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Electronic density of states of a U ( 1 ) quantum spin liquid with spinon Fermi surface. II. Zeeman magnetic field effects

The Zeeman effect lowers the energy of electrons with spin states which are antiparallel to the applied magnetic field but lifts that of spin parallel states. In quantum spin liquids where the spin and charge degrees of freedom are fractionalized, an anomalous Zeeman response may be expected. In the case of spin liquids with a spinon Fermi surface, the threshold energy to excite an electronic state is found to exhibit no Zeeman shift. This is specific to the spinon Fermi surface case. In contrast, other gapped spin liquids are expected to exhibit the standard Zeeman shift at the band edge even though they also exhibit spin-charge fractionalization. Further, when gauge-field fluctuations are included, we find that the Zeeman shift of the electronic states gets affected by the gauge field induced binding. In the electronic density of states spectra, weak gauge binding induces band-edge resonance peaks which exhibit the Zeeman shift in the same direction as that in the standard Zeeman effect, but the shift is reduced as the binding potential increases. With further increase in the binding potential, the resonance becomes true in-gap bound states and eventually the Zeeman shift direction reverses so it is opposite to the standard Zeeman effect. We propose that one can perform spin-polarized scanning tunneling microscope measurements as a test of the spinon Fermi sea ground state in quantum spin liquid candidate materials.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Intensity-dependent circular polarization and circumstellar magnetic fields from the observation of SiO masers

A new aspect of the propagation of astrophysical maser radiation in the presence of a magnetic field is described in which circular polarization is created. The resulting antisymmetric spectral line profile for this circular polarization resembles that produced by the ordinary Zeeman effect when the Zeeman splittings are much less than the spectral line breadth. It is caused by the change, with increasing maser intensity, in the axis of symmetry for the molecular quantum states from a direction that is parallel to the magnetic field to a direction that is parallel to the direction of propagation. When the maser is radiatively saturated, and the rate for stimulated emission is within an order of magnitude of the Zeeman splitting in frequency units, this 'intensity-dependent circular polarization' is greater than that due to the ordinary Zeeman effect by factors as large as 1000. The circular polarization that is observed in the spectra of circumstellar SiO (J = 1-0) masers associated with late-type giants and supergiants may then be caused by magnetic fields as weak as about 10 mG. With the standard Zeeman interpretation of the observations, magnetic fields of 10-100 G are indicated. The lower fields are similar to the limits obtained from the observation of the 22 GHz water masers which are typically somewhat further from the central star. The observed tendency for the fractional linear polarization of SiO masers to increase with increasing angular momentum of the molecular state is shown to be a likely result of anisotropic pumping. Errors are identified that invalidate a recent conflicting claim in the literature about the basic theory of maser polarization in the regime that is relevant here.

Nedoluha, Gerald E.↗

Fermi surface and Berry phase analysis for Dirac nodal line semimetals: Cautionary tale from SrGa 2 and BaGa 2

A Berry phase of odd multiples of 𝜋 inferred from quantum oscillations (QOs) has often been treated as evidence for nontrivial reciprocal space topology. However, disentangling the Berry phase values from the Zeeman effect and the orbital magnetic moment is often challenging. In centrosymmetric compounds, the case is simpler as the orbital magnetic moment contribution is negligible. Although the Zeeman effect can be significant, it is usually overlooked in most studies of QOs in centrosymmetric compounds. Here, we present a detailed study on the nonmagnetic centrosymmetric SrGa 2 and BaGa 2 , which are predicted to be Dirac nodal line semimetals based on density functional theory (DFT) calculations. Evidence of the nontrivial topology is found in magnetotransport measurements. The Fermi surface topology and band structure are carefully studied through a combination of angle-dependent QOs, angle-resolved photoemission spectroscopy (ARPES), and DFT calculations, where the nodal line is observed in the vicinity of the Fermi level. Strong de Haas–van Alphen fundamental oscillations associated with higher harmonics are observed in both compounds, which are well fitted by the Lifshitz-Kosevich (LK) formula. However, even with the inclusion of higher harmonics in the fitting, we found that the Berry phases cannot be unambiguously determined when the Zeeman effect is included. We revisit the LK formula and analyze the phenomena and outcomes that were associated with the Zeeman effect in previous studies. Our experimental results confirm that SrGa 2 and BaGa 2 are Dirac nodal line semimetals. Additionally, we highlight the often overlooked role of spin-damping terms in Berry phase analysis.

