arXiv subjects

Frank Freimuth

Publications and source records attributed to Frank Freimuth.

68 records · Page 4Linked to original sources

arXiv2013

Berry phase theory of Dzyaloshinskii-Moriya interaction and spin-orbit torques

Recent experiments on current-induced domain wall motion in chiral magnets suggest important contributions both from spin-orbit torques (SOTs) and from the Dzyaloshinskii-Moriya interaction (DMI). We derive a Berry phase expression for the DMI and show that within this Berry phase theory DMI and SOTs are intimately related, in a way formally analogous to the relation between orbital magnetization (OM) and anomalous Hall effect (AHE). We introduce the concept of the \textit{twist torque moment}, which probes the internal twist of wave packets in chiral magnets in a similar way like the orbital moment probes the wave packet's internal self rotation. We propose to interpret the Berry phase theory of DMI as a theory of \textit{spiralization} in analogy to the modern theory of OM. We show that the twist torque moment and the spiralization together give rise to a Berry phase governing the response of the SOT to thermal gradients, in analogy to the intrinsic anomalous Nernst effect. The Berry phase theory of DMI is computationally very efficient because it only needs the electronic structure of the collinear magnetic system as input. As an application of the formalism we compute the DMI in Pt/Co, Pt/Co/O and Pt/Co/Al magnetic trilayers and show that the DMI is highly anisotropic in these systems.

cond-mat.mtrl-sci↗

arXiv2013

Symmetry and magnitude of spin-orbit torques in ferromagnetic heterostructures

Current-induced spin torques are of great interest to manipulate the orientation of nanomagnets without applying external magnetic fields. They find direct application in non-volatile data storage and logic devices, and provide insight into fundamental processes related to the interdependence between charge and spin transport. Recent demonstrations of magnetization switching induced by in-plane current injection in ferromagnetic heterostructures have drawn attention to a class of spin torques based on orbital-to-spin momentum transfer, which is alternative to pure spin transfer torque (STT) between noncollinear magnetic layers and amenable to more diversified device functions. Due to the limited number of studies, however, there is still no consensus on the symmetry, magnitude, and origin of spin-orbit torques (SOTs). Here we report on the quantitative vector measurement of SOTs in Pt/Co/AlO trilayers using harmonic analysis of the anomalous and planar Hall effects as a function of the applied current and magnetization direction. We provide an all-purpose scheme to measure the amplitude and direction of SOTs for any arbitrary orientation of the magnetization, including corrections due to the interplay of Hall and thermoelectric effects. Based on general space and time inversion symmetry arguments, we show that asymmetric heterostructures allow for two different SOTs having odd and even behavior with respect to magnetization reversal. Our results reveal a scenario that goes beyond established models of the Rashba and spin Hall contributions to SOTs. The even SOT is STT-like but stronger than expected from the spin Hall effect in Pt. The odd SOT is composed of a constant field-like term and an additional component, which is strongly anisotropic and does not correspond to a simple Rashba field.

cond-mat.mes-hall↗

arXiv2013

Scattering-Independent Anomalous Nernst Effect in Ferromagnets

Using the full-potential linearized augmented plane-wave method within the density functional theory, we compute all contributions to the scattering independent part of the thermoelectric conductivity tensor, namely the intrinsic contribution and the side-jump contribution. For the ferromagnetic materials bcc Fe, hcp Co, fcc Ni and L1_0 ordered alloys FePd and FePt, our investigations of the energy and temperature dependence of the intrinsic and side-jump contributions show that they are both of equal importance. Overall, our calculations are able to correctly reproduce the order of magnitude and sign of the experimentally measured signal, suggesting that the scattering independent part plays an important role in the anomalous Nernst effect of ferromagnets.

cond-mat.mtrl-sci↗

arXiv2013

Engineering quantum anomalous Hall phases with orbital and spin degrees of freedom

Combining tight-binding models and first principles calculations, we investigate the quantum anomalous Hall (QAH) effect induced by intrinsic spin-orbit coupling (SOC) in buckled honeycomb lattice with sp orbitals in an external exchange field. Detailed analysis reveals that nontrivial topological properties can arise utilizing not only spin but also orbital degrees of freedom in the strong SOC limit, when the bands acquire non-zero Chern numbers upon undergoing the so-called orbital purification. As a prototype of a buckled honeycomb lattice with strong SOC we choose the Bi(111) bilayer, analyzing its topological properties in detail. In particular, we show the emergence of several QAH phases upon spin exchange of the Chern numbers as a function of SOC strength and magnitude of the exchange field. Interestingly, we observe that in one of such phases, namely, in the quantum spin Chern insulator phase, the quantized charge and spin Hall conductivities co-exist. We consider the possibility of tuning the SOC strength in Bi bilayer via alloying with isoelectronic Sb, and speculate that exotic properties could be expected in such an alloyed system owing to the competition of the topological properties of its constituents. Finally, we demonstrate that 3d dopants can be used to induce a sizeable exchange field in Bi(111) bilayer, resulting in non-trivial Chern insulator properties.

