Order Spin-orbit Coupling Research Articles

Impact of the electric field on isotropic and anisotropic spin Hamiltonian parameters.

One may obviously think that the best way to control magnetic properties relies on using a magnetic field. However, it is not convenient to focus a magnetic field on a small object, whereas it is much easier to do so with an electric field. Magnetoelectric coupling allows one to control the magnetization with the electric field and the polarization with the magnetic field and could therefore provide a solution to this problem. This paper aims at quantifying the impact of the electric field on both the isotropic magnetic exchange and the Dzyaloshinskii-Moriya interaction in the case of a binuclear system of S = 1/2 spins. This study follows previous studies that showed that very high Dzyaloshinskii-Moriya interaction, i.e., the antisymmetric exchange, can be generated when close to first order spin orbit coupling. We will, therefore, explore this regime in a model Cu(II) complex that exhibits a quasi-degeneracy of the dx2-y2 and dxy orbitals. This situation is indeed the one that allows us to obtain the largest spin orbit couplings in transition metal complexes. We will show that both the magnetic exchange and the Dzyaloshinskii-Moriya interaction are very sensitive to the electric field and that it would therefore be possible to modulate and control magnetic properties by the electric field. Finally, rationalizations of the obtained results will be proposed.

Controlling Dzyaloshinskii-Moriya interactions in the skyrmion host candidates FePd1−xPtxMo3N

Ferromagnets crystallizing in structures described by chiral cubic space groups, including compounds with the B20 or $\beta$-Mn structures, are known to host long-period chiral spin textures such as skyrmion lattices. These spin textures are stabilized by a competition between ferromagnetic exchange and antisymmetric Dyzaloshinskii-Moriya (DM) exchange, which is enhanced by the spin-orbit coupling associated with high-atomic-number elements. For real-world application, it is desirable to find materials that can host compact skyrmion lattices at readily accessible temperatures. Here, we report on the crystal chemistry and magnetic phase diagrams of a family of compounds with the filled $\beta$-Mn structure, FePd$_{1-x}$Pt$_x$Mo$_3$N with $T_C$ ranging from 175 K to 240 K. DC and AC magnetization measurements reveal magnetic phase diagrams consistent with the formation of a skyrmion pocket just below $T_C$. The magnitudes of ferromagnetic and DM exchanges are determined from the phase diagrams, demonstrating that the introduction of increasing amounts of Pt can be used to increase spin-orbit coupling in order to control the expected skyrmion lattice parameter between 140 nm and 65 nm while simultaneously increasing $T_C$.

Spin-valley coupled thermoelectric energy converter with strained honeycomb lattices

A caloritronic device setup is proposed that harnesses the intrinsic spin-valley locking of two-dimensional honeycomb lattices with graphene-like valleys, for instance, silicene and stanene. Combining first-principles and analytic calculations, we quantitatively show that when sheets of such materials are placed on a ferromagnetic substrate and held between two contacts at different temperatures, an interplay between the electron degrees-of-freedom of charge, spin, and valley arises. A manifestation of this interplay are finite charge, spin, and valley currents. Uniaxial strain that adjusts the buckling height in silicene-type of lattices, in conjunction with an applied electric field, is shown to further modulate the aforementioned currents. We link these calculations to a Seebeck-like thermopower generator and obtain expressions (and means to optimize them) for two spin-valley polarized performance metrics--the thermodynamic efficiency and thermoelectric figure of merit. A closing summary outlines possible enhancements to presented results through the inherent topological order and substrate-induced external Rashba spin-orbit coupling that exists in silicene-type materials.

Terahertz-infrared spectroscopy of single crystalline m-type hexaferrite BaTixFe12-xO19

We have studied polarization-dependent broad-band dielectric response of single-crystalline Ti-substituted barium hexaferrites BaTixFe12-xO19, x=0.64., 0.75, 1.1, in the frequency range from 10 to 8000 cm−1 and at temperatures from 5 to 300 K. In addition to a rich set of phonon resonances located at frequencies from 90 to 800 cm−1 we observed an unusual low-energy response (terahertz region, 10-100 cm−1) stemming from two different effects: relaxational process and second order spin-orbit coupling in Fe2+ ground state, that may set up new prospects for doped hexaferrites in terahertz technologies.

Unified low-energy effective Hamiltonian and the band topology of p -block square-net layer derivatives

In recent years, low-dimensional materials with tetragonal $P4/nmm$ (orthorhombic $Pnma$) space group having square-net (chain-like) substructure of $p$-block elements have been studied extensively. By using a first-principles calculation and a two-sites $\otimes$ two-orbitals tight-binding model, we construct the unified low-energy effective Hamiltonian and the $\mathbb{Z}_{2}$ topological phase diagram for such materials with different filling factors. Near the chemical potential, we show that the staggered arrangement of ions at 2c (4c) site yields the virtual hopping that have the same form with the second nearest-neighbor hopping between the square-net (chain-like) ions. We show that this hybridization and low-symmetry of the chain-like structure protects the quantum spin Hall insulator phase. Finally, the second order spin-orbit coupling on top of the atomic spin-orbit coupling is considered to clarify the origin of the non-zero Berry phase signals reported in recent quantum oscillation experiments.

