Measurement Of Spin Polarization Research Articles

Polarization in heavy ion collisions: A theoretical review

In these proceedings I discuss the recent progress in the theory of spin polarization in relativistic fluids. To date, a number of studies have begun to examine the impact of the shear tensor on the local spin polarization and whether this contribution can restore agreement between the measurements and the predictions obtained from a polarization induced by the gradients of the plasma. I present the derivation of the spin polarization vector of a fermion at local thermal equilibrium and I discuss the role of pseudo-gauge transformations and of dissipative effects. I list what we can learn from the polarization measured at lower energies. Finally, I discuss possible applications of spin polarization measurements in relativistic heavy ion collisions.

Neumann's principle based eigenvector approach for deriving non-vanishing tensor elements for nonlinear optics.

Physical properties are commonly represented by tensors, such as optical susceptibilities. The conventional approach of deriving non-vanishing tensor elements of symmetric systems relies on the intuitive consideration of positive/negative signflipping after symmetry operations, which could be tedious and prone to miscalculation. Here, we present a matrix-based approach that gives a physical picture centered on Neumann's principle. The principle states that symmetries in geometric systems are adopted by their physical properties. We mathematically apply the principle to the tensor expressions and show a procedure with clear physical intuition to derive non-vanishing tensor elements based on eigensystems. The validity of the approach is demonstrated by examples of commonly known second and third-order nonlinear susceptibilities of chiral/achiral surfaces, together with complicated scenarios involving symmetries such as D6 and Oh symmetries. We then further applied this method to higher-rank tensors that are useful for 2D and high-order spectroscopy. We also extended our approach to derive nonlinear tensor elements with magnetization, which is critical for measuring spin polarization on surfaces for quantum information technologies. A Mathematica code based on this generalized approach is included that can be applied to any symmetry and higher order nonlinear processes.

A simple setup for in situ alkali metal electronic spin polarimetry.

Faraday rotation is considered a gold standard measurement of the electronic spin polarization of an alkali metal vapor produced under optical pumping. However, during the production of large volumes of hyperpolarized xenon gas, transmission monitoring measurements, otherwise known as field cycling measurements, are generally employed to measure the spin polarization of alkali metal atoms in situ as this method is easier to implement than Faraday rotation on standard polarizer setups. Here, we present a simple, low-cost experimental setup to perform Faraday rotation measurements of the electronic spin polarization of alkali metal atoms that can be easily implemented on standard polarizer setups. We then compare Rb polarization measurements obtained with the Faraday rotation method to those obtained with the transmission monitoring method. To our knowledge, a direct comparison of these methods has never been made. Overall, we found good agreement between the two methods, but at low Rb density and high laser power, we found evidence of nonlinear magneto-optical effects that may prevent Faraday rotation from being used under these conditions.

Spin-polarized imaging of the antiferromagnetic structure and field-tunable bound states in kagome magnet FeSn

Kagome metals are an exciting playground for the explorations of novel phenomena at the intersection of topology, electron correlations and magnetism. The family of FeSn-based kagome magnets in particular attracted a lot of attention for simplicity of the layered crystal structure and tunable topological electronic band structure. Despite a significant progress in understanding their bulk properties, surface electronic and magnetic structures are yet to be fully explored in many of these systems. In this work, we focus on a prototypical kagome metal FeSn. Using a combination of spin-averaged and spin-polarized scanning tunneling microscopy, we provide the first atomic-scale visualization of the layered antiferromagnetic structure at the surface of FeSn. In contrast to the field-tunable electronic structure of cousin material Fe3Sn2 that is a ferromagnet, we find that electronic density-of-states of FeSn is robust to the application of external magnetic field. Interestingly, despite the field insensitive electronic band structure, FeSn exhibits bound states tied to specific impurities with large effective moments that strongly couple to the magnetic field. Our experiments provide microscopic insights necessary for theoretical modeling of FeSn and serve as a spring board for spin-polarized measurements of topological magnets in general.

