Magnetic Dipole Term Research Articles

Magnetic operators for Ti3+ and Cu2+ ground states

Abstract We have checked the XMCD sum rules through an analytical calculation of Cu 2+ L 2,3 edges in octahedral symmetry. It is found that XMCD sum rules are fully satisfied in the framework of the crystal field multiplet approach resulting from the very general arguments developed in their derivations by B.T. Thole and collaborators. Analytical expressions for the orbital magnetic moment 〈 L z 〉, the spin magnetic moment 〈 S z 〉 and the magnetic dipole term 〈 T z 〉 are obtained as functions of crystal field strength and spin–orbit couplings. The nullity of 〈 T z 〉 is specially examined through group theory considerations, and it is found that at low temperature the 〈 T z 〉 contribution can be much larger than the 〈 S z 〉 contribution in the spin sum rule. The case of Ti 3+ in octahedral symmetry is also considered and it is found that, even for no spin–orbit coupling, 〈 T z 〉 can be non-zero.

Measurement of the tau anomalous magnetic moment

We have analysed radiative e + e − → ττ(γ) events using 84 pb −1 of data collected by the L3 experiment during the 1992–1994 LEP runs at the Z resonance. The energy spectrum of the photons is compared to the predictions of QED including additional magnetic and electric dipole terms. No deviations from the standard model are observed so upper limits are set on the magnetic and electric dipole form factors of the tau.

X-ray-absorption sum rules in jj-coupled operators and ground-state moments of actinide ions.

Sum rules for magnetic x-ray dichroism, relating the signals of the spin-orbit split core level absorption edges to the ground-state spin and orbital operators, are expressed in jj-coupled operators. These sum rules can be used in the region of intermediate coupling by taking into account the cross term between the j=l+/-1/2 ground-state levels and are, therefore, particularly useful in the study of actinides. The calculated expectation values for the ground-state moments of the actinide ions in intermediate coupling show that the spin-orbit-induced operators, such as the magnetic-dipole term, differ strongly from their Hund's rule ground-state values. We also prove the general rule that, when there is a perturbing interaction which is weak compared to the spin-orbit interaction, the ratio of operators with the same total moment remains constant. This rendition is usually fulfilled for the crystal-field interaction in the lanthanides and actinides. The values of the ground-state moments as a function off count give rise to an interesting trend in the dichroism of the spin-orbit split-core edges. The branching ratio of the 3d and 4d circular dichroism signal gradually increases from nearly zero for 5f(1) to similar to 0.4 for 5f(5) and is close to unity for a more than half-filled shell. The unusual behavior of the branching ratio can be related to the higher (lower) value of the magnetic dipole term, Ti, for a less (more) than half-filled shell of the actinides in the presence of spin-orbit interaction. Uranium compounds will have a much larger value of T-z than the corresponding 4f compounds. Its precise value can be used as a measure for the f count.

The importance of the magnetic dipole term in magneto-circular x-ray absorption dichroism for 3d transition metal compounds

The application of the magneto-circular x-ray absorption dichroism (MCXD) spin sum rule for 3d transition metal compounds faces two problems: the unknown value of the magnetic dipole operator and the division between the and edges. A systematic study of the order of magnitude of the -operator for ions is presented. The variation of the -values with temperature is described and analysed, for all cases from to cations in two different situations. Firstly the perfect octahedral case is considered. It is shown that is non-zero for low temperature; but, as it originates only from d-electron spin - orbit splitting, it is washed out at room temperature. Secondly, a model of the surface situation is considered. In this case originates mainly from the crystal-field splitting. It then exhibits quite large values at any temperature and can by no means be neglected when applying the sum rule. The error introduced in the sum rule due to the mixing of and edges has been estimated.

Spin magnetic moments from angle resolved magnetic circular dichroism in resonant photoemission decay

Measurement of the resonant photoelectrons at the photon energy of the absorption edge gives a powerful extension of magnetic circular x-ray dichroism (MCXD). Because each type of core hole produced in absorption emits electrons in different directions decaying to different final states we can obtain more detailed information on the core hole produced by the absorption step and this gives improved knowledge of the original valence shell polarization. This can be used to tell apart the spin magnetic moment and magnetic dipole term.

