Relativistic Spin-orbit Interactions Research Articles

Giant chiral magnetoelectric oscillations in a van der Waals multiferroic

Helical spin structures are expressions of magnetically induced chirality, entangling the dipolar and magnetic orders in materials1–4. The recent discovery of helical van der Waals multiferroics down to the ultrathin limit raises prospects of large chiral magnetoelectric correlations in two dimensions5,6. However, the exact nature and magnitude of these couplings have remained unknown so far. Here we perform a precision measurement of the dynamical magnetoelectric coupling for an enantiopure domain in an exfoliated van der Waals multiferroic. We evaluate this interaction in resonance with a collective electromagnon mode, capturing the impact of its oscillations on the dipolar and magnetic orders of the material with a suite of ultrafast optical probes. Our data show a giant natural optical activity at terahertz frequencies, characterized by quadrature modulations between the electric polarization and magnetization components. First-principles calculations further show that these chiral couplings originate from the synergy between the non-collinear spin texture and relativistic spin–orbit interactions, resulting in substantial enhancements over lattice-mediated effects. Our findings highlight the potential for intertwined orders to enable unique functionalities in the two-dimensional limit and pave the way for the development of van der Waals magnetoelectric devices operating at terahertz speeds.

Intriguing dynamics pattern in F + HD

Chemical Dynamics Despite decades of studies, the role of relativistic spin-orbit interactions in the dynamics of chemical reactions remains an intriguing topic. Using a high-resolution velocity map imaging crossed beams technique, Chen et al. observed an interesting pattern in the differential cross sections in the F + HD → HF + D reaction near the partial wave resonances (see the Perspective by Rakitzis). Further theoretical analysis showed that this pattern originates from quantum interference between spin-orbit split partial wave resonances with different total parities. The effect of the fine structure of the partial waves observed for this long known yet not completely explored three-atom system represents one more remarkable demonstration of the truly quantum nature of chemical reaction dynamics. Science , this issue p. [936][1]; see also p. [886][2] [1]: /lookup/doi/10.1126/science.abf4205 [2]: /lookup/doi/10.1126/science.abg3184

Ferri-chiral compounds with potentially switchable Dresselhaus spin splitting

Spin splitting of energy bands can be induced by relativistic spin-orbit interactions in materials without inversion symmetry. Whereas polar space group symmetries permit Rashba (R-1) spin splitting with helical spin textures in momentum space, which could be reversed upon switching a ferroelectric polarization via applied electric fields, the ordinary Dresselhaus effect (D-1A) is ac-tive only in materials exhibiting nonpolar noncentrosymmetric crystal classes with atoms occupy-ing exclusively non-polar lattice sites. Consequently, the spin-momentum locking induced by D-1A is not electric field-switchable. An alternative type of Dresselhaus symmetry, referred to as D-1B, exhibits crystal class constraints similar to D-1A (all dipoles add up to zero), but unlike D-1A, at least one polar site is occupied. We find that this behavior exists in a class of ferri-chiral crys-tals, which in principle could be reversed upon a change in chirality. Focusing on alkali metal chalcogenides, we identify NaCu5S3 in the nonentiamorphic ferri-chiral structure, which exhibits CuS3 chiral units differing in the magnitude of their Cu displacements. We then synthesize NaCu5S3 (space group P6322) and confirm its ferri-chiral structure with power x-ray diffraction. Our electronic structure calculations demonstrate it exhibits D-1B spin splitting as well as a ferri-chiral phase transition, revealing spin splitting interdependent on chirality. Our electronic struc-ture calculations show that a few percent biaxial tensile strain can reduce (or nearly quench) the switching barrier separating the monodomain ferri-chiral P6322 states. We discuss what type of external stimuli might switch the chirality so as to reverse the (non-helical) Dresselhaus D-1B spin texture, offering an alternative to the traditional reversal of the (helical) Rashba spin texture.