Direct observation of spin polarization in epitaxial Fe3O4(001)/MgO thin films grown by magnetron sputtering

We obtained epitaxial single-crystal Fe3O4(001)/MgO(001) thin films by magnetron sputtering. The high quality of the grown Fe3O4 films was confirmed by reflection high-energy electron diffraction and x-ray photoelectron spectroscopy. Atomic magnetic properties of Fe3O4(001)/MgO(001) were investigated using vibrating sample magnetometry and x-ray magnetic circular dichroism. The values of saturation magnetization and magnetic moment are 407 ± 5 emu/cm3 (3.26 ± 0.04 μB/(f.u.)) and 3.31 ± 0.15 μB/(f.u.), respectively, in the Fe3O4 film as thin as 5 nm, which are close to the bulk values. The spin polarization was directly measured using spin-resolved photoemission spectroscopy. The measured spin polarization has a maximum value of −42% ± 3%, which is comparable to the theoretical value for the (2 × 2)R45° reconstructed Fe3O4(001) surface. Furthermore, the film thickness-dependent measurements indicate that the anti-phase boundaries significantly decrease the spin polarization rather than the lattice mismatch. Our results demonstrate that epitaxial Fe3O4(001)/MgO thin films grown by magnetron sputtering have desired magnetic properties, facilitating the potential application of Fe3O4-based spintronic devices.

Coexistence of antiferromagnetism and superconductivity in Mn/Nb(110)

We report on the structural and magnetic properties of single and double atomic layers of Mn on a clean and unreconstructed Nb(110) substrate. Low-temperature scanning tunneling spectroscopy measurements reveal a proximity-induced superconducting state in the Mn thin films, which are found to grow pseudomorphically on the Nb surface. Spin-polarized scanning tunneling microscopy measurements reveal a c(2x2) antiferromagnetic order in the Mn layers, with an out-of-plane spin-orientation. First-principles density functional theory calculations confirm the experimentally observed magnetic state, which is understood as the consequence of a strong intra- and inter-layer nearest-neighbor antiferromagnetic exchange coupling. These results are expected to be of importance for the design and the investigation of novel superconducting antiferromagnetic spintronic systems.

Measuring Spin Polarization of a Spin-Exchange Relaxation-Free Atomic Magnetometer at Extremely Large Optical Depths

This paper presents a method for measuring the spin polarization of spin-exchange relaxation-free (SERF) atomic magnetometers at extremely large optical depths. Owing to the slowing-down effect, the spin polarization can be extracted by measuring the slowing-down factor extracted from the precession frequency. However, this technique is limited by a significant error in the regime of extremely large optical depths, where the pump beam intensity for achieving the optimized spin polarization of alkali atoms is significantly increased. We observed that the instantaneous precession frequency measured in the regime where the spin-exchange rate is not much larger than the Larmor frequency was no longer a constant but varied with the pump beam intensity. Thus, a method for measuring spin polarization based on the ratio of the precession frequency to the measured instantaneous precession frequency is proposed. Based on the proposed method, the spin polarization at a temperature of 473K and optical depth of 64 is measured. The measurement results were accordant with theoretical analysis. The expanded uncertainties of the experimental results varied between 1.8% and 9.6%. The proposed method is also applicable to other atomic devices operated in the SERF regime with extremely large optical depths, such as co-magnetometers and atomic spin gyroscopes.

Spin polarization induced by the hydrodynamic gradients

We systematically analyze the effects of the derivatives of the hydrodynamic fields on axial Wigner function that describes the spin polarization vector in phase space. We have included all possible first-order derivative contributions that are allowed by symmetry and compute the associated transport functions at one-loop using the linear response theory. In addition to reproducing known effects due to the temperature gradient and vorticity, we have identified a number of potentially significant contributions that are overlooked previously. In particular, we find that the shear strength, the symmetric and traceless part of the flow gradient, will induce a quadrupole for spin polarization in the phase space. Our results, together with hydrodynamic gradients obtained from hydrodynamic simulations, can be employed as a basis for the interpretation of the Λ (anti-Λ) spin polarization measurement in heavy-ion collisions.

