Order Spin Orbit Research Articles

Spinning compact binary inspiral. II. Conservative angular dynamics

We establish the evolution equations of the set of independent variables characterizing the 2PN rigorous conservative dynamics of a spinning compact binary, with the inclusion of the leading order spin-orbit, spin-spin and mass quadrupole - mass monopole effects, for generic (noncircular, nonspherical) orbits. More specifically, we give a closed system of first order ordinary differential equations for the orbital elements of the osculating ellipse and for the angles characterizing the spin orientations with respect to the osculating orbit. We also prove that (i) the relative angle of the spins stays constant for equal mass black holes, irrespective of their orientation, and (ii) the special configuration of equal mass black holes with equal, but antialigned spins, both laying in the plane of motion (leading to the largest recoil found in numerical simulations) is preserved at 2PN level of accuracy, with leading order spin-orbit, spin-spin and mass quadrupolar contributions included.

ChemInform Abstract: Cobalt(II) Single‐Molecule Magnets

AbstractReview: 49 refs

Motion and gravitational wave forms of eccentric compact binaries with orbital-angular-momentum-aligned spins under next-to-leading order in spin–orbit and leading order in spin(1)–spin(2) and spin-squared couplings

A quasi-Keplerian parameterization for the solutions of second post-Newtonian (PN) accurate equations of motion for spinning compact binaries is obtained including leading order spin–spin and next-to-leading order spin–orbit interactions. Rotational deformation of the compact objects is incorporated. For arbitrary mass ratios the spin orientations are taken to be parallel or anti-parallel to the orbital angular momentum vector. The emitted gravitational wave forms are given in analytic form up to 2PN point particle, 1.5PN spin–orbit and 1PN spin–spin contributions, whereby the spins are assumed to be of 0PN order.

Spinning compact binary inspiral: Independent variables and dynamically preserved spin configurations

We establish the set of independent variables suitable to monitor the complicated evolution of the spinning compact binary during the inspiral. Our approach is valid up to the second post-Newtonian order, including leading order spin-orbit, spin-spin and mass quadrupol-mass monopole effects, for generic (noncircular, nonspherical) orbits. Then we analyze the conservative spin dynamics in terms of these variables. We prove that the only binary black hole configuration allowing for spin precessions with equal angular velocities about a common intantaneous axis roughly aligned to the normal of the osculating orbit, is the equal mass and parallel (aligned or antialigned) spin configuration. This analytic result puts limitations on what particular configurations can be selected in numerical investigations of compact binary evolutions, even in those including only the last orbits of the inspiral.

Low spin moment due to hidden multipole order from spin-orbital ordering in LaFeAsO

This work presents new development and applications of ab-initio simulation tools for material science. Focus lies on materials with strong electronic correlation and strong spin-orbit coupling. Improvements on methods for solving the impurity problem in LDA+DMFT is presented, as well as a reliant method for charge self-consistency in a LMTO based electronic structure code. A new adaptive scheme for Brillouin zone integration is developed, where we show a strong reduction of numerical noise compared to standard techniques. A reformulation of the standard LDA+U method aiming to reduce the number of free parameters is introduced. Fast and realistic reduction of the number of free parameters provides the possibility of high throughput calculations and enabled us to study a large number of compounds. An analysis method for polarization in terms of coupled multipoles, and their corresponding energy contributions is developed and applied. This led to the formulation of Katt's rules, a set of rules complementary to Hund's rules. Katt's rules applies for occupying the orbitals of an electronic shell with strong spin-orbit coupling. The analysis is also used to investigate the unconventional Uranium based superconductors URu2Si2, UPt3, UPd2Al3 and UNi2Al3, as well as the high temperature superconductor LaOFeAs. We also investigate the non-magnetic delta-phase of Plutonium, providing insight to the electronic structure and the branching ratios of 4d to 5f transitions seen in photo emission spectra.The influence of surface reconstruction on the magneto crystalline anisotropy is investigated in multilayer Fe/ZnSe, showing that Fe deposited on an unreconstructed interface strongly reduces the uniaxial component of the MAE. We provide a detailed understanding of the magnetic properties of Fe2P, opening possible routes for enhancing the MAE in this system. A general route to strong MAE in nano-laminates is presented, we apply this to propose a candidate with extremely strong anisotropy energy density, 5Fe/2W1-xReX for x=[0.6-0.8].

