Spin Momentum Densities Research Articles

On the orbit-induced spin density of tightly focused optical vortex beams: ellipticity and helicity

It has recently been established that a linearly-polarized optical vortex possesses spin angular momentum density in the direction of propagation (longitudinal spin) under tight-focusing. The helicity of light has long been associated with longitudinal spin angular momentum. Here we show that the longitudinal spin density of linearly-polarized vortices is anomalous because it has no associated helicity. It was also recently determined that the polarization-independent helicity of tightly-focused optical vortices is associated with their transverse spin momentum density. The key finding of this work is the fact that, in general, longitudinal spin can not necessarily be associated with helicity, and transverse spin is in general not associated with a zero helicity, and such extraordinary behaviour manifests most clearly for optical vortices under non-paraxial conditions.

Optical helicity of unpolarized light

Recently arXiv:2004.02970 showed that the extraordinary transverse spin momentum density of spatially confined optical fields is largely independent of polarization. Here it is shown that 3D structured optical vortices which possess the phase factor $exp(il\phi)$ have a contribution to the optical helicity density which is completely independent of polarization. In stark contrast to what is known in classical optics with plane waves and paraxial light, the physical consequence is that unpolarized light can exhibit optical activity and chiral light-matter interactions.

Bulk and element-specific magnetism of medium-entropy and high-entropy Cantor-Wu alloys

Magnetic Compton scattering, x-ray magnetic circular dichroism spectroscopy and bulk magnetometry measurements are performed on a set of medium (NiFeCo and NiFeCoCr) and high (NiFeCoCrPd and NiFeCoCrMn) entropy Cantor-Wu alloys. The bulk spin momentum densities determined by magnetic Compton scattering are remarkably isotropic, and this is a consequence of the smearing of the electronic structure by disorder scattering of the electron quasiparticles. Non-zero x-ray magnetic circular dichroism signals are observed for every element in every alloy indicating differences in the populations of the majority and minority spin states implying finite magnetic moments. When Cr is included in the solid solution, the Cr spin moment is unambiguously antiparallel to the total magnetic moment, while a vanishingly small magnetic moment is observed for Mn, despite calculations indicating a large moment. Some significant discrepancies are observed between the experimental bulk and surface magnetic moments. Despite the lack of quantitative agreement, the element specific surface magnetic moments seem to be qualitatively reasonable.

Study of magnetism in Fe doped CoCr2O4 using magnetic Compton scattering and first-principles computations

Temperature dependent spin momentum densities of polycrystalline CoCr2-xFexO4 (x = 0.4 and 1) with inverse spinel structure have been measured using magnetic Compton spectrometer. Estimated site specific and absolute spin moments are compared with the magnetization measurements to deduce the orbital magnetic moments. To supplement the present magnetic Compton scattering data, spin-polarized relativistic band structure calculations employing Korringa-Kohn-Rostoker Green’s-function formalism have also been performed. Ferri-magnetic nature of CoCr2-xFexO4 (x = 0.4 and 1) systems have been explained on the basis of distribution of Fe and Co atoms between tetrahedral and octahedral sites. The suggested mixed spinel structure arrangement is supported by experimentally observed spin magnetic moments and minimum ground state energies which shows the potential of magnetic Compton spectroscopy in resolving the structural-cum-magnetic issues of such oxides.

Calculating energy density and spin momentum density of Moon’s gravitational waves in rectilinear coordinates

In this research the energy density was calculated and the spin momentum density of Moon’s gravitational waves in the rectilinear coordinates’ system of Moon’s gravity and Earth’s global temperature. At first, we assumed an action principle that combines the gravitational field and gravitational waves, which formulate a closed system, together with Earth’s global temperature. And, then, we calculated the energy densities of those energy field and waves, which are calculated as their variances in the rectilinear coordinates, also to calculate their coefficients and standard errors of the calculated coefficients. The calculated results are consistent with the findings of our previous research [1], which shows the negative contribution of gravitational waves to Earth’s global temperature, while the gravitational field positively contributes to the global temperature. We also calculated spin momentum of Moon’s gravitational waves in the system of rectilinear coordinates.