Spin magnetic moments from angle resolved magnetic circular dichroism in resonant photoemission decay

Measurement of the resonant photoelectrons at the photon energy of the absorption edge gives a powerful extension of magnetic circular x-ray dichroism (MCXD). Because each type of core hole produced in absorption emits electrons in different directions decaying to different final states we can obtain more detailed information on the core hole produced by the absorption step and this gives improved knowledge of the original valence shell polarization. This can be used to tell apart the spin magnetic moment and magnetic dipole term.

Magnetic moments in as-deposited and annealed Ni layers on Fe(001): An x-ray-dichroism study.

We have performed linear and circular x-ray-dichroism measurements at the ${\mathit{L}}_{2,3}$ edges of Ni in as-deposited and annealed layers on an Fe(001) substrate. The linear dichroism results suggest that the magnetic dipole term 〈T〉 is small in these Ni layers. Upon annealing, the intermixing of Ni and Fe causes the Ni orbital moment to increase to twice the value for bulk fcc Ni. The possible origins of this increase are discussed. Fundamental importance is attributed to the higher localization of the Ni 3d states, due to the ``impurity'' nature intrinsic to Ni atoms diluted in Fe. \textcopyright{} 1996 The American Physical Society.

The electric quadrupole contribution to the circular birefringence of nonmagnetic anisotropic chiral media: a circular waveguide experiment

Constitutive relations which include electric quadrupole terms, in addition to electric and magnetic dipole terms, are used to describe the "optical activity", in particular the circular birefringence, of an anisotropic chiral medium which is nonmagnetic. The resulting permittivity and chirality tensors are then used to predict the rotation of the polarization plane of a linearly polarized wave propagating in a circular waveguide filled with the medium. The numerical predictions were tested by measurements between 2.4 and 4 GHz on a 2 m long artificial crystal in a circular waveguide and it was found that the rotation of the polarization was within 13% of the predicted value-good agreement after considering the possible sources of error. It is thus established that the effect of electric quadrupoles must be included when modeling the optical activity of anisotropic chiral media in the long wavelength regime. The anisotropic chiral media which are dealt with here can be classified according to the crystallographic point groups to which they belong, and they may therefore also be considered to be artificial crystals.

The optical activity of an artificial non-magnetic uniaxial chiral crystal at microwave frequencies

Constitutive relations which include electric quadrupole terms, in addition to electric and magnetic dipole terms, are used to predict the circular birefringence experienced by an electromagnetic wave propagating in an artificial uniaxial chiral crystal which is non-magnetic. The formulation is independent of the origin chosen for the computation of the multipole moments. Numerical values are presented, in the long wavelength regime, for the rotatory dispersion as a result of circular birefringence. It is shown that in this regime the rotatory dispersion has a quadratic frequency dependence, in accordance with the Drude model. The polarizability tensors which determine circular birefringence are computed from the multipole moments of a single structure. It is quantitatively demonstrated that neglect of the electric quadrupole contribution would lead to a serious error in the predicted value for the rotation angle of the polarization plane in the case of a uniaxial crystal. In fact, the contribution of the electric quadrupole moments to optical activity is comparable to that of the magnetic dipole moments. The geometry, dimensions and spacing of the chiral element were chosen for relative ease of fabrication of the crystal, and to allow experimentation at frequencies where microwave instrumentation is readily available. Hence it was possible to subject the numerical prediction of the expected rotatory dispersion, and the effect of the electric quadrupole contribution, to experimental investigation. This was done with good agreement.

An investigation of uranium M4,5 edge magnetic X-ray circular dichroism in US

Magnetic X-ray circular dichroism (MXCD) has been measured in a ferromagnetic uranium monosulphide crystal by monitoring the fluorescence signal over the uranium M4.5 edges. Despite sizeable absorption corrections, we have obtained a precise value of the dichroic branching ratio, which is compared with sum-rule predictions. We find that, in contrast to the case of cubic 3d transition metals where the magnetic dipole term (Tz) can be neglected, its contribution to the dichroism signal in the present case is larger than that of the spin polarization, (Sz). The dichroism spectrum is shown to exhibit considerably more structure than those of resonant magnetic diffraction from antiferromagnetic actinide compounds, and is found to be in good qualitative agreement with atomic calculations of 5f2 and 5f3 configurations.