A new imaging concept in spin polarimetry based on the spin-filter effect.

The concept of an imaging-type 3D spin detector, based on the combination of spin-exchange interactions in the ferromagnetic (FM) film and spin selectivity of the electron-photon conversion effect in a semiconductor heterostructure, is proposed and demonstrated on a model system. This novel multichannel concept is based on the idea of direct transfer of a 2D spin-polarized electron distribution to image cathodoluminescence (CL). The detector is a hybrid structure consisting of a thin magnetic layer deposited on a semiconductor structure allowing measurement of the spatial and polarization-dependent CL intensity from injected spin-polarized free electrons. The idea is to use spin-dependent electron transmission through in-plane magnetized FM film for in-plane spin detection by measuring the CL intensity from recombined electrons transmitted in the semiconductor. For the incoming electrons with out-of-plane spin polarization, the intensity of circularly polarized CL light can be detected from recombined polarized electrons with holes in the semiconductor. In order to demonstrate the ability of the solid-state spin detector in the image-type mode operation, a spin detector prototype was developed, which consists of a compact proximity focused vacuum tube with a spin-polarized electron source [p-GaAs(Cs,O)], a negative electron affinity (NEA) photocathode and the target [semiconductor heterostructure with quantum wells also with NEA]. The injection of polarized low-energy electrons into the target by varying the kinetic energy in the range 0.5-3.0 eV and up to 1.3 keV was studied in image-type mode. The figure of merit as a function of electron kinetic energy and the target temperature is determined. The spin asymmetry of the CL intensity in a ferromagnetic/semiconductor (FM-SC) junction provides a compact optical method for measuring spin polarization of free-electron beams in image-type mode. The FM-SC detector has the potential for realizing multichannel 3D vectorial reconstruction of spin polarization in momentum microscope and angle-resolved photoelectron spectroscopy systems.

Prediction of spin polarized Fermi arcs in quasiparticle interference in CeBi

We predict that CeBi in the ferromagnetic state is a Weyl semimetal. Our calculations within density functional theory show the existence of two pairs of Weyl nodes on the momentum path $(0,0,{k}_{z})$ at $15\phantom{\rule{0.28em}{0ex}}\mathrm{meV}$ above and $100\phantom{\rule{0.28em}{0ex}}\mathrm{meV}$ below the Fermi level. Two corresponding Fermi arcs are obtained on surfaces of mirror-symmetric (010)-oriented slabs at $E=15\phantom{\rule{0.28em}{0ex}}\mathrm{meV}$ and both arcs are interrupted into three segments due to hybridization with a set of trivial surface bands. By studying the spin texture of surface states, we find the two Fermi arcs are strongly spin polarized but in opposite directions, which can be detected by spin-polarized ARPES measurements. Our theoretical study of quasiparticle interference (QPI) for a nonmagnetic impurity at the Bi site also reveals several features related to the Fermi arcs. Specifically, we predict that the spin polarization of the Fermi arcs leads to a bifurcation-shaped feature only in the spin-dependent QPI spectrum, serving as a fingerprint of the Weyl nodes.

90°-deflection imaging electron analyzer for measuring wide 2D angular distribution and perpendicular spin texture

A 90°-deflection imaging electron analyzer for measuring wide 2D angular distribution and perpendicular spin texture is proposed. This analyzer, which we call “right-angle-deflection imaging analyzer (RADIAN)”, provides electrostatic 90°-deflection and 2D focusing of an electron beam. Here a large acceptance angle comparable to that of cylindrical mirror analyzer (CMA) is achieved without using a grid, while CMA uses grids at the entrance and the exit of an electrostatic field. The 90° deflection allows measuring spin polarization not only in the in-plane direction, but also in the surface-normal direction. Basic properties of RADIAN, calculated by ray tracing, are shown in comparison with those of the most widely used electron energy analyzer, i.e., concentric hemispherical analyzer (CHA). RADIAN has a much higher 2D focusing capability than CHA and allows a much larger acceptance angle for 2D imaging. Moreover, the high focusing capability of RADIAN allows us to obtain high energy resolution comparable to that obtained in CHA. A simple and effective way to achieve higher energy resolution is to combine two or more RADIANs in tandem. Double-pass and triple-pass analyzers in this combination are taken into account. For a practical application, we consider a combination of RADIAN with the recently proposed ±90° omnidirectional photoelectron acceptance lens. RADIAN can be suitably used to develop a wide-angle 2D imaging analyzer, and can also be used to develop a spin-resolved 2D imaging analyzer that can perform perpendicular-spin-texture imaging.

