions, whose calculated values are consistent with static and optical magnetoelectric measurements. In the case of the longitudinal response, orbital contributions dominate over spin contributions, but the net calculated longitudinal response remains much smaller than the experimentally measured one at low temperatures. We also discuss the absolute sign of the magnetoelectric coupling in the two time-reversed magnetic domains of Cr2O3.

cond-mat.mtrl-sci↗
arXiv2012

Anisotropy of spin relaxation and transverse transport in metals

Using first principles methods we explore the anisotropy of the spin relaxation and transverse transport properties in bulk metals with respect to the direction of the spin quantization axis in paramagnets or of the spontaneous magnetization in ferromagnets. Owing to the presence of the spin-orbit interaction the orbital and spin character of the Bloch states depends sensitively on the orientation of the spins relative to the crystal axes. This leads to drastic changes in quantities which rely on interband mixing induced by the spin-orbit interaction. The anisotropy is particularly striking for quantities which exhibit spiky and irregular distribution in the Brillouin zone, such as the spin-mixing parameter or the Berry curvature of the electronic states. We demonstrate this for three cases: (i) the Elliott-Yafet spin-relaxation mechanism in paramagnets with structural inversion symmetry; (ii) the intrinsic anomalous Hall effect in ferromagnets; and (iii) the spin Hall effect in paramagnets. We discuss the consequences of the pronounced anisotropic behavior displayed by these properties for spin-polarized transport applications.

cond-mat.mes-hall↗
arXiv2012

Maximally localized Wannier functions: Theory and applications

The electronic ground state of a periodic system is usually described in terms of extended Bloch orbitals, but an alternative representation in terms of localized "Wannier functions" was introduced by Gregory Wannier in 1937. The connection between the Bloch and Wannier representations is realized by families of transformations in a continuous space of unitary matrices, carrying a large degree of arbitrariness. Since 1997, methods have been developed that allow one to iteratively transform the extended Bloch orbitals of a first-principles calculation into a unique set of maximally localized Wannier functions, accomplishing the solid-state equivalent of constructing localized molecular orbitals, or "Boys orbitals" as previously known from the chemistry literature. These developments are reviewed here, and a survey of the applications of these methods is presented. This latter includes a description of their use in analyzing the nature of chemical bonding, or as a local probe of phenomena related to electric polarization and orbital magnetization. Wannier interpolation schemes are also reviewed, by which quantities computed on a coarse reciprocal-space mesh can be used to interpolate onto much finer meshes at low cost, and applications in which Wannier functions are used as efficient basis functions are discussed. Finally the construction and use of Wannier functions outside the context of electronic-structure theory is presented, for cases that include phonon excitations, photonic crystals, and cold-atom optical lattices.

cond-mat.mtrl-sci↗
arXiv2011

Wannier-based calculation of the orbital magnetization in crystals

We present a first-principles scheme that allows the orbital magnetization of a magnetic crystal to be evaluated accurately and efficiently even in the presence of complex Fermi surfaces. Starting from an initial electronic-structure calculation with a coarse ab initio k-point mesh, maximally localized Wannier functions are constructed and used to interpolate the necessary k-space quantities on a fine mesh, in parallel to a previously-developed formalism for the anomalous Hall conductivity [X.Wang, J. Yates, I. Souza, and D. Vanderbilt, Phys. Rev. B 74, 195118 (2006)]. We formulate our new approach in a manifestly gauge-invariant manner, expressing the orbital magnetization in terms of traces over matrices in Wannier space. Since only a few (e.g., of the order of 20) Wannier functions are typically needed to describe the occupied and partially occupied bands, these Wannier matrices are small, which makes the interpolation itself very efficient. The method has been used to calculate the orbital magnetization of bcc Fe, hcp Co, and fcc Ni. Unlike an approximate calculation based on integrating orbital currents inside atomic spheres, our results nicely reproduce the experimentally measured ordering of the orbital magnetization in these three materials.

cond-mat.mtrl-sci↗
arXiv2011

Orbital magnetoelectric coupling at finite electric field

We extend the band theory of linear orbital magnetoelectric coupling to treat crystals under finite electric fields. Previous work established that the orbital magnetoelectric response of a generic insulator at zero field comprises three contributions that were denoted as local circulation, itinerant circulation, and Chern-Simons. We find that the expression for each of them is modified by the presence of a dc electric field. Remarkably, the sum of the three correction terms vanishes, so that the total coupling is still given by the same formula as at zero field. This conclusion is confirmed by numerical tests on a tight-binding model, for which we calculate the field-induced change in the linear magnetoelectric coefficient.