Comment on two recent papers regarding next-to-leading order spin-spin effects in gravitational interaction

It is argued that the tetrad in a recent paper by Porto and Rothstein on gravitational spin-spin coupling should not have the given form. The fixation of that tetrad was suggested by Steinhoff, Hergt, and Sch\"afer as a possible source for the disagreement found in the spin-squared dynamics. However, this inconsistency will only show up in the next-to-leading order spin-orbit dynamics and not in the spin-squared dynamics. Instead, the disagreement found at the next-to-leading order spin-squared level is due to a sign typo in the spin-squared paper by Porto and Rothstein.

Recoil velocity at second post-Newtonian order for spinning black hole binaries

We compute the flux of linear momentum carried by gravitational waves emitted from spinning binary black holes at second post-Newtonian (2PN) order for generic orbits. In particular we provide explicit expressions of three new types of terms, namely, next-to-leading order spin-orbit terms at 1.5 post-Newtonian (1.5PN) order, spin-orbit tail terms at 2PN order, and spin-spin terms at 2PN order. Restricting ourselves to quasicircular orbits, we integrate the linear-momentum flux over time to obtain the recoil velocity as function of orbital frequency. We find that in the so-called superkick configuration the higher-order spin corrections can increase the recoil velocity up to a factor $\ensuremath{\sim}3$ with respect to the leading-order PN prediction. Whereas the recoil velocity computed in PN theory within the adiabatic approximation can accurately describe the early inspiral phase, we find that its fast increase during the late inspiral and plunge, and the arbitrariness in determining until when it should be trusted, makes the PN predictions for the total recoil not very accurate and robust. Nevertheless, the linear-momentum flux at higher PN orders can be employed to build more reliable resummed expressions aimed at capturing the nonperturbative effects until merger. Furthermore, we provide expressions valid for generic orbits, and accurate at 2PN order, for the energy and angular momentum carried by gravitational waves emitted from spinning binary black holes. Specializing to quasicircular orbits we compute the spin-spin terms at 2PN order in the expression for the evolution of the orbital frequency and found agreement with Mik\'oczi, Vas\'uth, and Gergely. We also verified that in the limit of extreme mass ratio our expressions for the energy and angular momentum fluxes match the ones of Tagoshi, Shibata, Tanaka, and Sasaki obtained in the context of black hole perturbation theory.

Spin fluctuations and orbital ordering in quasi-one-dimensional α-Cu(dca) 2(pyz) {dca = dicyanamide = N(CN) 2−; pyz = pyrazine}, a molecular analogue of KCuF 3

The magnetic properties of α-Cu(dca) 2(pyz) were examined by magnetic susceptibility, magnetization, inelastic neutron scattering (INS), muon-spin relaxation (μSR) measurements and by first-principles density functional theoretical (DFT) calculations and quantum Monte Carlo (QMC) simulations. The χ versus T curve shows a broad maximum at 3.5 K, and the data between 2 and 300 K is well described by an S = 1/2 Heisenberg uniform chain model with g = 2.152(1) and J/ k B = −5.4(1) K. μSR measurements, conducted down to 0.02 K and as a function of longitudinal magnetic field, show no oscillations in the muon asymmetry function A( t). This evidence, together with the lack of spin wave formation as gleaned from INS data, suggests that no long-range magnetic order takes place in α-Cu(dca) 2(pyz) down to the lowest measured temperatures. Electronic structure calculations further show that the spin exchange is significant only along the Cu–pyz–Cu chains, such that α-Cu(dca) 2(pyz) can be described by a Heisenberg antiferromagnetic chain model. Further support for this comes from the M versus B curve, which is strongly concave owing to the reduced spin dimensionality. α-Cu(dca) 2(pyz) is a molecular analogue of KCuF 3 owing to d x 2 - y 2 orbital ordering where nearest-neighbor magnetic orbital planes of the Cu 2+ sites are orthogonal in the planes perpendicular to the Cu–pyz–Cu chains.

3D spin density and orbital ordering of YTiO3observed by X-ray magnetic diffraction experiment

3D spin density and orbital ordering of YTiO₃observed by X-ray magnetic diffraction experiment

Measures of basins of attraction in spin-orbit dynamics

We consider a dissipative spin-orbit model where it is assumed that the orbit of the satellite is Keplerian, the obliquity is zero, and the dissipative effects depend linearly on the relative angular velocity. The measure of the basins of attraction associated to periodic and quasi-periodic attractors is numerically investigated. The results depend on the interaction among the physically relevant parameters, namely, the orbital eccentricity, the equatorial oblateness and the dissipative constant. In particular, it appears that, for astronomically relevant parameter values, for low eccentricities (as in the Moon’s case) about 96% of the initial data belong to the basin of attraction of the 1/1 spin-orbit resonance; for larger values of the eccentricities higher order spin-orbit resonances and quasi-periodic attractors become dominant providing a mechanism for explaining the observed state of Mercury into the 3/2 resonance.