cond-mat.mes-hall↗

arXiv2012

Conductance fingerprints of non-collinear magnetic states in single atom contacts: a first-principles Wannier functions study

We present a first-principles computational scheme for investigating the ballistic transport properties of one-dimensional nanostructures with non-collinear magnetic order. The electronic structure is obtained within density functional theory as implemented in the full-potential linearized augmented plane-wave (FLAPW) method and mapped to a tight-binding like transport Hamiltonian via non-collinear Wannier functions. The conductance is then computed based on the Landauer formula using the Green's function method. As a first application we study the conductance between two ferromagnetic Co monowires terminated by single Mn apex atoms as a function of Mn-Mn separation. We vary the Mn-Mn separation from the contact (about 2.5 to 5 Å) to the far tunneling regime (5 to 10 Å). The magnetization direction of the Co electrodes is chosen either in parallel or antiparallel alignment and we allow for different spin configurations of the two Mn spins. In the tunneling and into the contact regime the conductance is dominated by $s$-$d_{z^2}$-states. In the close contact regime (below 3.5 Å) there is an additional contribution for a parallel magnetization alignment from the $d_{xz}$- and $d_{yz}$-states which give rise to an increase of the magnetoresistance as it is absent for antiparallel magnetization. If we allow the Mn spins to relax a non-collinear spin state is formed close to contact. We demonstrate that the transition from a collinear to such a non-collinear spin structure as the two Mn atoms approach leaves a characteristic fingerprint in the distance-dependent conductance and magnetoresistance of the junction. We explain the effect of the non-collinear spin state on the conductance based on the spin-dependent hybridization between the $d_{xz,yz}$-states of the Mn spins and their coupling to the Co electrodes.

cond-mat.mes-hall↗

arXiv2012

Topological phases of Bi(111) bilayer in an external exchange field

Using first principles methods, we investigate topological phase transitions as a function of exchange field in a Bi(111) bilayer. Evaluation of the spin Chern number for different magnitudes of the exchange field reveals that when the time reversal symmetry is broken by a small exchange field, the system enters the time-reversal broken topological insulator phase, introduced by Yang {\it et al.} in Phys. Rev. Lett. 107, 066602 (2011). After a metallic phase in the intermediate region, the quantum anomalous Hall phase with non-zero Chern number emerges at a sufficiently large exchange field. We analyze the phase diagram from the viewpoint of the evolution of the electronic structure, edge states and transport properties, and demonstrate that different topological phases can be distinguished by the spin-polarization of the edge states as well as spin or charge transverse conductivity.

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

One-dimensional ballistic transport with FLAPW Wannier functions

We present an implementation of the ballistic Landauer-Büttiker transport scheme in one-dimensional systems based on density functional theory (DFT) calculations within the full-potential linearized augmented plane-wave (FLAPW) method. In order to calculate the conductance within the Green's function method we map the electronic structure from the extended states of the FLAPW calculation to Wannier functions which constitute a minimal localized basis set. Our approach benefits from the high accuracy of the underlying FLAPW calculations allowing us to address the complex interplay of structure, magnetism, and spin-orbit coupling and is ideally suited to study spin-dependent electronic transport in one-dimensional magnetic nanostructures. To illustrate our approach we study ballistic electron transport in non-magnetic Pt monowires with a single stretched bond including spin-orbit coupling, and in ferromagnetic Co monowires with different collinear magnetic alignment of the electrodes with the purpose of analysing the magnetoresistance when going from tunneling to the contact regime. We further investigate spin-orbit scattering due to an impurity atom. We consider two configurations: a Co atom in a Pt monowire and vice versa. In both cases, the spin-orbit induced band mixing leads to a change of the conductance upon switching the magnetization direction from along the chain axis to perpendicular to it. The main contribution stems from ballistic spin-scattering for the magnetic Co impurity in the non-magnetic Pt monowire and for the Pt scatterer in the magnetic Co monowire from the band formed from states with $d_{xy}$ and $d_{x^2-y^2}$ orbital symmetry. We quantify this effect by calculating the ballistic anisotropic magnetoresistance which displays values up to as much as 7% for ballistic spin-scattering and gigantic values of around 100% for the Pt impurity in the Co wire.