Magnetic properties and spin momentum densities of Ni excess Ni-Mn-Sn Heusler alloys

Abstract The role of excess Ni in Ni2+xMn1−xSn (x = 0.05, 0.1) Heusler alloys has been reported using temperature dependent magnetic Compton spectroscopy. The experimental Compton profiles from magnetic electrons have been analyzed to quantify the contribution of Mn 3d electrons, Ni sites and sp-electrons in building-up the total spin moments. The experimentally deduced spin momentum densities, total and element-specific spin moments are examined using theoretical investigations within the spin polarized relativistic Korringa-Kohn-Rostoker method. The build-up of spin moments has been explored in terms of total and projected density of states. Site-dependent Ni magnetic moment is also discussed. Heisenberg exchange coupling parameters are also computed to study the change in Ruderman-Kittel-Kasuya-Yosida type exchange interaction on increasing Ni concentration in the Ni-Mn-Sn system.

Transverse spin in the scattering of focused radially and azimuthally polarized vector beams

We study the effect of focusing of the radially and azimuthally polarized vector beams on the spin angular momentum (SAM) density and Poynting vector of scattered waves from a Mie particle. Remarkably, the study reveals that the SAM density of the scattered field is solely transverse in nature for radially and azimuthally polarized incident vector beams; however the Poynting vector shows usual longitudinal character. We also demonstrate that the transverse SAM density can further be tuned with wavelength and focusing of the incident beam by exploiting the interference of different scattering modes. These results may stimulate further experimental technique of detecting the transverse spin and Belinfante's spin-momentum densities.

Magnetic Compton scattering study of Laves phase ZrFe2 and Sc doped ZrFe2: Experiment and Green function based relativistic calculations

Spin momentum densities of ferromagnetic ZrFe2 and Zr0.8Sc0.2Fe2 have been measured using magnetic Compton scattering with 182.65 keV circularly polarized synchrotron radiations. Site specific spin moments, which are responsible for the formation of total spin moment, have been deduced from Compton line shapes. At room temperature, the computed spin moment of ZrFe2 is found to be slightly higher than that of Sc doped ZrFe2 which is in consensus with the magnetization data. To compare the experimental data, we have also computed magnetic Compton profiles (MCPs), total and partial spin projected density of states (DOS) and the site specific spin moments using spin-polarized relativistic Korringa-Kohn-Rostoker method. It is observed that the spin moment at Fe site is aligned antiparallel to that of Zr site in both ZrFe2 and Zr0.8Sc0.2Fe2. The MCP results when compared with vibrating sample magnetometer based magnetization data, show a very small contribution of orbital moment in the formation of total magnetic moments in both the compounds. The DOS of ferromagnetic ground state of ZrFe2 and Zr0.8Sc0.2Fe2 are interpreted on the basis of a covalent magnetic model beyond the Stoner rigid band model. It appears that on alloying between a magnetic and a non-magnetic partner (with low valence), a polarization develops on the non-magnetic atom which is anti-parallel to that of the magnetic atom.

Transverse Spin and Spin-Orbit Coupling in Silicon Waveguides

Evanescent and tightly confined propagating waves exhibit a remarkable transverse spin density since the longitudinal component of the electric field is not negligible. In this work, we obtain via numerical simulations the electric field components of the fundamental guided modes of two waveguides typically used in silicon photonics: the strip and the slot waveguide. We obtain the relation between transverse and longitudinal field components, the transverse spin densities and other important parameters, such as the longitudinal component of the so-called Belinfante spin momentum density. By asymmetrically placing a circularly-polarized point-like dipole source in regions showing local circular polarization, the guided mode is excited unidirectionally via spin-orbit coupling. In contrast to metal plates supporting surface plasmons, the multimode behavior of silicon waveguides results in different spin-orbit coupling properties for each guided mode. Our results may find application in silicon photonic devices, integrated quantum optics and polarization manipulation at the nanoscale.