Nanomachining-enabled strain manipulation of magnetic anisotropy in the free-standing GaMnAs nanostructures

Strain perturbs atomic ordering in solids, with far-reaching consequences from an increased carrier mobility to localization in Si, stabilization of electric dipoles and nanomechanical transistor action in oxides, to the manipulation of spins without applying magnetic fields in n-GaAs. In GaMnAs, a carrier-mediated ferromagnetic semiconductor, relativistic spin-orbit interactions – highly strain-dependent magnetic interactions – play a crucial role in determining the magnetic anisotropy (MA) and anisotropic magnetoresistance (AMR). Strain modifies the MA and AMR in a nanomachined GaMnAs structure as measured by the anomalous Hall effect (AHE) and the planar Hall effect (PHE). Here, we report an MA modification by strain relaxation in an isolated GaMnAs Hall bar structure and by applying a range of local strains via fabricating asymmetrically mechanically buckled GaMnAs micro-Hall bar structures. In the AHE and PHE measurements, we observe a reduction in the in-plane MA and an enhancement in the out-of-plane MA as the compressive strain due to the lattice mismatch relaxes in the suspended structure. The functionality of such mechanical manipulation, as well as the two-level mechanical state and the corresponding AHE responses, is demonstrated by a fully scalable binary mechanical memory element in a GaMnAs single Hall cross structure.

Thermoelectric properties of heavy fermion CeRhIn5 using density functional theory combined with semiclassical Boltzmann theory.

Experimental evidences show that Ce-based compounds can be good candidates for thermoelectric applications due to their high thermoelectric efficiencies at low temperatures. However, thermoelectric properties have been studied less than the other properties for CeRhIn5, a technologically and fundamentally important compound. Thus, we comprehensively investigate the thermoelectric properties, including the Seebeck coefficient, electrical conductivity, electronic part of thermal conductivity, power factor and electronic figure of merit, by a combination of quantum mechanical density functional and semiclassical Boltzmann theories, including relativistic spin–orbit interactions using different exchange–correlation functionals at temperatures T ≤ 300 K for CeRhIn5 along its a and c crystalline axes. The temperature dependences of the thermoelectric quantities are investigated. Our results reveal a better Seebeck coefficient, electrical conductivity, power factor and thermoelectric efficiency at T ≪ 300, in agreement with various other Ce-based compounds, when a high degree of localization is considered for the 4f-Ce electrons. The Seebeck coefficient, power factor and thermoelectric efficiency are made more efficient near room temperature by decreasing the degree of localization for 4f-Ce electrons. Our results also show that the thermoelectric efficiency along the a crystalline axis is slightly better than that of the c axis. We also investigate the effects of hydrostatic pressure on the thermoelectric properties of the compound at low and high temperatures. The results show that the effects of imposing pressure strongly depend on the degree of localization considered for 4f-Ce electrons.

Relativistic spin-orbit interactions of photons and electrons

Laboratory optics, typically dealing with monochromatic light beams in a single reference frame, exhibits numerous spin-orbit interaction phenomena due to the coupling between the spin and orbital degrees of freedom of light. Similar phenomena appear for electrons and other spinning particles. Here we examine transformations of paraxial photon and relativistic-electron states carrying the spin and orbital angular momenta (AM) under the Lorentz boosts between different reference frames. We show that transverse boosts inevitably produce a rather nontrivial conversion from spin to orbital AM. The converted part is then separated between the intrinsic (vortex) and extrinsic (transverse shift or Hall effect) contributions. Although the spin, intrinsic-orbital, and extrinsic-orbital parts all point in different directions, such complex behavior is necessary for the proper Lorentz transformation of the total AM of the particle. Relativistic spin-orbit interactions can be important in scattering processes involving photons, electrons, and other relativistic spinning particles, as well as when studying light emitted by fast-moving bodies.

Noncommutative quantum mechanics and skew scattering in ferromagnetic metals

The anomalous Hall effect in ferromagnetic metals is classified into two based on the mechanism. The first one is the intrinsic Hall effect due to the Berry curvature in momentum space; this is a Hall effect that solely arises from the band structure of solids. On the other hand, another contribution to the Hall effect, so-called extrinsic mechanism, comes from impurity scatterings such as skew scattering and side jump; for the extrinsic mechanism, the spin-orbit interaction of the impurity ions is often required. These two mechanisms are often discussed separately; the intrinsic Hall effect is dominant in the intermediate resistivity region while the latter, i.e., skew scattering, becomes important in the clean limit. In this work, it is shown theoretically that the non-commutative nature of the real-space coordinates in the presence of the Berry curvature causes the skew scattering by the nonmagnetic impurity without relativistic spin-orbit interactions, in sharp contrast to the conventional cases.