36 MATERIALS SCIENCE↗

Linear Polarization Measurements of Chromospheric Emission Lines

We have used the Zurich Imaging Stokes Polarimeter (ZIMPOL I) with the McMath-Pierce 1.5 m main telescope on Kitt Peak to obtain linear polarization measurements of the off-limb chromosphere with a sensitivity better than 1 x 10(exp -5). We found that the off-disk observations require a combination of good seeing (to show the emission lines) and a clean heliostat (to avoid contamination by scattered light from the Sun's disk). When these conditions were met, we obtained the following principal results: 1. Sometimes self-reversed emission lines of neutral and singly ionized metals showed linear polarization caused by the transverse Zeeman effect or by instrumental cross talk from the longitudinal Zeeman effect in chromospheric magnetic fields. Otherwise, these lines tended to depolarize the scattered continuum radiation by amounts that ranged up to 0.2%. 2. Lines previously known to show scattering polarization just inside the limb (such as the Na I lambda5889 D2 and the He I lambda5876 D3 lines) showed even more polarization above the Sun's limb, with values approaching 0.7%. 3. The O I triplet at lambda7772, lambda7774, and lambda7775 showed a range of polarizations. The lambda7775 line, whose maximum intrinsic polarizability, P(sub max), is less than 1%, revealed mainly Zeeman contributions from chromospheric magnetic fields. However, the more sensitive lambda7772 (P(sub max) = 19%) and lambda7774 (P(sub max) = 29%) lines had relatively strong scattering polarizations of approximately 0.3% in addition to their Zeeman polarizations. At times of good seeing, the polarization spectra resolve into fine structures that seem to be chromospheric spicules.

Sheeley, N. R., Jr.↗

Zeeman degeneracy effects in collisional intense-field resonance fluorescence

Resonance fluorescence due to intense laser fields from a Zeeman degenerate atom being perturbed by collisional interactions is calculated in the impact regime by using the quantum-fluctuation-regression theorem. Various interesting effects are found. For example, the scattered intensity spectrum for a J = 0 to J = 1 transition for polarization parallel to the laser polarization is essentially an asymmetric triplet, whereas for a perpendicular polarization due to collisions the spectrum is essentially a doublet (whose frequencies do not correspond with any of those of the triplet). Further, the width of the fluorescent component (whose frequency is close to the unperturbed frequency) actually decreases with increasing laser power.

Cooper, J.↗

Measurements of magnetic fields in solar prominences

Magnetic fields can be measured, in solar prominences, by means of two different basic mechanisms that are responsible for the introduction (or the reduction) of a given amount of polarization in spectral lines: these are the Zeeman effect and the Hanle effect. Through the splitting of the magnetic components of a spectral line, the Zeeman effect is capable of introducing a certain amount of circular polarization across the line profile. The Hanle effect consist of a modification of the linear polarization that is induced in spectral lines by the anisotropic illumination of the prominence plasma by the photospheric radiation field. These two effects are briefly discussed.

Deglinnocenti, Egidio Landi↗

Proximity-enhanced valley Zeeman splitting at the WS 2 /graphene interface

The valley Zeeman physics of excitons in monolayer transition metal dichalcogenides provides valuable insight into the spin and orbital degrees of freedom inherent to these materials. Being atomically-thin materials, these degrees of freedom can be influenced by the presence of adjacent layers, due to proximity interactions that arise from wave function overlap across the 2D interface. Here, we report 60 T magnetoreflection spectroscopy of the A- and B- excitons in monolayer WS 2 , systematically encapsulated in monolayer graphene. While the observed variations of the valley Zeeman effect for the A- exciton are qualitatively in accord with expectations from the bandgap reduction and modification of the exciton binding energy due to the graphene-induced dielectric screening, the valley Zeeman effect for the B- exciton behaves markedly different. We investigate prototypical WS 2 /graphene stacks employing first-principles calculations and find that the lower conduction band of WS 2 at the <?CDATA $K/K^{^{\prime}}$?> K / K ′ valleys (the <:tex-math><?CDATA $\mathrm{CB}^-$?> C B − band) is strongly influenced by the graphene layer on the orbital level. Specifically, our detailed microscopic analysis reveals that the conduction band at the Q point of WS 2 mediates the coupling between <?CDATA $\mathrm{CB}^-$?> C B − and graphene due to resonant energy conditions and strong coupling to the Dirac cone. This leads to variations in the valley Zeeman physics of the B- exciton, consistent with the experimental observations. Our results therefore expand the consequences of proximity effects in multilayer semiconductor stacks, showing that wave function hybridization can be a multi-step energetically resonant process, with different bands mediating the interlayer interactions. Such effects can be further exploited to resonantly engineer the spin-valley degrees of freedom in van der Waals and moiré heterostructures.