Magnetic Behavior of Superconductor 2H-NbSe2 Intercalated with Iron: First Principle Study

We investigated the structural, electronic and magnetic properties of iron-intercalated niobium selinium, $Fe_{x}NbSe_{2}$ for $x = 0$ and 0.25, from first principle calculations. The tendency towards the localization in superconductors criterion which has been extracted from our results placed the $NbSe_{2}$ compound in vicinity of Fe-based superconductors. The DFT plus on-site coulomb repulsion U (DFT+U) and the exact exchange for correlated electrons (DFT+EECE)-based hybrid functional were used including the spin-orbit coupling (SOC) to understand the role of correlation and SOC effects in this type of systems. The calculation predicts the correct antiferromagnetic (AF) ground state, from both the generalized gradient approximation (GGA) and GGA+U. A shift up in the Fermi energy was observed after the intercalation of 2H-NbSe2 with iron, indicating a charge transfer from Fe to the host compound. The obtained magnetic moment of Fe is enhanced by a correlation effect in both DFT+U and DFT+EECE over the small value from GGA-only. Moreover, a large unquenched orbital magnetic moment is saturated to $m_{orb} \sim 0.6\mu _{B}$ under a moderate correlation effect of $U_{eff}\sim 2.0eV$ . We also show that the correlation effect is important along side with SOC in order to get a true picture for the band filling consistent with that of the crystal field splitting and a large unquenched $m_{orb}$ which has been found experimentally in such systems. Therefore, the combination of correlation and SOC effects is a decisive choice for further studies of such systems.

Interplay of spin-dependent delocalization and magnetic anisotropy in the ground and excited states of [Gd2@C78]- and [Gd2@C80

The magnetic properties and electronic structure of the ground and excited states of two recently characterized endohedral metallo-fullerenes, [Gd2@C78]- (1) and [Gd2@C80]- (2), have been studied by theoretical methods. The systems can be considered as [Gd2]5+ dimers encapsulated in a fullerene cage with the fifteen unpaired electrons ferromagnetically coupled into an S = 15/2 high-spin configuration in the ground state. The microscopic mechanisms governing the Gd-Gd interactions leading to the ferromagnetic ground state are examined by a combination of density functional and ab initio calculations and the full energy spectrum of the ground and lowest excited states is constructed by means of ab initio model Hamiltonians. The ground state is characterized by strong electron delocalization bordering on a σ type one-electron covalent bond and minor zero-field splitting (ZFS) that is successfully described as a second order spin-orbit coupling effect. We have shown that the observed ferromagnetic interaction originates from Hund's rule coupling and not from the conventional double exchange mechanism. The calculated ZFS parameters of 1 and 2 in their optimized geometries are in qualitative agreement with experimental EPR results. The higher excited states display less electron delocalization, but at the same time they possess unquenched first-order angular momentum. This leads to strong spin-orbit coupling and highly anisotropic energy spectrum. The analysis of the excited states presented here constitutes the first detailed study of the effects of spin-dependent delocalization in the presence of first order orbital angular momentum and the obtained results can be applied to other mixed valence lanthanide systems.

Relativistic theory of magnetic inertia in ultrafast spin dynamics

The influence of possible magnetic inertia effects has recently drawn attention in ultrafast magnetization dynamics and switching. Here we derive rigorously a description of inertia in the Landau-Lifshitz-Gilbert equation on the basis of the Dirac-Kohn-Sham framework. Using the Foldy-Wouthuysen transformation up to the order of $1/c^4$ gives the intrinsic inertia of a pure system through the 2$^{\rm nd}$ order time-derivative of magnetization in the dynamical equation of motion. Thus, the inertial damping $\mathcal{I}$ is a higher order spin-orbit coupling effect, $\sim 1/c^4$, as compared to the Gilbert damping $\Gamma$ that is of order $1/c^2$. Inertia is therefore expected to play a role only on ultrashort timescales (sub-picoseconds). We also show that the Gilbert damping and inertial damping are related to one another through the imaginary and real parts of the magnetic susceptibility tensor respectively.