An ab initio study of nuclear volume effects for isotope fractionations using two‐component relativistic methods

We investigate the accuracy of two-component Douglas-Kroll-Hess (DKH) methods in calculations of the nuclear volume term (≡ lnK(nv)) in the isotope fractionation coefficient. lnK(nv) is a main term in the chemical equilibrium constant for isotope exchange reactions in heavy element. Previous work based on the four-component method reasonably reproduced experimental lnK(nv) values of uranium isotope exchange. In this work, we compared uranium reaction lnK(nv) values obtained from the two-component and four-component methods. We find that both higher-order relativistic interactions and spin-orbit interactions are essential for quantitative description of lnK(nv). The best alternative is the infinite-order Douglas-Kroll-Hess method with infinite-order spin-orbit interactions for the one-electron term and atomic-mean-field spin-same-orbit interaction for the two-electron term (IODKH-IOSO-MFSO). This approach provides almost equivalent results for the four-component method, while being 30 times faster. The IODKH-IOSO-MFSO methodology should pave the way toward computing larger and more general molecules beyond the four-component method limits.

N incorporation and associated localized vibrational modes in GaSb

We present results of electronic structure calculations on the N-related localized vibrational modes in the dilute nitride alloy GaSb1−xNx. By calculating the formation energies of various possible N incorporation modes in the alloy, we determine the most favorable N configurations, and we calculate their vibrational mode frequencies using density functional theory under the generalized gradient approximation to electron exchange and correlation, including the effects of the relativistic spin-orbit interactions. For a single N impurity, we find substitution on an Sb site, NSb, to be most favorable, and for a two-N-atom complex, we find the N-N split interstitial on an Sb site to be most favorable. For these defects, as well as, for comparison, defects comprising two N atoms on neighboring Sb sites and a N-Sb split interstitial on an Sb site, we find well-localized vibration modes (LVMs), which should be experimentally observable. The frequency of the triply degenerate LVM associated with NSb is determined to be 427.6 cm−1. Our results serve as a guide to future experimental studies to elucidate the incorporation of small concentrations of N in GaSb, which is known to lead to a reduction of the band gap and opens the possibility of using the material for long-wavelength applications.

New Layered-Type Quaternary Chalcogenides, Tl2PbMQ4 (M = Zr, Hf; Q = S, Se): Structure, Electronic Structure, and Electrical Transport Properties

We have synthesized and characterized new thallium chalcogenides of the general formula Tl2PbMQ4 (M = Zr, Hf; Q = S, Se) from the constituent elements via high-temperature reaction conditions. These sulfides and selenides crystallize in the monoclinic crystal system (space group C2/c). The unit cell parameters refined from single-crystal X-ray diffraction data for Tl2PbZrS4 are a = 15.455(4) Å, b = 8.214(2) Å, c = 6.751(2) Å, β = 109.093(3)°, and V = 809.9(4) Å(3), with Z = 4. No corresponding tellurides were obtained from similar reaction conditions. The isostructural quaternary chalcogenides form a layered structure, composed of alternating metal and chalcogen layers. The latter are packed along the a axis as in the face-centered cubic packing (ABC), while the metal layers alternate between Tl layers and mixed Pb/Zr layers. All metal atoms are located in differently distorted Q6 octahedra, with the TlQ6 polyhedra being the least regular ones. Density functional theory based electronic structure calculations with inclusion of relativistic spin-orbit interactions predict (indirect) energy band gaps of 0.66 and 0.33 eV for Tl2PbZrS4 and Tl2PbHfSe4, respectively. Optical spectroscopy revealed significantly larger (direct) band gaps of 1.2 and 1.6 eV. The semiconducting character is in agreement with the charge-balanced formula (Tl(+))2Pb(2+)M(4+)(Q(2-))4. The electrical transport properties also show the semiconducting nature of these materials. For Tl2PbHfSe4, the Seebeck coefficient increases from +190 μV K(-1) at room temperature to +420 μV K(-1) at 520 K.