36 MATERIALS SCIENCE↗

Coronal Polarimetry: Determining the Magnetic Origins of Coronal Mass Ejections

Synopsis: The mechanism for the release of stored magnetic energy in solar eruptions remains a major unsolved problem of Heliophysics. Choosing between triggers requires knowledge of pre-eruptive magnetic fields (B). Although linear polarization in visible/infrared (VIR) coronal emission lines reveals intriguing clues about coronal mass ejection (CME) precursor topology, small telescope apertures limit current capability for measuring vector field. Current coronal observations are insufficient to diagnose 3D coronal magnetic fields in CME precursors. Coronal cavities are the ideal candidates for CME precursor studies. BLOS in cavities is a direct measure of stored magnetic free energy, and the presence and location of topological X-points (reconnection locations) and O-points (circulation of B about axis) distinguish predictions of the flux rope-torus-instability and sheared-arcade-breakout CME models. - Finding: Coronal cavities are ubiquitous throughout the solar cycle, erupt as CMEs, and have coronal polarimetric signatures that distinguish between model predictions. - Recommendation: Coronal cavities should be targeted in a comprehensive multiwavelength study of CME precursors & associated eruption-driving mechanisms. Large ground-based VIR telescopes can measure both coronal magnetic field topology and strength through a combination of the saturated Hanle and BLOS -sensitive Zeeman effects. - Finding: The 4m Daniel K. Inouye Solar Telescope (DKIST) and proposed 1.5m Coronal Solar Magnetism Observatory Large Coronagraph (COSMO-LC) make a major leap forward in VIR coronal sensitivity, enabling measurement of vector B. - Recommendation: A dedicated coronal synoptic telescope with a large field-of-view (i.e., COSMO-LC) is needed to identify the dominant CME driving mechanisms, by measuring coronal magnetic fields from precursor state into eruption. In the UV, a new opportunity has arisen to make use of the strong H I Lyman-α coronal line, which obtains a measurement of B that is independent of the Zeeman effect. - Finding: Small-telescope spectropolarimetric capability in the unsaturated Hanle regime provides an independent and complementary coronal magnetic diagnostic to large ground-based telescope measurements. - Recommendation: The proposed 12-cm Coronal Lyman-α Resonance Observatory (CLARO) spectropolarimetric coronagraph demonstrates a path forward for space-based observations of the coronal magnetic field that should be incorporated into future missions away from the Sun-Earth line (e.g., COMPLETE).

magnetic energy↗

Detection of the clock transition in thulium atoms by using repump laser radiation

A population transfer from the upper level of the clock transition in thulium atoms to the ground level is demonstrated by using radiation with a wavelength of 402 nm. The method for detecting the clock transition excitation that is not affected by technical fluctuations of the number of atoms in an optical lattice is investigated. The hyperfine splitting of the |4f{sup 12}({sup 3}F{sub 2})5d{sub 5/2} 6s{sup 2}; J = 7/2〉 level in the thulium atom is measured to be 1480(9) MHz. The suggested method for population transfer can be applied to both the hyperfine components of the clock transition intended for compensating Zeeman effect in a thulium optical clock. (paper)

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Zeeman Tuning Rates in the v3 Band of NO2

Zeeman spectra of the v3 fundamental (at approximately 1620 c/m) of nitrogen dioxide (14N02) have been recorded with magnetic fields of approximately 500 Gauss using a FTS (at the Kitt Peak National Observatory), as well as a tunable diode laser. At low magnetic fields the Zeeman effect is small compared to the spin-rotation interaction, and the Zeeman tuning rates are expected to be linear with magnetic field. Measured tuning rates of the Q-branch (KA = 2 - 9, N = 2 - 6) sigma transitions are compared to those expected for 2Sigma transitions in low magnetic fields, 2mu ogB/(2N+l). These measurements are required in the data analysis of an ultra-sensitive (pptv) in situ detector based on magnetic-rotation spectroscopy.

