Spin-dependent Momentum Distribution Research Articles

Magnetic supersolid phases of two-dimensional extended Bose–Hubbard model with spin–orbit coupling

We investigate the quantum phases and phase transitions for spin–orbit coupled two-species bosons with nearest-neighbor (NN) interaction in a two-dimensional square lattice using inhomogeneous dynamical Guztwiller mean-field method. Under the effect of spin–orbit coupling and NN interaction, we uncover a rich variety of different magnetic supersolid (SS) phases. In the presence of intraspecies NN interaction, the phase diagram exhibits the phase-twisted double-checkerboard SS (PT-DCSS) and phase-striped double-checkerboard SS (PS-DCSS) phases. For both intra- and interspecies NN interactions, apart from the phase-twisted lattice SS (PT-LSS) and phase-striped lattice SS (PS-LSS) phases, some nontrivial SS phases with interesting properties occur. More importantly, we find that the emergences of these nontrivial SS phases are dependent of the interspecies on-site interaction. To further characterize the SS phases, we also discuss the spin-dependent momentum distributions and magnetic textures. The magnetic textures, such as antiferromagnetic, spiral and stripe orders are shown. Finally, we give the fully analytical insights into the numerical results.

Creating Spin-One Fermions in the Presence of Artificial Spin–Orbit Fields: Emergent Spinor Physics and Spectroscopic Properties

We propose the creation and investigation of a system of spin-one fermions in the presence of artificial spin–orbit coupling, via the interaction of three hyperfine states of fermionic atoms to Raman laser fields. We explore the emergence of spinor physics in the Hamiltonian described by the interaction between light and atoms, and analyze spectroscopic properties such as dispersion relation, Fermi surfaces, spectral functions, spin-dependent momentum distributions and density of states. Connections to spin-one bosons and SU(3) systems is made, as well relations to the Lifshitz transition and Pomeranchuk instability are presented.

Spin-orbit-driven transitions between Mott insulators and finite-momentum superfluids of bosons in optical lattices

Synthetic spin-orbit coupling in ultracold atomic gases can be taken to extremes rarely found in solids. We study a two dimensional Hubbard model of bosons in an optical lattice in the presence of spin-orbit coupling strong enough to drive direct transitions from Mott insulators to superfluids. Here we find phase-modulated superfluids with finite momentum that are generated entirely by spin-orbit coupling. We investigate the rich phase patterns of the superfluids, which may be directly probed using time-of-flight imaging of the spin-dependent momentum distribution.

Experimental studies of few-body systems at MAMI

Few-body experiments at the Mainz Microtron were focused on a number of selected topics. Double-polarization experiments to determine the neutron electric form factor Gen have been performed using both deuterium and polarized helium-3 targets. The structure of 3He has been studied in the reactions 3H e e(ee,e′n) and 3H e e(ee,e′p) with large (transversal) missing momenta and in quasi-elastic electron scattering. Electromagnetically induced two-nucleon knockout has been investigated in order to study the role of correlated nucleon-nucleon motion in the nucleus. Measurements of the (e,e′pn) reaction on 3He and 16O were performed for the first time. A triple-polarization experiment of type 3H e e(ee,e′ep)d has been performed, where, in addition, the spin of the knocked out proton is analyzed. This measurement provides information on the spin-dependent momentum distribution of proton-deuteron clusters in the 3He nucleus. Hence, by tagging the outgoing deuteron spin-polarized 3He might also serve as an effective polarized proton target for electron scattering experiments. Moreover, in inclusive 3,4He(e,e′) measurements at low momentum transfer, the effect of 3-body-forces has been studied.

Experiments on few-nucleon systems at MAMI

The experimental effort at the Mainz Microtron with respect to few-body physics is focused on a number of selected topics. The structure of 3He has been studied in the reactions \(^3\vec{{\rm H}}{\rm e}(\vec{e},e{\prime}n)\) and \(^3\vec{{\rm H}}{\rm e}(\vec{e},e{\prime}p)\) with large (transversal) missing momenta and in quasi-elastic electron scattering. Experiments to determine the neutron electric form factor G en have been performed – a measurement at a four-momentum transfer Q 2 ∼ 1.5(GeV/c)2 took place in July 2007. Electromagnetically induced two-nucleon knockout has been investigated in order to study the role of correlated nucleon-nucleon motion in the nucleus. Measurements of the (e,e′ pn) reaction on 3He and 16O were performed for the first time. A triple-polarization experiment of type \(^3\vec{{\rm H}}{\rm e}(\vec{e},e{\prime}\vec{p})d\) has been performed in August 2007, where, in addition, the spin of the knocked-out proton is analyzed. This measurement provides information on the spin-dependent momentum distribution of proton-deuteron clusters in the 3He nucleus. By using this deuteron-tagging method spin-polarized 3He might also serve as an effective polarized proton target for electron scattering experiments.

Spin dependent momentum distributions of proton-deuteron clusters in3Hefrom electron scattering on polarized3He:Theoretical predictions

The process $\overrightarrow{^3{\rm He}}(e,e'\vec{p})d $ (or $\overrightarrow{^3{\rm He}}(e,e'\vec{d})p $) is studied theoretically in a Faddeev treatment with the aim to have access to the spin-dependent momentum distribution of ${\vec p} {\vec d} $ clusters in polarized $^3$He. Final state interactions and meson exchange currents turn out to have a strong influence in the considered kinematical regime (below the pion threshold). This precludes the direct access to the momentum distribution except for small deuteron momenta. Nevertheless, the results for the longitudinal and transverse response functions are interesting as they reflect our present day understanding of the reaction mechanism and therefore data would be very useful.