In SituPhotoemission Study ofPr1−xCaxMnO3Epitaxial Thin Films with Suppressed Charge Fluctuations

We have performed an in situ photoemission study of Pr1-xCaxMnO3 (PCMO) thin films grown on LaAlO3 (001) substrates and observed the effect of epitaxial strain on the electronic structure. We found that the chemical potential shifted monotonically with doping, unlike bulk PCMO, implying the disappearance of incommensurate charge fluctuations of bulk PCMO. In the valence-band spectra, we found a doping-induced energy shift toward the Fermi level (EF) but there was no spectral weight transfer, which was observed in bulk PCMO. The gap at EF was clearly seen in the experimental band dispersions determined by angle-resolved photoemission spectroscopy and could not be explained by the metallic band structure of the C-type antiferromagnetic state, probably due to localization of electrons along the ferromagnetic chain direction or due to another type of spin-orbital ordering.

Phase transition and critical properties of spin–orbital interacting systems

Abstract Phase transition and critical properties of Ising-like spin–orbital interacting systems in 2-dimensional triangular lattice are investigated. We first show that the ground state of the system is a composite spin–orbital ferro-ordered phase. Though Landau effective field theory predicts the second-order phase transition of the composite spin–orbital order, however, the critical exponents obtained by the renormalization group approach demonstrate that the spin–orbital order–disorder transition is far from the second-order, rather, it is more close to the first-order. The unusual critical behavior near the transition point is attributed to the fractionalization of the composite order parameter.

Ion beam induced modification of exchange interaction and spin–orbit coupling in the Co2FeSi Heusler compound

A Co2FeSi (CFS) film with L21 structure was irradiated with different fluences of 30 keV Ga+ ions. Structural modifications were subsequently studied using the longitudinal (LMOKE) and quadratic (QMOKE) magneto-optical Kerr effect. Both the coercivity and the LMOKE amplitude were found to show a similar behaviour upon irradiation: they are nearly constant up to ion fluences of ≈6 × 1015 ion cm−2, while they decrease with further increasing fluences and finally vanish at a fluence of ≈9 × 1016 ion cm−2, when the sample becomes paramagnetic. However, contrary to this behaviour, the QMOKE signal nearly vanishes even for the smallest applied fluence of 3 × 1014 ion cm−2. We attribute this reduction of the QMOKE signal to an irradiation-induced degeneration of second or higher order spin–orbit coupling, which already happens at small fluences of 30 keV Ga+ ions. On the other hand, the reduction of coercivity and LMOKE signal with high ion fluences is probably caused by a reduction of the exchange interaction within the film material.

Exciton‐spin relaxation in weakly confining quantum dots due to spin–orbit interaction

AbstractIn weakly confining quantum structures such as interfacial islands or quantum disks the exciton‐spin relaxation is governed by two independent electron and hole spin flip processes between the optically active and dark states. A microscopic theory for these transitions is presented which is based on second order spin–orbit and carrier–phonon interaction processes. We found that the sequential relaxation between bright and dark states leads to much faster exciton‐spin relaxation than for strongly confining (“small”) quantum dots where the dominant process stems from electron–hole exchange interaction plus hole deformation potential coupling. In addition, the fast exciton spin relaxation implies that the (exciton‐bound) electron spin flip time is also much shorter than for a single electron. (© 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

The spin−orbit energy estimated from two-component spin−orbit calculations as correction terms for the Gaussian-2 (G2) theory

Two-component relativistic effective core potential (RECP) approaches are employed to derive spin–orbit energies from the energy difference of spin–orbit two-component RECP and spin averaged RECP calculations. These spin–orbit energies include both the spin–orbit splitting of open-shell species and the higher order spin–orbit contributions for all species. The present spin–orbit energies, which can be estimated from the single reference configuration calculations at various levels of theory such as Hartree–Fock and coupled-cluster methods, are utilized as additional correction terms in the Gaussian-2 (G2) theory for Br and I containing species. The improvement in reaction energies due to the present scheme is similar to those reported for other types of spin–orbit calculations based on multireference configuration interaction calculations. The present scheme straightforwardly provides spin–orbit correction terms for the compounded methods such as the G2 theory. Even the spin–orbit corrections at the HF level are reliable enough to improve the performance of the G2 theory, reducing the error to the chemical accuracy (±0.1 eV or 2 kcal mol−1) that is the target prescribed in G2 theory.