Correlation between the spin magnetic dipole term and the magnetic anisotropy in Co/Pd multilayers

Using the sum rules for magnetic X-ray dichroism we obtain trends for the spin—orbit interaction and the z-components of the orbital magnetic moments of Co in Co/Pd multilayers with perpendicular easy axis of magnetization. We found a correlation between the spin magnetic dipole term T z , which is related to the spin—orbit interaction, and the crystal-field. This is the first experimental evidence that the origin of the perpendicular easy axis of the magnetization in magnetic layers is determined by a fine interplay between the crystal-field and spin—orbit coupling.

On correlating TEM cell and OATS emission measurements

The use of single-port broad-band TEM cells for both near-field and far-field radiated emission testing is considered. The approach is to model the radiation from the device under test (DUT) as due to an equivalent set of multipoles. Assuming the DUT is electrically small only the initial multipole moments, the electric and magnetic dipole terms, need be retained. A sequence of TEM cell measurements is then used to determine the equivalent DUT dipole moments, The dipole model then allows one to simulate DUT emissions both in free space and over a ground screen. Thus, emission measurements over an open area test site (OATS) as called for by various standards may be simulated. Such measurement schemes have previously been successfully developed for standard two port TEM cells. However, certain broad-band TEM cells are single-port devices; thus, some modification of the previous approach is required. This paper reviews the basics of the multipole model as it relates to TEM cells, details various measurement schemes appropriate to single-port TEM cells, and presents examples of measured emission data, both near field and far field, in all cases considered, the correlation between emission data measured directly over a ground screen and simulated ground screen data based on TEM cell measurements is excellent. >

Limitation of the magnetic-circular-dichroism spin sum rule for transition metals and importance of the magnetic dipole term.

Magnetic-circular-dichroism (MCD) spectra and the spin magnetic dipole term ($〈{T}_{z}〉$) for bulk $3d$ transition metals and their surfaces were calculated from full potential linearized augmented plane wave electronic band structure results. The recently proposed MCD spin sum rule is found to result in a much larger error [of up to 50% for the Ni(001) surface] than does its orbital counterpart. In support of recent experiments for bulk, we find that by combining the MCD orbital and spin sum rules the ratio of spin and orbital moments can be determined from the MCD spectra even for low dimension systems with an error of 10% when the $〈{T}_{z}〉$ contribution is included.

Theory of natural circular dichroism in molecules oriented by photoselection

The polarization properties of light absorption by molecular chromophores partially aligned by photoselection are presented in complete form. Circular dichroism (CD) in a photoselectively oriented ensemble of absorbers arises from two types of magnetic dipole terms and, in systems of low symmetry, from electric quadrupole terms, the relative contributions of these depending on the polarization properties of the probe and actinic light beams. The anisotropic circular dichroism measured in such experiments may contain information about molecular moments that is not directly available from other spectroscopic techniques, although separation of the magnetic dipole and electric quadrupole contributions will be generally possible only in systems of C2 or D2 symmetry. Theoretical descriptions are presented of possible experimental configurations for measuring oriented CD by modulating circular polarization in the probe beam, exciting beam, or in dual beams. The possible effect of photoselection-orientation on the time evolution of circular dichroism signals measured in laser flash-photolysis experiments is discussed.

Validity and the applicablity of magnetic-circular-dichroism sum rules for transition metals (invited)

X-ray magnetic-circular-dichroism (MCD) spectra are calculated using the thin film full potential linearized augmented plane wave energy band method for transition metal surfaces. Together with a model analysis, a clear physical insight is provided for this new and exciting phenomenon. The MCD sum rule for the orbital moments originally derived from a single ion model are found to be valid to within 5–10% even in the band approach which treats the strongly hybridized multiband structure. However, the spin sum rule may result in a larger error due to the effects of s,p−d hybridization. In addition, the magnetic dipole term is very important in the spin sum rule, especially for atoms with lower local symmetry.