Measuring the transverse spin density of light.

We generate tightly focused optical vector beams whose electric fields spin around an axis transverse to the beams' propagation direction. We experimentally investigate these fields by exploiting the directional near-field interference of a dipolelike plasmonic field probe placed adjacent to a dielectric interface. This directionality depends on the transverse electric spin density of the excitation field. Near- to far-field conversion mediated by the dielectric interface enables us to detect the directionality of the emitted light in the far field and, therefore, to measure the transverse electric spin density with nanoscopic resolution. Finally, we determine the longitudinal electric component of Belinfante's elusive spin momentum density, a solenoidal field quantity often referred to as "virtual."

Temperature-dependent spin magnetization density in Mn-rich Ni-Mn-Sn shape memory alloy by magnetic Compton scattering

Temperature-dependent spin momentum densities in Ni2Mn1.4Sn0.6 shape memory alloy have been measured using 182 keV circularly polarized synchrotron radiations. Near the martensitic phase transition , experimental magnetic Compton profiles (MCPs) unravel a dominating spin moment contribution from Mn sites. First-principles calculations are found to produce higher magnetic moment for orthorhombic structure than that for the L21 (cubic) structure, which is in tune with the present MCP data. It is also concluded that the spin moments of excess Mn atoms lying at Sn sites are antiferromagnetically coupled with Mn local spin moment in both the phases.

Magnetic properties of NiFe2−xRExO4 (RE=Dy, Gd) using magnetic Compton scattering

Temperature dependent spin momentum densities of NiFe2−xRExO4 (x=0, 0.05; RE=Dy, Gd) ferrites have been measured using a magnetic Compton spectrometer available at SPring-8, Japan. The experimental profiles of NiFe2O4 (NFO) with doping of Dy and Gd show almost similar spin moment as of undoped NFO. The contribution of different constituents in the formation of total spin moment is also deduced from the analysis of Compton line shape. It is seen that 5% doping of Dy3+ or Gd3+ ions at Fe3+ sites leads to a redistribution of spin moment at Fe3+ and RE3+ sites. The magnetic Compton data when compared with the magnetization data (using a vibrating sample magnetometer) show almost a constant orbital moment (0.21±0.03µB/f.u.) in the doped and undoped NFO.

ChemInform Abstract: Magnetic Compton Scattering: A Reliable Probe to Investigate Magnetic Properties

AbstractReview: 8 refs.

Study of spin and orbital magnetization in Dy- and Gd-doped Co ferrite using magnetic Compton scattering

Temperature dependent experimental magnetic Compton profiles (MCPs) of inverse spinel CoFe2−xRExO4 (x = 0.05; RE = Dy, Gd) have been decomposed into constituent profiles to determine site-specific spin moments. A comparison of MCPs of doped and undoped CoFe2O4 shows a decrease in spin moment on 5% doping of Dy and Gd. Reduction in spin moment is explained on the basis of migration of Co2+ ions from octahedral to tetrahedral sites, which is also supported by photoelectron spectroscopy measurements. The orbital moments deduced from combination of spin momentum density and magnetization data are found to be almost similar in doped ferrites.

Magnetic Compton Scattering Study of Ni<sub>2</sub>Mn<sub>1.4</sub>Sn<sub>0.6</sub> Shape Memory Alloy

Spin momentum density in Ni2Mn1.4Sn0.6 shape memory alloy has been measured using magnetic Compton scattering technique. The experiment has been performed using 182 keV circularly polarized synchrotron radiation at temperature 10 K at SPring-8, Japan. Experimental magnetic Compton profile has been decomposed to determine the site specific magnetic moments, where the magnetic moment at Mn site was found to be dominating. It is seen that the total spin moment in present non-stoichiometric alloy is smaller than that of stoichiometric Ni2MnSn.

