Magnetic Circular Dichroism Sum Rules Research Articles

Quantitative atomic order characterization of a Mn2FeAl Heusler epitaxial thin film

In this work, we investigate the effect of anti-site disorder on the half-metallic properties of a Mn2FeAl Heusler alloy thin film. The film was grown on TiN-buffered MgO 001 substrates via magnetron sputtering. A detailed structural characterization using x-ray diffraction (XRD) and anomalous XRD showed that the film crystallizes in the partially disordered L21 B structure with 33% disorder between the Mn(B) and Al(D) sites. We measure a positive anisotropic magnetoresistance in the film, which is an indication of non-half metallic behaviour. Our x-ray magnetic circular dichroism sum rules analysis shows that Mn carries the magnetic moment in the film, with a positive Fe moment. Experimentally determined moments correspond most closely with those found by density functional calculated for the L21 B structure with Mn(B) and Al(D) site disorder, matching the experimental structural analysis. We thus attribute the deviation from half-metallic behaviour to the formation of the L21 B structure. To realize a half-metallic Mn2FeAl film it is important that the inverse Heusler XA structure is stabilized with minimal anti-site atomic disorder.

Rare-earth orbital moment contributions to the magnetic anisotropy in magnetostrictive Tb0.3Dy0.7Fe2

Soft x-ray Magnetic Circular Dichroism spectroscopy at the Dy and Tb M4,5 and the Fe L2,3 edges was performed on a sputter deposited polycrystalline Terfenol-D (Tb0.3Dy0.7Fe2) film on sapphire substrates at temperatures from 100 to 300 K to evaluate the elementwise contribution to the magnetocrystalline anisotropy and coercive field. The elemental spin and orbital magnetic moments were calculated using the x-ray Magnetic Circular Dichroism sum rules. As temperatures decreased, the Tb and Fe moments plateau at 200 K with values of 7.6 μB/atom and 1.8 μB/atom, respectively, while the Dy moment increases to 8.9 μB/atom at 100 K. Between 300 and 200 K, the change in magnetic anisotropy is dominated by thermally induced magnetoelastic effects while for temperatures below 200 K magnetocrystalline anisotropy (MCA) changes are dominant. The MCA changes below 200 K appear to be due to increases in the Dy orbital moment with decreasing temperature in this temperature regime.

Magnetic circular dichroism versus orbital magnetization

The magnetic circular dichroism sum rule yields an extremely useful ground-state observable, which provides a quantitative measure of spontaneous time-reversal symmetry breaking (T-breaking) in a given material. Here I derive its explicit expression within band structure theory, in the general case: trivial insulators, topological insulators, and metals. Orbital magnetization provides a different measure of T-breaking in the electronic ground state. The two observables belong to the class of “geometrical” observables; both are local and admit a “density” in coordinate space. In both of them, one could include or exclude selected groups of bands in order to acquire element-specific information about the T-breaking material. Only in the case of an isolated flat band do the contributions to the two observables coincide. Finally, I provide the corresponding geometrical formula—in a different Hilbert space—for a many-body interacting system.Received 13 January 2020Accepted 13 April 2020DOI:https://doi.org/10.1103/PhysRevResearch.2.023139Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.Published by the American Physical SocietyPhysics Subject Headings (PhySH)Research AreasElectronic structureMagnetismTechniquesX-ray magnetic circular dichroismCondensed Matter, Materials & Applied Physics

Magnetic Circular Dichroism and Electronic Structure of [Re2X4(PMe3)4]+ (X = Cl, Br)

Magnetic circular dichroism (MCD) and electronic absorption spectroscopies have been used to probe the electronic structure of the classical paramagnetic metal-metal-bonded complexes [Re2X4(PMe3)4](+) (X = Cl, Br). A violation of the MCD sum rule is observed that indicates the presence of ground-state contributions to the MCD intensity. The z-polarized δ → δ* band in the near-IR is formally forbidden in MCD but gains intensity through a combination of ground- and excited-state mechanisms to yield a positive C term.