First principles investigations of MCD spectra and sum rules for 3d transition metal surfaces

Results of precise calculations of the X-ray magnetic-circular-dichroism (MCD) spectra and orbital magnetic moment, 〈 L z 〉, based on our thin film full potential linearized augmented plane wave energy band method and a tight binding analysis carried out for Fe(001), Co(0001) and Ni(001) surfaces are shown to provide clear physical insight for this new and exciting phenomenon. In addition to the spin magnetic moment enhancement, the orbital magnetic moment is also found to be enhanced at the surface due to band narrowing. A double peak structure of the MCD spectra for Fe(001) and Co(001) is predicted. For Ni(001), the absorption side peak 6 eV above the main peak is attributed to contributions from the d component in a high-lying state. The MCD orbital sum rule is found to be valid to within 5–10% even in the band approach. However, for the spin sum rule, large errors are found for Ni systems and, in addition, the magnetic dipole term is also found to be very important in this sum rule for atoms without cubic symmetry. This raises a question about the applicability of the spin sum rule to obtain the spin magnetic moment from MCD spectra. Finally, the effects of a photo-induced core hole are found to be strongly screened, and to induce an enhancement of 〈 L z 〉.

An eigenvalue theory of circular birefringence and dichroism in a non-magnetic chiral medium

By means of known constitutive relations for the D and H fields, which include both electric quadrupole and magnetic dipole terms, an eigenvalue theory is developed for electromagnetic wave propagation in an absorbing chiral medium. The theory allows the polarization eigenvectors to be determined, which the medium supports, and also their refractive indices and absorption coefficients. Uniaxial and cubic crystals, as well as an ideal gas, are treated in this way, and expressions are derived for their circular birefringence and dichroism in terms of property tensors of the medium. These expressions are shown to be independent of the arbitrary origin to which the multipole moments are referred. The theory is also applicable to artificial chiral materials which are optically active in the microwave regime.

Nuclear moments and laser spectroscopy

Laser spectroscopy measurements have yielded a wealth of new information about the moments and charge radii of unstable isotopes. The procedures of evaluating these moments from the magnetic dipole and electric quadrupole terms of the hyperfine structure arew discussed. Examples are presented, with emphasis on the isotopic chains of odd-proton nuclei, and their essential features are put into the context of current theoretical model descriptions for spherical and deformed nuclei. Finally, new developments of extremely sensitive experimental techniques are discussed with regard to an application to nuclei very far from stability.

Angular dependence of X-ray absorption spectra

A detailed account of the dependence of X-ray absorption spectra (XAS) on polarisation and light beam directions is given. Anisotropic XAS measured on single crystals, layered compounds, polymers and oriented powders are tabulated. The X-ray absorption cross section by non-magnetic samples is derived, including electric dipole and quadrupole contributions. Orders of magnitude are found for magnetic dipole and electric dipole-octupole terms. Using a spherical tensor expansion of the absorption cross section, simple analytical formulae are given for the angular dependence of the electric dipole and quadrupole contributions to XAS for all crystal point groups. These formulae are valid down to the edge and include many-body effects. The are applied to two experimental examples, the iron K-edge in haematite and the copper K-edge in CuCl42-. For the latter case, spherical tensor components are interpreted in terms of molecular orbitals. The influence of unpolarised and circularly polarised X-rays is discussed, as well as various experimental problems met in angle-resolved XAS. In an appendix, the quadrupole contribution to angular XAS is derived within the multiple-scattering formalism, along with closed expressions for the dipole and quadrupole spherical tensor components.

IDEALIZED ELECTRIC- AND MAGNETIC-FIELD SENSORS BASED ON SPHERICAL SHEET IMPEDANCES

ABSTRACT This paper considers the response of electric- and magnetic-field sensors in terms of spherical modal expansions to identify the electric-and magnetic-dipole terms which are associated with the ideal angular response to an incident plane wave. Considering an idealized spherical resistive sheet sensor, the dipole surface current densities are computed and bandwidth and figure of merit determined to optimize the choice of Rs. For practical sensors the response in general includes various multipole terms besides the desired dipole terms. Expanding the response in terms of spherical harmonics allows one to identify the dipole term and from this gives one a definition of upper frequency response. In addition a norm over the unit sphere of the difference between the actual response and the ideal response gives another way to define upper frequency response. An example of a magnetic -sensor design which approximates the resistive-sheet sphere is also considered.