Effective Lande Factors Research Articles

ANOMALOUS WIDENING OF 5434.5 LINE IN SUNSPOTS: SUPER-STRONG MAGNETIC FIELDS?

We present results of spectralobservations of two sunspots in six metal lines near Fe I5434.5 A, which have effective Lande factors g eff from –0.014 to 2.14. The observations were made on July 8 andAugust 25, 2015, with the ATsU-5 telescope of GAO NASof Ukraine using a circular polarization analyzer andspectra registration with the SBIG ST-8300 CCD camera.The following line parameters are compared: observedsplitting of I ± V profiles, the width and depth of the StokesI profiles. Significant differences of the measured magneticfield strengths B eff were found in separate places of thespots and by lines with different g eff values. The Fe I 5434.5Ǻ line (g eff = –0.014) shows measurable splitting in somelocations of the sunspots, which corresponds to themagnetic field B obs ≈ 20 kG. Comparison of the widths anddepths of the line profiles revealed several special places inthe sunspots, where the Fe I 5434.5 Ǻ line was expandedadditionally by ≈ 15–35%, whereas other lines with largerLande factors did not have such a feature. One of thereasons for this expansion could be a sharp and localincrease of turbulent velocities, but no active processes suchas solar flares or significant Doppler flows were observed atthese locations. A semi-empirical model constructed for thefirst sunspot by FeI 5434.5 line using inverse code withTikhonov`s stabilizers shows an anomalous feature – themaximum of microturbulent velocities in the upperphotosphere and the temperature minimum zone instead ofthe usual small increase of microturbulence at these heights.This may be the effect of very strong magnetic fields ofmixed polarity or unresolved turbulent structures. As to firstcase, the estimated value of the magnetic field in suchlocations of sunspots is ~10 5 G, which requires additionalcareful verification.

СУТТЄВА НЕОДНОРІДНІСТЬ МАГНІТНОГО ПОЛЯ В ГОЛОВНІЙ СОНЯЧНІЙ ПЛЯМІ АКТИВНОЇ ОБЛАСТІ NOAA 10488

The main conclusion of our work is that in the greatest sunspot of the active region NOAA 10488 there was a large dispersion of magnetic field strengths, at which the minimum and maximum strengths differed by approximately an order of magnitude. This result applies to the central part of the sunspot umbra, for a square with sides 2 × 2 Mm2 in the picture plane. Observation material was obtained on the Echelle spectrograph of the horizontal solar telescope of the Astronomical Observatory of Taras Shevchenko National University of Kyiv. This instrument allows to analyze the Zeeman effect simultaneously in thousands of spectral lines of almost the entire visible region of the spectrum. For our analysis, four iron FeI lines with wavelengths of 6290.97, 6301.51, 6302.50 and 6498.97 Ǻ and effective Lande factors 1.481, 1.669, 2.487 and 1.375, respectively, were used. In the studied sunspot, only FeI 6302.5 from these lines has a complete Zeeman splitting, which corresponds to magnetic field of 3400 G. However, the splitting of the other three lines corresponds to magnetic fields in a very wide range, from several hundred Gauss to 3700 G, which indicates significant inhomogeneity of the magnetic field. Also, the shape of bisectors of I ± V profiles does not correspond to a case of homogeneous field. In particular, theoretically, in a homogeneous and non-longitudinal magnetic field, bisectors should be have the maximum splitting in the nuclei of these lines, whereas in reality the picture is more complicated. All three of these lines show a tendency to increase splitting in distant wings, at distances of 120-250 mAh from their centers. This effect is possible under the two-component structure of the magnetic field (background field + spatially unresolved structures) having magnetic strengths in the range of 4.5-8 kGs in spatially unresolved structures. Magnetic polarity in both components is the same, namely N. The observational data indicate that the magnetic field value differed significantly not only on the surface, but also in height in the studied sunspot.

Recent developments in the determination of the amplitude and phase of quantum oscillations for the linear chain of coupled orbits

De Haas-van Alphen oscillations are studied for Fermi surfaces (FS) illustrating the model proposed by Pippard in the early sixties, namely the linear chain of orbits coupled by magnetic breakdown. This FS topology is relevant to many multiband quasi-two-dimensional (q-2D) organic metals such as κ-(BEDT–TTF)2Cu(NCS)2 and θ-(BEDT–TTF)4CoBr4(C6H4Cl2) which are considered in detail. Whereas the Lifshits-Kosevich model only involves a first order development of field- and temperature-dependent damping factors, second order terms may have significant contribution to the Fourier components amplitude for such q-2D systems at high magnetic field and low temperature. The strength of these second order terms depends on the relative value of the involved damping factors, which are in turns strongly dependent on parameters such as the magnetic breakdown field, effective masses and, most of all, effective Lande factors. In addition, the influence of field-dependent Onsager phase factors on the oscillation spectra is considered.