Orbital anisotropy in paramagnetic manganese oxide nanostripes

We have detected a clear magnetic anisotropy in the temperature and field dependent Mn ${L}_{2,3}$ magnetic circular dichroism (MCD) spectra of 28 \AA{} wide paramagnetic manganese oxide nanostripes, which we relate to the presence of a largely unquenched orbital moment revealed by MCD sum rule analysis. Polarization, angle, and temperature dependent linear dichroism spectra indicate that the observed anisotropy is related to a depletion of 3$d$ states with ${m}_{l}=\ifmmode\pm\else\textpm\fi{}2$ orbital quantum number in the ground state of the paramagnetic system. Strongly anisotropic electrostatic coupling provides an internal source of spatial symmetry breaking which might generally yield paramagnetic anisotropy phenomena in $3d$ oxide nanostructures.

Magnetic circular dichroism in real-time time-dependent density functional theory

We apply the adiabatic time-dependent density functional theory to magnetic circular dichroism (MCD) spectra using the real-space, real-time computational method. The standard formulas for the MCD response and its A and B terms are derived from the observables in the time-dependent wave function. We find real-time method is well suited for calculating the overall spectrum, particularly at higher excitation energies where individual excited states are numerous and overlapping. The MCD sum rules are derived and intepreted in the real-time formalism; we find that they are very useful for normalization purposes and assessing the accuracy of the theory. The method is applied to MCD spectrum of C(60) using the adiabatic energy functional from the local density approximation. The theory correctly predicts the signs of the A and B terms for the lowest allowed excitations. However, the magnitudes of the terms only show qualitative agreement with experiment.

Soft X‐ray absorption spectroscopy and magnetic circular dichroism study of electroless‐deposited CoNiFe ternary alloy soft magnetic films

We studied microscopic magnetic properties of each consistent atom in boron added CoNiFe electroless-deposited soft magnetic films, which is a promising candidate for the soft magnetic underlayer of the perpendicular magnetic recording medium, by X-ray absorption spectra (XAS) and magnetic circular dichroism (MCD) measurement. It was found that various monoxides and Fe sesquioxide coexisted with the metals at the upper part of the films. The results of MCD sum rule showed the expected values of orbital angular moment 〈L z〉 for the film with macroscopic magnetic domain boundaries were larger than those of without domains at Co and Ni atoms and smaller at Fe atom. The appearance of macroscopic magnetic domain boundaries probably originated from the increase in 〈L z〉 of Co and/or Ni atoms. (© 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)

X-ray magnetic circular dichroism sum rule correction for the light transition metals

Distinguishable L2 and L3 edges and a clear separation into j 3/2 and j 1/2 excitations are necessary for the application of L2,3 edge X-ray magnetic circular dichroism (XMCD) sum rules, which provide element-specific information about spin and orbital magnetic moments. This separation is present for the heavy transition metals (TM), like Co and Ni, due to their large L2,3 spin–orbit splitting. However, for the light TM, the 2p spin–orbit splitting is strongly reduced and quantum mechanical mixing of j 3/2 and j 1/2 excitations is present. This mixing reduces the observed XMCD related spin and magnetic dipole term contributions and prevents the direct application of XMCD spin sum rules. A large number of 2p → 3d absorption spectra have been fitted nearly perfectly by a simple and phenomenological model, which takes into account lifetime effects and provides quantitative information about jj-mixing at the light TMs. On the basis of this mixing coefficient, sum rule correction factors have been determined. The proposed model results in renormalized magnetic projected XMCD spin moments, verified for different compounds of V, Cr, and Mn. A comparison with complementary methods gives consistent results. This or a similar fitting procedure and the estimated correction factors can be used in the future as a light element XMCD spin renormalization technique.

Magnetic properties ofConanochains

Using the full potential linearized augmented plane wave method, spin and orbital magnetic moments along with the magnetocrystalline anisotropy energies (MAE) of linear shape $\mathrm{Co}$ nanochains consisting of two to seven atoms were explored. The MAE and orbital magnetic moments are strongly oscillatory against the size of nanochains. The magnetic circular dichroism sum rules were validated, but the relationship between MAE and the anisotropy of orbital moments was denied for these ultrasmall nanoentities due to large spin-flip contribution to MAE.