Interlayer magnetism in Fe3−xGeTe2

Fe$_{3-x}$GeTe$_2$ is a layered van der Waals magnetic material with a relatively high ordering temperature and large anisotropy. While most studies have concluded the interlayer ordering to be ferromagnetic, there have also been reports of interlayer antiferromagnetism in Fe$_{3-x}$GeTe$_2$. Here, we investigate the interlayer magnetic ordering by neutron diffraction experiments, scanning tunneling microscopy (STM) and spin-polarized STM measurements, density functional theory plus U calculations and STM simulations. We conclude that the layers of Fe$_{3-x}$GeTe$_2$ are coupled ferromagnetically and that in order to capture the magnetic and electronic properties of Fe$_{3-x}$GeTe$_2$ within density functional theory, Hubbard U corrections need to be taken into account.

Gadolinium-implanted GaN studied by spin-polarized positron annihilation spectroscopy

In this study, Gd ion implantation and annealing were performed at ${900}^{\ensuremath{\circ}}\phantom{\rule{0.16em}{0ex}}\mathrm{C}$ for nominally undoped wurtzite GaN grown by metal-organic chemical vapor deposition. Spin-polarized positron annihilation measurements showed that vacancy clusters including at least 12 vacancies per cluster were the major positron-trapping centers and that the electrons in the vacancy clusters were spin-polarized. These observations could be explained by first-principles calculations. The previous speculation about the defect-assisted ferromagnetism of Gd-implanted GaN may be supported if vacancy clusters are considered.

Majorana bound states in topological insulators with hidden Dirac points

We address the issue whether it is possible to generate Majorana bound states at the magnetic-superconducting interface in two-dimensional topological insulators with hidden Dirac points in the spectrum. In this case, the Dirac point of edge states is located at the energies of the bulk states such that two types of states are strongly hybridized. Here, we show that well-defined Majorana bound states can be obtained even in materials with hidden Dirac point provided that the width of the magnetic strip is chosen to be comparable with the localization length of the edge states. The obtained topological phase diagram allows one to extract precisely the position of the Dirac point in the spectrum. In addition to standard zero-bias peak features caused by Majorana bound states in transport experiments, we propose to supplement future experiments with measurements of charge and spin polarization. In particular, we demonstrate that both observables flip their signs at the topological phase transition, thus, providing an independent signature of the presence of topological superconductivity. All features remain stable against substantially strong disorder.

Bogoliubov Fermi surfaces in spin- 12 systems: Model Hamiltonians and experimental consequences

Bogoliubov Fermi surfaces (BFSs) are topologically protected regions of zero energy excitations in a superconductor whose dimension equals that of the underlying normal state Fermi surface. Examples of Hamiltonians exhibiting this "ultranodal" phase are known to preserve charge-conjugation ($C$) and parity ($P$) but break time-reversal ($T$). In this work, we provide examples of model Hamiltonians that do not necessarily preserve this symmetry pattern but have well-defined sign-changing Pfaffians yielding BFSs. While their topological character has not been recognized previously, some of the models we present have been extensively studied in prior literature. We further examine thermodynamic and electronic properties arising from the ultranodal state. In particular, we study the effect of a weak Zeeman field close to the topological transition and propose distinguishing features of BFSs using residual specific heat and tunneling conductance. Our calculation of the superfluid density in a toy multi-band model indicates a window of interband pairing strength where BFSs are stable with a positive superfluid density. We also present additional signatures of BFSs in spin-polarized spectral weight and total magnetization measurements.