cond-mat.mes-hall↗

arXiv2011

Ab Initio Theory of Scattering-Independent Anomalous Hall Effect

We report on first-principles calculations of the side-jump contribution to the anomalous Hall conductivity (AHC) directly from the electronic structure of a perfect crystal. We implemented our approach for a short-range scattering disorder model within the density functional theory and computed the full scattering-independent AHC in elemental bcc Fe, hcp Co, fcc Ni, and L1o FePd and FePt alloys. The full AHC thus calculated agrees systematically with experiment to a degree unattainable so far, correctly capturing the previously missing elements of side-jump contributions, hence paving the way to a truly predictive theory of the anomalous Hall effect and turning it from a characterization tool to a probing tool of multi-band complex electronic band structures.

cond-mat.mes-hall↗

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

Anisotropic spin Hall effect from first principles

We report on first principles calculations of the anisotropy of the intrinsic spin Hall conductivity (SHC) in nonmagnetic hcp metals and in antiferromagnetic Cr. For most of the metals of this study we find large anisotropies. We derive the general relation between the SHC vector and the direction of spin polarization and discuss its consequences for hcp metals. Especially, it is predicted that for systems where the SHC changes sign due to the anisotropy the spin Hall effect may be tuned such that the spin polarization is parallel either to the electric field or to the spin current.

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

Wannier-function approach to spin excitations in solids

We present a computational scheme to study spin excitations in magnetic materials from first principles. The central quantity is the transverse spin susceptibility, from which the complete excitation spectrum, including single-particle spin-flip Stoner excitations and collective spin-wave modes, can be obtained. The susceptibility is derived from many-body perturbation theory and includes dynamic correlation through a summation over ladder diagrams that describe the coupling of electrons and holes with opposite spins. In contrast to earlier studies, we do not use a model potential with adjustable parameters for the electron-hole interaction but employ the random-phase approximation. To reduce the numerical cost for the calculation of the four-point scattering matrix we perform a projection onto maximally localized Wannier functions, which allows us to truncate the matrix efficiently by exploiting the short spatial range of electronic correlation in the partially filled d or f orbitals. Our implementation is based on the FLAPW method. Starting from a ground-state calculation within the LSDA, we first analyze the matrix elements of the screened Coulomb potential in the Wannier basis for the 3d transition-metal series. In particular, we discuss the differences between a constrained nonmagnetic and a proper spin-polarized treatment for the ferromagnets Fe, Co, and Ni. The spectrum of single-particle and collective spin excitations in fcc Ni is then studied in detail. The calculated spin-wave dispersion is in good overall agreement with experimental data and contains both an acoustic and an optical branch for intermediate wave vectors along the [100] direction. In addition, we find evidence for a similar double-peak structure in the spectral function along the [111] direction.

cond-mat.mtrl-sci↗

arXiv2008

Magnetically-induced ferroelectricity in orthorhombic manganites: microscopic origin and chemical trends

The microscopic origin of the magnetically-driven ferroelectricity in collinear AFM-E orthorhombic manganites is explained by means of first-principles Wannier functions. We show that the polarization is mainly determined by the "asymmetric electron hopping" of orbitally-polarized Mn eg states, implicit in the peculiar in-plane zig-zag spin arrangement in the AFM-E configuration. In ortho-HoMnO3, Wannier function centers are largely displaced with respect to corresponding ionic positions, implying that the final polarization is strongly affected by a purely electronic contribution, at variance with standard ferroelectrics where the ionic-displacement is dominant. However, the final value of the polarization is the result of competing effects, as shown by the opposite signs of the contributions to the polarization coming from the Mn eg and t2g states. Furthermore, a systematic analysis of the link between ferroelectricity and the spin, orbital and lattice degrees of freedom in the manganite series has been carried out, in the aim of ascertaining chemical trends as a function of the rare-earth ion. Our results show that the Mn-O-Mn angle is the key quantity in determining the exchange coupling: upon decreasing the Mn-O-Mn angle, the first- (second-) nearest neighbor ferromagnetic (antiferromagnetic) interaction decreases (remains constant), in turn stabilizing either the AFM-A or the AFM-E spin configuration for weakly or strongly distorted manganites, respectively. The Mn eg contribution to the polarization dramatically increases with the Mn-O-Mn angle and decreases with the "long" Mn-O bond length, whereas the Mn t2g contribution decreases with the "short" Mn-O bond-length, partially cancelling the former term.

cond-mat.str-el↗