Sum rules for resonant inelastic x-ray scattering: Explicit form and angular dependence in perpendicular geometry

Resonant inelastic x-ray scattering (RIXS) and resonant photoemission spectroscopy (RPES) can be used to selectively measure the ground-state properties of atoms in solid materials. For the two types of experiment we compare the sum rules developed in the past years to extract quantitative information from the measured spectra. We show that if the measurements are not sensitive to the emitted photon polarization state (in RIXS) or to the photoelectron spin orientation (in RPES), the two experiments exhibit the same angular dependence of the spectral intensities but differ in some numerical coefficients in the sum rules. In particular we give explicit expressions for the RIXS sum rules in the so-called perpendicular geometry for all the cases of practical interest. These rules can serve, in combination with the well-known x-ray magnetic circular dichroism sum rules in absorption, to evaluate the quadrupole and octupole moments of the scattering atoms.

X-ray magnetic circular dichroism study of SmAl2 using the M4,5 x-ray absorption edges

The application of x-ray magnetic circular dichroism sum rules to the M4,5 edges of rare-earth metals has been developed for Sm3+. The jj mixing of intensities between the spin–orbit split M4,5 edges and the influence of the magnetic dipole term, T, on the sum rules have been evaluated by comparison with results from neutron scattering and magnetometry. This analysis leads to the unusual result that 〈Tz〉 is parallel to the orbital magnetic moment, 〈Lz〉, but antiparallel to the spin magnetic moment, 〈Sz〉.

Soft X-ray magnetic circular dichroism in Fe and Fe 0.50 Co 0.48 V 0.02 films: quantitative analysis of transmission

Magnetic circular dichroism (MCD) in X-ray absorption has been measured at the L 2, 3 edges of Fe in ex-situ grown Fe and Fe 0.50 Co 0.48 V 0.02 films by means of the transmission method. A new approach is developed for fitting the observed transmittance, which describes the resonance lineshapes as (generalized) Fano profiles. Analytical integration of each single resonance allows a more reliable determination of the orbital and spin magnetic moments based on the MCD sum rules. The results are consistent with an increase of the Fe spin and orbital magnetic moment in Fe-Co alloys as obtained by other experiments and band structure calculations.

Electron correlation and charge transfer at the Ni/Co interface

The evolving magnetism and electronic structure at the Ni/Co interface have been studied using x-ray absorption spectroscopy (XAS) and x-ray photoemission spectroscopy (XPS) with circularly polarized x rays. Deposition of ultrathin Ni films on thin films of Co grown on Cu(001) results in an intensity enhancement across the Co L2.3 absorption edge. By comparison, the intensity of the Ni L2.3 edge decreases as a function of Ni film thickness. The relative changes in the Ni and Co XAS intensities are interpreted as an electronic charge transfer from the Co to the Ni. Distinct changes in the Co 2p XAS and XPS line shapes after addition of the Ni overlayer imply a modification of the Co 3d electron correlation due to the charge transfer. The change in the electronic structure is related to the interface magnetism using magnetic circular dichroism sum rule analysis.

Interpretation of x-ray circular dichroism: Multiple-scattering theory approach

The relationship between x-ray-absorption magnetic circular dichroism (MCD) and the magnetic properties of a metal is investigated within the framework of spin-polarized relativistic multiple-scattering theory. The MCD sum rules discovered by Thole et al. which relate the energy-integrated MCD intensities to the spin and orbital magnetic moments of the solid, are rederived. Several rules that relate a MCD spectrum to the $l$-projected spin and orbital magnetization densities of empty states of the solid, are also obtained. The application of these rules is discussed.