Evaluation of orbital moment in Ni-Zn ferrites: A magnetic Compton scattering study

Temperature dependent magnetic Compton profiles of Ni1−xZnxFe2O4 (x = 0.0, 0.1, 0.2) ferrites have been decomposed into component profiles to determine the site-specific magnetic moments. For a quantitative evaluation of orbital moment, the spin momentum density data have been combined with magnetization data. Interestingly, the orbital magnetic moment decreases from 0.25 ± 0.03 μB/f.u. (for x = 0.0) to 0.09 ± 0.03 μB/f.u. (for x = 0.2) which is in contrast to spin moment. A decrease in ratio of orbital to spin moments in Ni rich ferrites is explained on the basis of spin-orbit coupling and crystal field interaction.

Enhancement of ferromagnetism in Ni excess Cu1−xNixMnSb half Heusler alloys

Spin momentum densities of Cu1−xNixMnSb (for x = 0.17 and 0.22), derived from experimental magnetic Compton profiles (MCPs), show an increase in magnetic moment while going from x = 0.17 → 0.22, which is attributed to Mn 3d states. MCPs along with magnetization data suggest a negligible contribution of orbital moment. The MCPs and spin moments at Mn 3d states computed using the spin polarized relativistic Korringa-Kohn-Rostoker technique are in good agreement with the experimental data. An unusual increase in magnetic moment (2.77 ± 0.03 μB/f.u. for x = 0.17 to 3.94 ± 0.03 μB/f.u. for x = 0.22) is due to significant rise in local magnetic moment on Mn site. For x = 0.22 (0.17), presence of antiferromagnetic phase is observed to be 2 (31)%.

Investigation of orbital magnetization in inverse spinel cobalt ferrite using magnetic Compton scattering

We present the spin momentum densities of CoFe2O4 measured at 8 and 300 K using magnetic Compton scattering. The magnetic Compton profiles were decomposed into component profiles of constituents namely Fe and Co, to determine their role in the formation of total spin moment. It is seen that the major contribution (about 80%) in the spin moment is from Co, whereas the itinerant electrons show a small reverse polarization. Moreover, it is clearly visualized that the spin moment at Co reduces from 2.55 → 2.35 μB/f.u. while going from 8 → 300 K. The magnetic Compton profiles, when compared with the magnetization data, show about 17% contribution of orbital moment to the total magnetic moment at both temperatures. The origin of the orbital moment is explained on the basis of rotation of hole on t2g orbital of Co+2 ion.

A magnetic Compton scattering study of Ga rich Co–Ni–Ga ferromagnetic shape memory alloys

The temperature dependent spin momentum densities of Co1.8NiGa1.2 and Co2Ni0.76Ga1.24 alloys have been measured using the magnetic Compton scattering technique. The individual contributions of constituents in the formation of the total spin moment are also calculated using Compton line shape analysis. The magnetic Compton data when compared with the magnetization data obtained using a vibrating sample magnetometer show a negligible orbital contribution. The spin moments deduced from the experimental Compton data are compared with the theoretical results obtained from the full potential linearized augmented plane wave method and are found to be in good agreement. The origin of the magnetism in both alloys is also described in terms of the eg and t2g contributions of Ni and Co.

On the role of Al doping in La0.7Ca0.3MnO3: A magnetic Compton scattering study

Spin and orbital magnetic moments in hole doped manganite La0.7Ca0.3Mn1−xAlxO3 (x = 0, 0.02, and 0.06) have been scrutinized using experimental spin momentum densities. An analysis of magnetic Compton profiles shows that the spin moment of Mn 3d has a major contribution towards the total spin moment and its contribution decreases as we increase the concentration of Al. The present experiment along with magnetization data predict orbital moment of −0.29 ± 0.03 μB/f.u. in the parent compound (x = 0), which almost disappears on substitution of Al. The results are explained on the basis of imbalance in Mn3+ and Mn4+ charge ratio in these compounds.