Observation of backscattering induced by magnetism in a topological edge state

The boundary modes of topological insulators are protected by the symmetries of the nontrivial bulk electronic states. Unless these symmetries are broken, they can give rise to novel phenomena, such as the quantum spin Hall effect in one-dimensional (1D) topological edge states, where quasiparticle backscattering is suppressed by time-reversal symmetry (TRS). Here, we investigate the properties of the 1D topological edge state of bismuth in the absence of TRS, where backscattering is predicted to occur. Using spectroscopic imaging and spin-polarized measurements with a scanning tunneling microscope, we compared quasiparticle interference (QPI) occurring in the edge state of a pristine bismuth bilayer with that occurring in the edge state of a bilayer, which is terminated by ferromagnetic iron clusters that break TRS. Our experiments on the decorated bilayer edge reveal an additional QPI branch, which can be associated with spin-flip scattering across the Brioullin zone center between time-reversal band partners. The observed QPI characteristics exactly match with theoretical expectations for a topological edge state, having one Kramer's pair of bands. Together, our results provide further evidence for the nontrivial nature of bismuth and in particular, demonstrate backscattering inside a helical topological edge state induced by broken TRS through local magnetism.

Dead magnetic layers at the interface: Moment quenching through hybridization and frustration

In this paper, the authors combine spin-polarized scanning tunneling microscopy measurements with density functional theory calculations to unravel the magnetic ground state of a Mn double layer on the W(001) surface. The Mn surface layer forms a checkerboard antiferromagnetic state while the subsurface Mn layer appears to be magnetically dead due to strong hybridization with the W substrate

Demonstration of vacuum strain effects on a light-collection lens used in optical polarimetry.

The precision by which an electron spin polarization measurement can be made using a noble-gas polarimeter depends directly on the accuracy of a light-polarization measurement. Since the electron-noble gas collisions occur in a vacuum chamber and the optical polarimeter is generally outside the chamber, this work examines the effect the vacuum window has on the perceived optical polarization. A model light source, lens system, and optical polarimeter are used that approximate the situation found in a typical atomic physics experiment. It was demonstrated that a pressure difference of 1 atm on a lens will alter the perceived polarization by as much as 0.05% with typical borosilicate (BK) lenses. This effect was demonstrated to scale with the thickness of the lens used and changes signs when the direction of the stress is reversed.

Tunable magnetism of a single-carbon vacancy in graphene

Creating a single-carbon vacancy introduces (quasi-)localized states for both σ and π electrons in graphene. Theoretically, interactions between the localized σ electrons and quasilocalized π electrons of a single-carbon vacancy in graphene are predicted to control its magnetism. However, experimentally confirming this prediction through manipulating the interactions remains an outstanding challenge. Here we report the manipulation of magnetism in the vicinity of an individual single-carbon vacancy in graphene by using a scanning tunnelling microscopy (STM) tip. Our spin-polarized STM measurements, complemented by density functional theory calculations, indicate that the interactions between the localized σ and quasilocalized π electrons could split the π electrons into two states with opposite spins even when they are well above the Fermi level. Via the STM tip, we successfully manipulate both the magnitude and direction of magnetic moment of the π electrons with respect to that of the σ electrons. Three different magnetic states of the single-carbon vacancy, exhibiting magnetic moments of about 1.6 μB, 0.5 μB, and 0 μB respectively, are realized in our experiment.

Isotropic Magnetoelectric Effect in Multiferroic Material Studied by Resonant X-ray Scattering

Isotropic ME effect was observed in multiferroic Tb1-xGdxMn2O5, where electric polarization reappears along the b axis as a response to application of a magnetic field along each crystallographic axis. This isotropic ME effect is distinct from those observed in other RMn2O5 and multiferroic materials. Employing resonant X-ray scattering, we revealed that the isotropic ME effect is attributed to competition between two different magnetic ordering. In addition, measurement of oxygen spin polarization under magnetic field suggests that charge transfer between Mn and O ions have microscopic contribution to the ME effect.