Enhanced Co orbital moments in Co–rare-earth permanent-magnet films

Soft x-ray magnetic circular dichroism (MCD) data were collected at the Co $L$ edges from a series of epitaxial $R\ensuremath{-}\mathrm{Co}$ ($R=\mathrm{P}\mathrm{r},\phantom{\rule{0ex}{0ex}}\mathrm{N}\mathrm{d},\phantom{\rule{0ex}{0ex}}\mathrm{S}\mathrm{m},\phantom{\rule{0ex}{0ex}}\mathrm{D}\mathrm{y},\phantom{\rule{0ex}{0ex}}\mathrm{a}\mathrm{n}\mathrm{d}\phantom{\rule{0ex}{0ex}}\mathrm{H}\mathrm{o}$) intermetallic compound films grown by sputter deposition. The Co orbital-to-spin moment ratios were extracted from the data using the MCD sum rules. An enhanced Co orbital moment, as compared to that of bulk hcp-Co, is seen in all but one of the films. The enhancement is dependent on both the average $R\ensuremath{-}\mathrm{Co}$ bond length and on the $R$ species. These results suggest that a significant transition-metal (TM) orbital moment is the origin of the TM sublattice contribution to the magnetocrystalline anisotropy energy in $R\ensuremath{-}\mathrm{TM}$ compounds.

Application of the x-ray magnetic circular dichroism sum rules to Co/Pt multilayers (abstract)

The presence of perpendicular anisotropy in Co/Pt multilayers is often attributed to an enhanced orbital magnetization at the surface or interfaces of the multilayers. By the application of the 〈Lz/Sz〉 sum rule to magnetic x-ray circular dichroism spectra it is possible to probe directly the orbital to spin ratio. In this study a comparison has been made of this ratio between Co/Pt multilayers with different anisotropies and also with single films of Co with and without Pt. The multilayers were prepared in high vacuum by evaporation on Si substrates with a 2.4 nm Pt buffer and a 1.2 nm Pt capping layers, characterized by x-ray diffraction and magneto-optic Kerr effect. The magnetic circular dichroism experiments were carried out at Daresbury laboratory in 75% polarization in ±1 T perpendicular applied fields as a function of temperature from 25 to 300 K. We find that the 〈Lz/Sz〉 ratio is enhanced for a multilayer with perpendicular anisotropy compared to a similar multilayer with in-plane anisotropy.

Magnetic circular dichroism in CoS 2 at the Co L 2,3 and M 2,3 core edges

Magnetic circular dichroism (MCD) has been observed at the Co L 2,3 and M 2,3 core-absorption edges in a single crystal of ferromagnetic CoS 2 using circularly polarized helical undulator radiation. The features in the MCD spectra are interpreted on the basis of reported band-structure calculations. By applying the MCD sum rules to the L 2,3 MCD spectrum, we obtained a ratio of the orbital-to-spin magnetic moments of 0.14.

Experimental investigation of the magnetic circular dichroism sum rules (abstract)

High quality L2,3 edges magnetic circular dichroism (MCD) data of in situ grown Fe, Co, and Ni ferromagnetic thin films were measured using transmission x-ray absorption technique. These data were utilized to investigate the validity of the recently proposed x-ray MCD sum-rules that offer a new means for deducing orbital- and spin-magnetic moments from MCD data. We find that the orbital to spin magnetic moment ratios of Fe, Co, and Ni deduced from MCD data according to the sum-rules are at ±30% discrepancy with those deduced from neutron scattering data. This inconsistency may be attributed to the neglecting of multi-electron excitations and band structure effects in the derivation of the sum-rules or due to uncertainties in the neutron scattering results. Caveats for MCD data taken with the fluorescence yield x-ray absorption technique will also be 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 investigation of the validity and range of applicability of the x-ray magnetic circular dichroism sum rule.

X-ray magnetic circular dichroism (MCD) spectra and orbital angular momentum, [l angle][ital L][sub [ital z]][r angle], for transition metal bulk and surfaces were studied for both ground state and core hole excitations using a highly precise local density approach. For Fe(001), we predict a double peak structure in both the MCD and total absorption spectra and a strong enhancement of [l angle][ital I][sub [ital z]][r angle]. Surprisingly, the MCD orbital sum rule is found to be valid to within (5--10)%. Finally, the results suggest possible solutions to several problems faced in applying the MCD sum rule to measure [l angle][ital L][sub [ital z]][r angle].