cond-mat.mtrl-sci↗
arXiv2011

The role of spin-flip transitions in the anomalous Hall effect of FePt alloy

We carry out first-principles calculations which demonstrate the importance of the non-spin-conserving part of the spin-orbit interaction for the intrinsic anomalous Hall conductivity of ordered FePt alloys. The impact of this interaction is strongly reduced if Pt is replaced by the lighter isoelectronic element Pd. An analysis of the interband transitions responsible for the anomalous velocity reveals that spin-flip transitions occur not only at avoided band crossings near the Fermi level, but also between well-separated pairs of bands with similar dispersions. We also predict a strong anisotropy in the anomalous Hall conductivity of FePt caused entirely by low-frequency spin-flip transitions.

cond-mat.mes-hall↗
arXiv2010

Band theory of spatial dispersion in magnetoelectrics

Working in the crystal-momentum representation, we calculate the optical conductivity of noncentrosymmetric insulating crystals at first order in the wave vector of light. The time-even part of this tensor describes natural optical activity and the time-odd part describes nonreciprocal effects such as gyrotropic birefringence. The time-odd part can be uniquely decomposed into magnetoelectriclike and purely quadrupolar contributions. The magnetoelectriclike component reduces in the static limit to the traceless part of the frozen-ion static magnetoelectric polarizability while at finite frequencies it acquires some quadrupolar character in order to remain translationally invariant. The expression for the orbital contribution to the conductivity at transparent frequencies is validated by comparing numerical tight-binding calculations for finite and periodic samples.

cond-mat.mes-hall↗
arXiv2010

Chern-Simons orbital magnetoelectric coupling in generic insulators

We present a Wannier-based method to calculate the Chern-Simons orbital magnetoelectric coupling in the framework of first-principles density-functional theory. In view of recent developments in connection with strong Z2 topological insulators, we anticipate that the Chern-Simons contribution to the magnetoelectric coupling could, in special cases, be as large or larger than the total magnetoelectric coupling in known magnetoelectrics like Cr2O3. The results of our calculations for the ordinary magnetoelectrics Cr2O3, BiFeO3 and GdAlO3 confirm that the Chern-Simons contribution is quite small in these cases. On the other hand, we show that if the spatial inversion and time-reversal symmetries of the Z2 topological insulator Bi2Se3 are broken by hand, large induced changes appear in the Chern-Simons magnetoelectric coupling.

cond-mat.mtrl-sci↗
arXiv2010

The rise of spin-flip transitions in the anomalous Hall effect of FePt alloy

We carry out first-principles calculations which demonstrate the importance of spin-flip transitions for the intrinsic anomalous Hall conductivity of ordered FePt alloys. We show the such transitions get enhanced by large spin-orbit coupling of Pt atoms, becoming negligible when Pt is replaced by lighter isoelectronic Pd. We find that spin-flip transitions in FePt originate not only from conventional band anticrossings at the Fermi level, but also from transitions between well-separated pairs of bands with similar dispersions. We also predict a strong anisotropy in the anomalous Hall conductivity of FePt, which comes from spin-flip transitions entirely, and investigate the influence of disorder on it.

cond-mat.mes-hall↗
arXiv2010

Theory of orbital magnetoelectric response

We extend the recently-developed theory of bulk orbital magnetization to finite electric fields, and use it to calculate the orbital magnetoelectric response of periodic insulators. Working in the independent-particle framework, we find that the finite-field orbital magnetization can be written as a sum of three gauge-invariant contributions, one of which has no counterpart at zero field. The extra contribution is collinear with and explicitly dependent on the electric field. The expression for the orbital magnetization is suitable for first-principles implementations, allowing to calculate the magnetoelectric response coefficients by numerical differentiation. Alternatively, perturbation-theory techniques may be used, and for that purpose we derive an expression directly for the linear magnetoelectric tensor by taking the first field-derivative analytically. Two types of terms are obtained. One, the `Chern-Simons' term, depends only on the unperturbed occupied orbitals and is purely isotropic. The other, `Kubo' term, involves the first-order change in the orbitals and gives isotropic as well as anisotropic contributions to the response. In ordinary magnetoelectric insulators both terms are generally present, while in strong Z2 topological insulators only the former type is allowed, and is quantized. In order to validate the theory we have calculated under periodic boundary conditions the linear magnetoelectric coupling for a 3-D tight-binding model of an ordinary magnetoelectric insulator, using both the finite-field and perturbation-theory expressions. The results are in excellent agreement with calculations on bounded samples.

cond-mat.mes-hall↗
arXiv2009

Orientation Dependence of the Intrinsic Anomalous Hall Effect in hcp Cobalt

We carry out first-principles calculations of the dependence of the intrinsic anomalous Hall conductivity of hcp Co on the magnetization direction. The Hall conductivity decreases smoothly from 481 S/cm to 116 S/cm as the magnetization is tilted from the c-axis to the ab-plane. This factor-of-four reduction compares well with measurements on single crystals, while the angular average of 226 S/cm is in excellent agreement with the value of 205 S/cm measured in polycrystalline films. The strong anisotropy of the anomalous Hall conductivity is a consequence of spin-orbit induced changes in the electron states near the Fermi level as the magnetization is rotated.