Few-body physics with polarized beams and targets at IUCF

An experiment utilizing a polarized 3He target and other 3-nucleon experiments at the Indiana University Cyclotron Facility are discussed. The 3 He ( p , pN) reaction has been used to investigate the spin dependent momentum distributions of protons and neutrons in 3He. It was found that with large momentum transfer the PWIA is valid, thus allowing extraction of the distributions directly from the data. A similar experiment is currently under preparation to investigate the spin structure of the deuteron via the 2 H ( p , pN) reaction. Other experiments will study n-d and p-d breakup spin observables in final state interaction kinematics where intermediate energy Faddeev calculations predict large 3-body force effects.

Spin Dependent Momentum Distributions in Deformed Nuclei

We study the properties of the spin-dependent one-body density in momentum space for odd- A polarized deformed nuclei within the mean field approximation. We derive analytic expressions connecting intrinsic and laboratory momentum distributions. The latter are related to observable transition densities in p-space that can be proved in one nucleon knockout reactions from polarized targets. It is shown that most of the information contained in the intrinsic spin-dependent momentum distribution is lost when the nucleus is not polarized. Results are presented and discussed for two prolate nuclei, 21Ne and 25Mg, and for one oblate nucleus, 37Ar. The effects of deformation are highlighted by comparison to the case of odd- A nuclei in the spherical model.

Calculation of spin-dependent momentum distributions in iron: Compton scattering and positron annihilation

Spin-dependent momentum distributions in ferromagnetic iron are calculated in detail using the linear combination of Gaussian orbitals method. Theoretical results for Compton scattering and positron annihilation are presented in the form of momentum distributions, Compton profiles, one-dimensional angular correlation of annihilation radiation curves, Lock-Crisp-West folded plots and reciprocal form factors B(z), and are compared with experiment wherever possible. It is observed that the present theoretical results show satisfactory agreement with experiment. It is further observed that although the different theories (e.g. augmented plane waves, linear muffin-tin orbitals, present linear combination of Gaussian orbitals) agree among each other about the spin-dependent momentum distributions in ferromagnetic iron, minor differences exist between these theories and experiment. These differences are ascribed to the limitations of the independent-particle approximation, in particular to the effects of non-locality, e--e- and e+-e- many-body correlations, etc.

Magnetic compton scattering with circularly polarised synchrotron radiation

The spin-dependent momentum distributions in iron and a few other ferromagnets have now been measured with circularly polarised radiation in the 30–60 keV energy range, obtained by viewing the tangent point of the Daresbury Synchrotron wiggler line at a small angle (<0.2 mrad) to the orbital plane. Even at four times the critical energy of the wiggler, radiation with 70% circular polarisation can be selected and scattered beam count rates approaching 10 3 achieved by matching the monochromator pass band to the resolution of the solid state detector. New data on ferromagnetic iron show a smaller negative polarisation effect than the earlier experiments, in line with recent measurements elsewhere, but the central dip remains larger than either the APW or KKR predictions. Recently the anisotropy in the spin-dependent momentum distribution has been measured in a new experiment using transmission geometry and this shows that the disagreement is strongly associated with the [100] projection direction.

Spin-dependent momentum distribution in iron studied with circularly polarized synchrotron radiation.

The spin-dependent Compton profile of ferromagnetic iron has been measured with circularly polarized synchrotron radiation extracted at 46 and 62 keV from the Daresbury storage ring by viewing radiation from the 5-T magnet at 0.24 mrad above and below the electron orbital plane. For the first time (to our knowledge) in a photon scattering experiment the line shape is well established. The negative magnetization resulting from $s\ensuremath{-}p$ polarization is evident here as a 25% dip around zero momentum, which is greater than that predicted by an augmented-plane-wave calculation of this effect.

Magnetic compton scattering with circularly polarised synchrotron radiation

The Compton cross-section contains a term which couples the electron spin to the circularly polarised radiation field making it possible, in principle at least, to study the spin-dependent momentum distribution of electrons in ferromagnetic materials. The intensity of circularly polarised synchrotron radiation, emitted at a small angle to the orbital plane of the circulating electrons has been calculated for the three-pole wiggler magnet on the new Synchrotron Radiation Source (SRS) at the Daresbury Laboratory. The feasibility of a magnetic Compton scattering experiment, in which this component of the beam is selected, has been evaluated for wavelengths in the range 0.1 Å to 1.0 Å. The results, calculated for a 5 mm thick magnetised iron sample, show that, within the life-time of the stored synchrotron beam (≈ 8 h) more than 10 6 counts should be accumulated under the spin-dependent Compton profile. This intensity approaches that of conventional Compton experiments with unpolarised gamma-ray sources and clearly indicates that studies of ferromagnetic materials in the wavelength region 0.25–0.5 Å should be possible on the SRS and other similar machines.

Determination of the spin-dependent electron momentum distribution by double Compton scattering

The method of double Compton scattering for obtaining the electron spin-dependent momentum distribution is analyzed. It is shown that the effect, although small, is sufficiently large to be measured by present Compton-scattering experiments.

Spin-dependent momentum distribution in iron

Spin-dependent Compton profiles and positron annihilation angular distributions were calculated by the APW method for ferromagnetic iron and compared with the corresponding experiments. Good agreement obtained between theory and experiment on positron annihilation may support the calculated band structure over the complete extent of the occupied bands, especially the results obtained by the present theory for the s-d hybridization occurring in the d-bands.

Magnetic Scattering of X Rays from Electrons in Molecules and Solids

The scattering of moderately high-energy x rays from electrons in magnetic solids is analyzed. We show that (a) the incoherent Compton scattering of polarized x rays can be used to determine the spin-dependent momentum distribution function of electrons in ferromagnetic materials, and (b) the coherent Bragg scattering of unpolarized x rays can be used to determine the magnetic structure of antiferromagnetic solids below their transition temperature.