(Invited) Tailoring Graphene for Spintronics

The development of graphene spintronic devices requires that, in addition to its capability to passively transmit spins over long distances, new magnetic functionalities are incorporated to graphene. By growing epitaxially graphene on single crystal metal surfaces under UHV conditions [1] and either adsorbing molecules on it or intercalating heavy atoms below it, long range magnetic order or giant spin-orbit coupling, respectively, can be added to graphene. i) Achieving long range magnetic order by a monolayer of electron acceptor molecules adsorbed on graphene /Ru(0001). Epitaxial graphene is spontaneously nanostructured forming an hexagonal array of 100 pm high nanodomes with a periodicity of 3 nm [2]. Cryogenic Scanning Tunnelling Microscopy (STM) and Spectroscopy and DFT simulations show that TCNQ molecules deposited on gr/Ru(0001) acquire charge from the (doped) substrate and develop a sizeable magnetic moment revealed by a prominent Kondo resonance. The molecular monolayer self-assembled on graphene develops spatially-extended spin-split electronic bands. The predicted spin alignment in the ground state is visualized by spin-polarized STM at 4.6 K [3]. The system shows promising perspectives to become an effective graphene-based spin filter device. ii) Introducing a giant spin-orbit interaction on graphene/Ir(111) by intercalation of Pb. The intercalation of an ordered array of Pb atoms below graphene results in a series of sharp pseudo-Landau levels in the differential conductance revealed by STS at 4.6 K. The vicinity of Pb enhances by four orders of magnitude the, usually negligible, spin-orbit interaction of graphene. The spatial variation of the spin-orbit coupling creates a pseudo-magnetic field that originates the observed pseudo-Landau levels [4]. This may allow the processing and controlled manipulation of spins in graphene.

Anisotropic magnetoresistance in an antiferromagnetic semiconductor.

Recent studies in devices comprising metal antiferromagnets have demonstrated the feasibility of a novel spintronic concept in which spin-dependent phenomena are governed by an antiferromagnet instead of a ferromagnet. Here we report experimental observation of the anisotropic magnetoresistance in an antiferromagnetic semiconductor Sr2IrO4. Based on ab initio calculations, we associate the origin of the phenomenon with large anisotropies in the relativistic electronic structure. The antiferromagnet film is exchange coupled to a ferromagnet, which allows us to reorient the antiferromagnet spin-axis in applied magnetic fields via the exchange spring effect. We demonstrate that the semiconducting nature of our AFM electrode allows us to perform anisotropic magnetoresistance measurements in the current-perpendicular-to-plane geometry without introducing a tunnel barrier into the stack. Temperature-dependent measurements of the resistance and anisotropic magnetoresistance highlight the large, entangled tunabilities of the ordinary charge and spin-dependent transport in a spintronic device utilizing the antiferromagnet semiconductor.

Erratum: Effective one-body Hamiltonian of two spinning black holes with next-to-next-to-leading order spin-orbit coupling [Phys. Rev. D84, 084028 (2011)

Erratum: Effective one-body Hamiltonian of two spinning black holes with next-to-next-to-leading order spin-orbit coupling [Phys. Rev. D<b>84</b>, 084028 (2011)

Magnetic anisotropy in the boron nitride monolayer doped by 3d transitional metal substitutes at boron-site

Based on density functional theory with the generalized gradient approximation, a computational study is carried out to reveal the magnetism of the hexagonal boron nitride monolayers (h-BN) doped by 3d transitional metal atoms at boron-site. The magnetic moments and magnetic anisotropy energies (MAEs) of the most stable structures are given. Among the systems investigated, the MAE of Fe doped h-BN is 1.19 meV with an easy axis in the h-BN plane, while that of Mn is 0.63 meV with an easy axis perpendicular to the plane. For Sc and Co, the doped systems are nonmagnetic. For Ti, V, Cr, Ni, Cu, and Zn, the MAEs are relatively small. Theoretical analyses by perturbation theory and molecular orbital clarify that the MAE of Fe originates from the second order spin orbit coupling, whereas the MAE of Mn is contributed by the unquenched orbital momentum.

Magnetic and superconducting ordering in one-dimensional nanostructures at the LaAlO3/SrTiO3interface

We formulate a model for magnetic and superconducting ordering at LaAlO3/SrTiO3 interfaces containing both localized magnetic moments and itinerant electrons. Though these both originate in Ti 3d orbitals, the former may be due to electrons more tightly-bound to the interface while the latter are extended over several layers. Only the latter contribute significantly to metallic conduction and superconductivity. In our model, the interplay between the two types of electrons, which is argued to be ferromagnetic, combined with strong spin-orbit coupling of the itinerant electrons, leads to magnetic ordering. Furthermore, we propose a model for interfacial superconductivity, consisting of random superconducting grains in the bulk STO driven, via coupling to the interface conduction band, towards long-ranged or quasi-long-ranged order. Most interestingly, the magnetic order and strong spin orbit coupling can lead in this manner to unconventional interfacial superconductivity, yielding a possible realization of Majorana physics.