cond-mat.mtrl-sci↗
arXiv2008

Nonadiabatic wavepacket dynamics: k-space formulation

The time evolution of wavepackets in crystals in the presence of a homogeneous electric field is formulated in k-space in a numerically tractable form. The dynamics is governed by separate equations for the motion of the waveform in k-space and for the evolution of the underlying Bloch-like states. A one-dimensional tight-binding model is studied numerically, and both Bloch oscillations and Zener tunneling are observed. The long-lived Bloch oscillations of the wavepacket center under weak fields are accompanied by oscillations in its spatial spread. These are analyzed in terms of a k-space expression for the spread having contributions from both the quantum metric and the Berry connection of the Bloch states. We find that when sizeable spread oscillations do occur, they are mostly due to the latter term.

cond-mat.mtrl-sci↗
arXiv2008

Dichroic f-sum rule and the orbital magnetization of crystals

We consider the magnetic circular dichroism spectrum of a crystal with broken time-reversal symmetry in the electric-dipole approximation. Using the Kubo-Greenwood formula for the absorptive part of the antisymmetric optical conductivity, its frequency integral is recast as a ground-state property. We show that in insulators this quantity is proportional to the circulation of the occupied Wannier orbitals around their centers (more precisely, to the gauge-invariant part thereof). This differs from the net circulation, or ground state orbital magnetization, which has two additional contributions: (i) the remaining Wannier self-rotation, and (ii) the ``itinerant'' circulation arising from the center-of-mass motion of the Wannier orbitals, both on the surface and in the interior of the sample. Contributions (i) and (ii) are not separately meaningful, since their individual values depend on the particular choice of Wannier functions. Their sum is however gauge-invariant, and can be inferred from a combination of two experiments: a measurement of the magneto-optical spectrum over a sufficiently wide range to evaluate the sum rule, and a gyromagnetic determination of the total orbital magnetization.

cond-mat.mtrl-sci↗
arXiv2007

Fermi-surface calculation of the anomalous Hall conductivity

While the intrinsic anomalous Hall conductivity is normally written in terms of an integral of the electronic Berry curvature over the occupied portions of the Brillouin zone, Haldane has recently pointed out that this quantity (or more precisely, its ``non-quantized part'') may alternatively be expressed as a Fermi-surface property. Here we present an {\it ab-initio} approach for computing the anomalous Hall conductivity that takes advantage of this observation by converting the integral over the Fermi sea into a more efficient integral on the Fermi surface only. First, a conventional electronic-structure calculation is performed with spin-orbit interaction included. Maximally-localized Wannier functions are then constructed by a post-processing step in order to convert the {\it ab-initio} electronic structure around the Fermi level into a tight-binding-like form. Working in the Wannier representation, the Brillouin zone is sampled on a large number of equally spaced parallel slices oriented normal to the total magnetization. On each slice, we find the intersections of the Fermi-surface sheets with the slice by standard contour methods, organize these into a set of closed loops, and compute the Berry phases of the Bloch states as they are transported around these loops. The anomalous Hall conductivity is proportional to the sum of the Berry phases of all the loops on all the slices. Illustrative calculations are performed for Fe, Co and Ni.

cond-mat.mtrl-sci↗
arXiv2007

Spectral and Fermi surface properties from Wannier interpolation

We present an efficient first-principles approach for calculating Fermi surface averages and spectral properties of solids, and use it to compute the low-field Hall coefficient of several cubic metals and the magnetic circular dichroism of iron. The first step is to perform a conventional first-principles calculation and store the low-lying Bloch functions evaluated on a uniform grid of k-points in the Brillouin zone. We then map those states onto a set of maximally-localized Wannier functions, and evaluate the matrix elements of the Hamiltonian and the other needed operators between the Wannier orbitals, thus setting up an ``exact tight-binding model.'' In this compact representation the k-space quantities are evaluated inexpensively using a generalized Slater-Koster interpolation. Because of the strong localization of the Wannier orbitals in real space, the smoothness and accuracy of the k-space interpolation increases rapidly with the number of grid points originally used to construct the Wannier functions. This allows k-space integrals to be performed with ab-initio accuracy at low cost. In the Wannier representation, band gradients, effective masses, and other k-derivatives needed for transport and optical coefficients can be evaluated analytically, producing numerically stable results even at band crossings and near weak avoided crossings.

cond-mat.mtrl-sci↗