Mahon, C. H.↗

Experimental determination of energy-level structures of diamond silicon-vacancy centers in off-axis magnetic fields

Here, we report the development of an experimental approach to efficiently determine the energy level structure of an individual silicon vacancy (SiV) center in a magnetic field along an arbitrary direction. This approach uses two coupling rates (one each for the ground and the excited states) to characterize the combined effects of static strain and dynamic Jahn-Teller coupling and exploits the fact that orbital Zeeman effects vanish when the magnetic field is normal to the SiV axis. With an analytical expression for the energy level structure of the SiV under a transverse magnetic field, the two coupling rates can be directly derived from two measurements: one on the frequency separation between two spin-conserved transitions and the other on the coherent population trapping resonance of the SiV ground spin states. A detailed comparison between the numerical calculation and the experimental result on the dependence of the spin-conserved splitting on both the amplitude and direction of the magnetic field further reveals unequal orbital magnetic coupling for the ground and excited states, indicating that unequal orbital quenching factors are needed for an accurate description of the SiV energy level structure in a magnetic field.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

A technique for measuring magnetic fields on solar-type stars

A method is developed and tested by which magnetic-field strengths and area filling-factors of magnetic regions on late-type stars may be inferred from high-resolution, absorption-line profiles that have been broadened by the Zeeman effect. The technique involves fitting such profiles with a triplet of components, the shape of which is derived from profiles of lines of low Zeeman sensitivity. Tests of the systematic and random errors indicate that such magnetic flux measurements have an uncertainty of 20% for stars with field strengths of 2000 gauss if at least 10% of the stellar surface contains magnetic regions.

Marcy, G. W.↗

g-factor engineering with InAsSb alloys toward zero band gap limit

Band gap is known as an effective parameter for tuning the Landé g factor in semiconductors and can be manipulated in a wide range through the bowing effect in ternary alloys. In this work, using the recently developed virtual substrate technique, high-quality InAsSb alloys throughout the whole Sb composition range are fabricated and a large g factor of g≈-90 at the minimum band gap of ~0.1 eV, which is almost twice that in bulk InSb, is found. Further analysis to the zero gap limit reveals a possible gigantic g factor of g≈-200 with a peculiar relativistic Zeeman effect that disperses as the square root of magnetic field. Such a g-factor enhancement toward the narrow gap limit cannot be quantitatively described by the conventional Roth formula, as the orbital interaction effect between the nearly triply degenerated bands becomes the dominant source for the Zeeman splitting. These results may provide insights into realizing large g factors and spin-polarized states in semiconductors and topological materials.

36 MATERIALS SCIENCE↗

Relativistic Effects in Magnetic Circular Dichroism: Restricted Magnetic Balance and Temperature Dependence

Magnetic circular dichroism of transition metal complexes and open-shell systems are challenging to simulate and analyze, mainly due to the interplay of spin–orbit couplings and finite-magnetic-field induced Zeeman effects with the complex selection rules dictated by the circularly polarized light. In this study, we introduce an ab initio relativistic two-component formalism based on the restricted magnetic-balanced Hamiltonian for simulating MCD spectra. Both homogeneous finite magnetic field and relativistic effects are included variationally in the ground state reference. Finite-field London orbitals are used to enforce the constrained gauge-origin independence in the calculation using localized atomic orbitals. Through benchmark studies of AuCl 4 – , Pt(CN) 4 2– , and Mo(CN) 8 3– , we discuss how relativistic effects are manifested in MCD for both closed-shell and open-shell molecular complexes and how the interplay between spin–orbit coupling and magnetic field modulates the MCD selection rules. Finally, an investigation on temperature-dependent MCD is carried out and compared to experiment.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