Spin Frustration and Orbital Order in Vanadium Spinels

We present the results of our theoretical study on the effects of geometrical frustration and the interplay between spin and orbital degrees of freedom in vanadium spinel oxides $A$V$_2$O$_4$ ($A$ = Zn, Mg or Cd). Introducing an effective spin-orbital-lattice coupled model in the strong correlation limit and performing Monte Carlo simulation for the model, we propose a reduced spin Hamiltonian in the orbital ordered phase to capture the stabilization mechanism of the antiferromagnetic order. Orbital order drastically reduces spin frustration by introducing spatial anisotropy in the spin exchange interactions, and the reduced spin model can be regarded as weakly-coupled one-dimensional antiferromagnetic chains. The critical exponent estimated by finite-size scaling analysis shows that the magnetic transition belongs to the three-dimensional Heisenberg universality class. Frustration remaining in the mean-field level is reduced by thermal fluctuations to stabilize a collinear ordering.

Spin Wave and Orbital Ordering in the C-type Antiferromagnetic Phase of Nd1-xSrxMnO3

Spin Wave and Orbital Ordering in the C-type Antiferromagnetic Phase of Nd_1-<i>x</i>Sr_<i>x</i>MnO₃

Ab initio calculations of vibronic activity in phosphorescence microwave double resonance spectra of p-dichlorobenzene

The phosphorescence spectrum of p-dichlorobenzene has been calculated using multiconfiguration self-consistent-field wave functions and the quadratic response technique. Attention has been paid to the intensity distribution of the singlet–triplet (3B1 u →1A g ) transition through a number of vibronic subbands. The second order spin–orbit coupling (SOC) contribution to the spin splitting of the 3B1 u (3ππ*) state is found to be almost negligible, and the calculations therefore provide a good estimate for the zero-field splitting (ZFS) parameters based only on the electron spin–spin coupling expectation values. Nuclear quadrupole resonance constants for the different Cl isotopes are also calculated to accomplish the ZFS assignment. The electric dipole activity of the spin sublevels in the triplet–singlet transitions to the ground-state vibrational levels is estimated by calculations of derivatives using distorted geometries which are shifted from the equilibrium position along different vibrational modes. A vibrational analysis of the phosphorescence spectrum, based on the SOC-induced mixing of the singlet and triplet states calculated along different vibrational modes, provides reasonable agreement with experimental data.

Fourier transform spectroscopy of NbS

Emission bands attributed to the NbS radical have been observed in the near infrared and visible regions with FTS techniques using an electrodeless 2450 MHz discharge as a source. Transitions within the doublet and quartet manifolds were recorded at high resolution. The present paper gives the first rotational analysis of this molecule. Numerous bands within the doublet and quartet manifolds have been analyzed, resulting in the characterization of seven different electronic states, three in the doublet and four in the quartet manifold. The states have been labeled in analogy with NbO. The analyzed electronic states are: X 4 Σ −, C 4 Σ −, A′ 4 Φ, D 4 Δ, a 2 Δ, c 2 Π, and e 2 Φ. Four additional substates in the doublet manifold have also been analyzed. In all, 27 vibrational sublevels have been included in the analysis, the total number of rotational lines being about 18 000. The positions of the analyzed transitions are: C 4 Σ − → X 4 Σ − near 15 670 cm −1, D 4 Δ → A′ 4 Φ near 7740 cm −1, c 2 Π → a 2 Δ near 5850 cm −1 and e 2 Φ → a 2 Δ near 8500 cm −1. The overall picture is consistent with the corresponding analysis of NbO. However, three energy separations could not be derived from the experimental data in the case of NbS, i.e., the a 2 Δ− X 4 Σ −, A′ 4 Φ− X 4 Σ − and a 2 Δ 5/2– a 2 Δ 3/2 splittings. These were set to 4992, 5490, and 992 cm −1, respectively, from preliminary ab initio calculations. In this way, a tentative energy level scheme could be drawn. The first order spin–orbit parameter of the A′ 4 Φ state was indeterminable from the experimental data and was set to the value 170 cm −1, derived from the same calculations.

Jahn–Teller effect in the organic ferromagnet TDAE–C 60

We report on the measurements of the 13C NMR lineshape in the organic ferromagnet TDAE–C 60 between room temperature and 4 K as well as on a simulation of the lineshape in this temperature interval. It is shown that the sudden increase in the inhomogeneous 13C NMR linewidth in the middle of the ferromagnetic phase can be explained by the freeze out of the pseudorotations of the axes of the Jahn–Teller distortions of the C 60 − ions. The correlation times for the Jahn–Teller dynamics of the C 60 − ions have been extracted from a comparison of experimental and simulated 13C NMR lineshapes. A strong correlation between spin ordering and orbital ordering has been found.