Observational Evidences for Extremely Strong Magnetic Fields in Solar Flares

New observational data related to the X1.1/2N solar flare of 17 July 2004 were investigated and compared with some old data for other powerful flares and non-flare regions. Observations were carried out with the Echelle spectrograph of the Kyiv University Astronomical Observatory. The Stokes I ± V profiles of several metallic lines with different effective Lande factors geff have been analyzed including the FeI 5434.5 line with very low magnetic sensitivity (geff = –0.014). The obvious evidences of the emissive Zeeman effect were found as in lines with great and middle Lande factors as in FeI 5434.5 line. On the basis of all analyzed data one can conclude that upper magnetic field limit in flares can reach 70 - 90 kG, i.e. about more order higher than the well-known magnetic fields in great sunspots. The possible physical nature of such superstrong fields is discussed.

The Zeeman Effect in the G Band

We investigate the possibility of measuring magnetic field strength in G-band bright points through the analysis of Zeeman polarization in molecular CH lines. To this end we solve the equations of polarized radiative transfer in the G band through a standard plane-parallel model of the solar atmosphere with an imposed magnetic field and through a more realistic snapshot from a simulation of solar magnetoconvection. This region of the spectrum is crowded with many atomic and molecular lines. Nevertheless, we find several instances of isolated groups of CH lines that are predicted to produce a measurable Stokes V signal in the presence of magnetic fields. In part this is possible because the effective Lande factors of lines in the stronger main branch of the CH A2Δ-X2Π transition tend to zero rather quickly for increasing total angular momentum J, resulting in a Stokes V spectrum of the G band that is less crowded than the corresponding Stokes I spectrum. We indicate that, by contrast, the effective Lande factors of the R and P satellite subbranches of this transition tend to ±1 for increasing J. However, these lines are in general considerably weaker and do not contribute significantly to the polarization signal. In one wavelength location near 430.4 nm, the overlap of several magnetically sensitive and nonsensitive CH lines is predicted to result in a single-lobed Stokes V profile, raising the possibility of high spatial resolution narrowband polarimetric imaging. In the magnetoconvection snapshot we find circular polarization signals of the order of 1%, prompting us to conclude that measuring magnetic field strength in small-scale elements through the Zeeman effect in CH lines is a realistic prospect.

Detection of Polarization from the E 4 - A 4 System of FeH in Sunspot Spectra

Here we report the first detection of polarization signals induced by the Zeeman effect in spectral lines of the E 4Π-A 4Π system of FeH located around 1.6 μm. Motivated by the tentative detection of this band in the intensity spectrum of late-type dwarfs, we have investigated the full Stokes sunspot spectrum and have found circular and linear polarization signatures that we associate with the FeH lines of the E 4Π-A 4Π band system. We investigate the Zeeman effect in these molecular transitions and point out that in Hund's case (a) coupling, the effective Lande factors are never negative. For this reason, the fact that our spectropolarimetric observations indicate that the Lande factors of pairs of FeH lines have opposite signs prompts us to conclude that the E 4Π-A 4Π system must be in intermediate angular momentum coupling between Hund's cases (a) and (b). We emphasize that theoretical and/or laboratory investigations of this molecular system are urgently needed for exploiting its promising diagnostic capabilities.

Analysis of the Photospheric Lines of the Magnetic CP Star HR 7575

The photospheric lines in the visual region of the cool magnetic CP star HR 7575 have been analyzed using a high-dispersion spectrogram obtained at the Dominion Astrophysical Observatory. The fully line-blanketed ATLAS9 model atmospheres of 10-times the solar metal content were employed to calculate the elemental abundances. The effective temperature Teff, derived from the optical and ultraviolet energy distributions, points to 8500 ± 300 K, while the ionization balance of iron is not reproduced at this effective temperature. The abundances derived from individual Cr I, Cr II, and Fe II lines apparently depend on their effective Lande factors. This implies that the Cr and Fe lines are intensified by the strong magnetic field on HR 7575. Their abundance enhancement is estimated to be about 0.7 dex based on a computation of the Unno-Beckers equation. The overall abundance patterns of HR 7575 are comparable to other cool magnetic CP stars. Of the analyzed elements, only Mg and Sc have nearly solar abundances, while Cr, Mn, Sr, and rare earths are overabundant by 1 to 5 dex.

Optical pumping in CdS1-xSex nanocrystals

We report on the magneto-optical properties of large CdS0.4Se0.6 nanocrystals in a glass matrix. Optical pumping in the two high-energy bands of the photoluminescence spectrum is studied with resonant excitation and in the presence of a magnetic field. We also investigate magnetic field-induced polarization of luminescence for non-polarized excitation. We show that the higher energy band is most likely to be due to excitonic recombination. The Lande g-factor is found to be anisotropic. Its maximum value is estimated from the study of magnetic field-induced circular polarization. The second band is attributed to donor-hole recombination. We show that electrons on the donor level are partly optically oriented by circularly polarized light and that the transition may be excited either from the A or from the B valance band. The maximum degree of circular polarization is calculated in the case of optical pumping with resonant excitation of the A exciton for an assembly of wurtzite nanocrystals with randomly oriented c axes. It is found to be equal to 5/7 instead of 1 in the bulk material. In the case of magnetic field-induced polarization, the effective Lande factors for the different luminescence bands are calculated and compared with the experimental results.