Periastron advance in neutron star–black hole binaries

As neutron star - black hole binaries are expected to be discovered through future pulsar surveys using upcoming facilities, it is necessary to understand various observable properties of such systems. In the present work, we study the advance of the periastron of such binaries under the post-Newtonian formalism over a wide range of parameters. We find that the first and second order post-Newtonian effects and the leading order spin-orbit coupling effects are significant for such binaries but higher order effects can be neglected.

Electronic Structure of the Lowest Triplet State of Flavin Mononucleotide

The electronic structure of flavin mononucleotide (FMN), an organic cofactor that plays a role in many important enzymatic reactions, has been investigated by electron paramagnetic resonance (EPR) spectroscopy, optical spectroscopy, and quantum chemistry. In particular, the triplet state of FMN, which is paramagnetic (total spin S = 1), allows an investigation of the zero field splitting parameters D and E, which are directly related to the two singly occupied molecular orbitals. Triplet EPR spectra and optical absorption spectra at different pH values in combination with time dependent density functional theory (TDDFT) reveal that the highest occupied orbital (HOMO) and lowest unoccupied orbital (LUMO) of FMN are largely unaffected by changes in the protonation state of FMN. Rather, the orbital structure of the lower lying doubly occupied orbitals changes dramatically. Additional EPR experiments have been carried out in the presence of AgNO(3), which allows the formation of an Ag-FMN triplet state with different zero field splitting parameters and population and depopulation rates. Addition of AgNO(3) only induces small changes in the optical spectrum, indicating that the Ag(+) ion only contributes to the zero field splitting by second order spin-orbit coupling and leaves the orbital structure unaffected. By a combination of the three employed methods, the observed bands in the UV/vis spectra of FMN at different pH values are assigned to electronic transitions.

Gravitational wave phasing for spinning compact binaries in inspiraling eccentric orbits

We present a semi-analytic prescription to obtain gravitational wave (GW) phasing for spinning compact binaries in inspiraling eccentric orbits, while restricting the spin effects to the leading order spin-orbit coupling. We demonstrate that only the radial part of the orbital dynamics is amenable for a Keplerian-type solution that is compatible with the standard post-Newtonian (PN) accurate quasi-Keplerian parametrization for nonspinning compact binaries. We also derive PN-accurate equations governing the evolution of the Eulerian angles that are crucial to obtain temporally evolving GW polarization states and compute the associated fully 1PN accurate amplitude corrected GW polarization states. We show that it is not possible to obtain a Keplerian-type parametric solution for the angular part of the above dynamics in a noninertial frame that follows the precessing orbital plane [N. J. Cornish and J. S. Key, Phys. Rev. D 82, 044028 (2010)]. Further, we point out certain undesirable features present in their approach for doing GW phasing, like the use of precessing polarization vectors to construct the polarization states.

Effective one-body Hamiltonian of two spinning black holes with next-to-next-to-leading order spin-orbit coupling

Building on the recently computed next-to-next-to-leading order (NNLO) post-Newtonian spin-orbit Hamiltonian for spinning binaries [J. Hartung and J. Steinhoff, arXiv:1104.3079.] we improve the effective-one-body description of the dynamics of two spinning black holes by including NNLO effects in the spin-orbit interaction. The calculation that is presented extends to NNLO the next-to-leading order spin-orbit Hamiltonian computed in [T. Damour, P. Jaranowski, and G. Schaefer, Phys. Rev. D 78, 024009 (2008).]. The present effective-one-body Hamiltonian reproduces the spin-orbit coupling through NNLO in the test-particle limit case. In addition, in the case of spins parallel or antiparallel to the orbital angular momentum, when circular orbits exist, we find that the inclusion of NNLO spin-orbit terms moderates the effect of the next-to-leading order spin-orbit coupling.

ChemInform Abstract: Cobalt(II) Single‐Molecule Magnets

AbstractReview: 49 refs

Cobalt(ii) single-molecule magnets

This short tutorial review covers recent progress in the field of polynuclear cobalt(ii)-based complexes, which display slow magnetic relaxation at low temperature. Cobalt(ii) single-molecule magnets (SMMs) can display much larger magnetic anisotropies and hence, potentially higher blocking temperatures than SMMs based on ions where the zero-field splitting originates from a second order spin-orbit coupling, such as manganese(iii).

Gravitational waveforms from unequal-mass binaries with arbitrary spins under leading order spin-orbit coupling

The paper generalizes the structure of gravitational waves from orbiting spinning binaries under leading order spin-orbit coupling, as given in the work by K\"onigsd\"orffer and Gopakumar [PRD 71, 024039 (2005)] for single-spin and equal-mass binaries, to unequal-mass binaries and arbitrary spin configurations. The orbital motion is taken to be quasi-circular and the fractional mass difference is assumed to be small against one. The emitted gravitational waveforms are given in analytic form.