Magnetic structure of hexagonal YMnO3and LuMnO3from a microscopic point of view

The aim of this work is to unravel a basic microscopic picture behind complex magnetic properties of hexagonal manganites. For these purposes, we consider two characteristic compounds: YMnO3 and LuMnO3, which form different magnetic structures in the ground state. First, we establish an electronic low-energy model, which describes the behavior of the Mn 3d bands of YMnO3 and LuMnO3, and derive parameters of this model from the first-principles calculations. From the solution of this model, we conclude that, despite strong frustration effects in the hexagonal lattice, the relativistic spin-orbit interactions lift the degeneracy of the magnetic ground state so that the experimentally observed magnetic structures are successfully reproduced by the low-energy model. Then, we analyze this result in terms of interatomic magnetic interactions, which were computed using different approximations (starting from the model Hamiltonian as well as directly from the first-principles electronic structure calculations in the local-spin-density approximation). We argue that the main reason why YMnO3 and LuMnO3 tend to form different magnetic structures is related to the behavior of the single-ion anisotropy, which reflects the directional dependence of the lattice distortion: namely, the expansion and contraction of the Mn-trimers, which take place in YMnO3 and LuMnO3, respectively. On the other hand, the magnetic coupling between the haxagonal planes is controlled by the next-nearest-neighbor interactions, which are less sensitive to the direction of the trimerization. Finally, using the Berry-phase formalism, we evaluate the magnetic-state dependence of the ferroelectric polarization, and discuss potential applications of the latter in magnetoelectric switching phenomena.

Magnetoelectric resonance with electromagnons in a perovskite helimagnet

Maxwell’s equations describe the interrelation between temporally changing electric (E) and magnetic (H) fields in a given medium. In materials that exhibit relativistic spin–orbit interactions, we also expect their polarization (P) and magnetization (M) to be dynamically coupled. This in turn could enable greater control over the cross-coupling between the electric and magnetic fields of light in the development of photonic devices1. Such magnetoelectric phenomena are expected to be enhanced within materials that support electromagnons—fundamental excitations that exhibit both electric and magnetic dipole moments. Here we report the discovery of electromagnons in the perovskite (Eu,Y)MnO3, which arise from fluctuations in the spontaneous polarization generated by cycloidal spin order2,3,4,5. The resulting dynamical M–P cross-coupling causes the material to exhibit colossal directional dichroism—a difference in the absorption of light propagating in opposite directions—at the resonance frequency (sub-THz) associated with these excitations.

General relativistic spin-orbit and spin–spin effects on the motion of rotating particles in an external gravitational field

We analytically compute the orbital effects induced on the motion of a spinning particle geodesically traveling around a central rotating body by the general relativistic two-body spin-spin and spin-orbit interactions. We use the weak-field and slow-motion leading-order approximation. Neither assumptions on the eccentricity nor the inclination of the orbit of the particle have been assumed. No specific orientations of the spins involved have been chosen. (Abridged)

Isospin symmetry breaking at high spin in the mirror nucleiAr35andCl35

High-spin states in $^{35}\mathrm{Ar}$ and $^{35}\mathrm{Cl}$ have been populated in the $^{24}\mathrm{Mg}$($^{16}\mathrm{O}$, $\ensuremath{\alpha}n$) and $^{24}\mathrm{Mg}$($^{16}\mathrm{O}$, $\ensuremath{\alpha}p$) reactions, respectively, at a beam energy of 70 MeV. The comparison between the level schemes of these mirror nuclei shows a striking asymmetry in the population yield of high-spin analog states of positive parity, which indicates different intensities of $E1$ transitions connecting positive- and negative-parity structures in both nuclei. Large energy differences are observed between analog states of negative parity with configurations of dominant pure single-particle character. This results from the comparison with large-scale shell-model calculations in the ${s}_{1/2}{d}_{3/2}{f}_{7/2}{p}_{3/2}$ valence space. It is shown that important contributions to the energy differences arise from the multipole Coulomb and the relativistic electromagnetic spin-orbit interactions.

The hydrogen atom in crossed static electromagnetic and non-resonant laser fields

The energy splittings and wave function of a hydrogen atom in crossed uniform static electromagnetic and non-resonant monochromatic electric fields of arbitrary mutual orientation are obtained within the "one-shell" approximation. The intensities of the Lyman lines are also obtained. A special analytical method is used. Relativistic corrections and spin-orbit interactions are not considered.

First- and second-order contributions to the effective Hamiltonian parameters for Gd 3+( 8S) and Mn 2+( 6S)

The effective operator formalism is used to calculate the values of effective Hamiltonian parameters which arise from higher order perturbation corrections due to the relativistic crystal field and spin-orbit interactions. The method is illustrated on two examples: the Gd 3+ ion in the C 3h-symmetry and the Mn 2+ ion in the C 3v-symmetry. Transitions to all excited orbitals for l = s, p, d, f and n = l+1,…, 10 are included in calculations. The role of second-order perturbation corrections is significant for both excitations within the ground configuration and outside it.