Anisotropic g-Factors of Co2+ Ion in Complex Salts

The anisotropic g -factors of Co 2+ ion in the crystal field of orthorhombic symmetry have been calculated taking into account the effects of the excited orbital states. Following the same procedure as developed by Abragam and Pryce, the admixture of the excited orbital states to the ground state can be comprized in effective Lande factors for the fictitious orbital angular momentum l (=1). The dependence of the g -factors on the crystal field parameters has been calculated and compared with some experimental data.

Antiferromagnetic Ordering Effect on the Infrared Absorption Spectrum of CoF2

The ground state of the free Co2+ ion, 4F(3d7), splits into an orbital triplet 4T1, another triplet 4T2, and a singlet 4A2 in a cubic field. Among these states, the 4T1 state has the lowest energy. The degeneracy of the ground state 4T1 is further lifted by the spin-orbit interaction and the crystalline field with rhombic symmetry and thus the fine structure multiplet consists of six Kramers' doublets. Newman and Chrenko1 observed several absorption peaks in the 0.15 to 0.20 eV range both above and below the Néel temperature (TN=38°K). These peaks correspond to transitions within the ground state multiplet. Changes in the spectrum below TN appear in the number of the peaks and their intensities. Recently, Dietz2 has found out that these are magnetic dipole transitions. The explanation of these experimental facts by the crystal field theory is reported. Nakamura and Taketa3 pointed out an important role of the rhombic crystal field in understanding the anomalous behavior of the temperature dependence of the magnetic anisotropy. We show that the rhombic component of the crystal field is also important in explaining the number of peaks and their relative intensities. The numerical values of the axial crystal field Δ, the rhombic crystal field Γ, the over-all spin-orbit coupling constant λ, effective Lande factors −ρ and −η, and the exchange integral J are determined from the experimental data of peak positions above TN and the temperature dependence of the magnetic anisotropy χ∥−χ⊥.4 For this purpose the expressions for χ∥ and χ⊥ are derived, taking the effect of the unquenched orbital angular momentum into account. Better agreement with observed anisotropy are obtained by our theory than by Nakamura and Taketa's. The values of parameters thus obtained are: Δ = −707 cm−1, Γ = −183 cm−1, λ = −157 cm−1, ρ = 1.125, η = 1.59, and J = 2.6 cm−1. By using these values, g values are calculated. The result is gx = 6.18, gy = 4.07, and gz = 2.03, where y and z axes are taken along the c axis and the line connecting two nearest neighbor F− ions, respectively. These values are very close to the observed ones.5 And further, we predict the energy separation of the lowest two Kramers' doublets to be 175 cm−1 (255°K). This is in good agreement with the observed value of 240°K determined from the Shottky-type anomaly in the specific heat measurement, although the observed value is rather uncertain.6 The magnitude of the splitting of each peak by the molecular field, intensities of the split peaks, and the dichroic behavior for polarized light are also calculated. The comparison with the observed spectrum below TN shows that the number of peaks in the observed spectrum exceeds that given by the theory and that observed intensities below TN are not explained by the theory. The former disagreement is expected to be resolved by taking into account a simultaneous excitation to different excited states of two adjacent Co ions coupled by the exchange interaction, instead of molecular field approximation. Finally, the expression for the antiferromagnetic resonance frequency is derived. The contribution from the anisotropy due to the crystal field is quite large. The frequency is estimated to be 21 cm−1.

On the Magnetic Susceptibility and Anisotropy of Trivalent Vanadium Alum under the Crystalline Electric Field having predominantly Cubic Symmetry with a Small Trigonal Symmetry

On the assumption that the cubic field for V3+ is not strong enough to break down the Russell-Saunders (l-l) coupling, the magnetic susceptibility of V3+ has been calculated in a generalized way using Abragam and Pryce's Hamiltonian and wave functions. The susceptibility expression contains four parameters α, α' (the effective crystalline Lande factors), Δ (the trigonal field orbital parameter) and λ (the crystalline spin-orbit coupling constant). An excellent agreement with the experimental results of Van den Handel and Siegert and Dutta Roy are obtained by taking α = 1.10, α' = 1.35, Δ = - 1390 cm-1, D = 4.8 cm-1 and λ = 64 cm-1. The reduction of λ from its free ion value 104 cm-1 is due to the inclusion of the covalency factor. (f2 = 0.62, arising from overlap of the 3d-orbital wave functions of V3+ with the σ- and π-wave functions of the surrounding oxygen.) The values of α, α' and Δ are consistent with reasonable values of the cubic and trigonal field parameters.