Calculation of X-ray natural circular dichroism

A method is presented to calculate the natural circular dichroism recently discovered in the X-ray range (XNCD). The basic formula represents XNCD as an odd second-rank tensor and leads to a sum rule that relates XNCD to the mixing of odd and even orbitals in the ground state. A multiple-scattering theory of XNCD is presented, and calculated spectra for the L-edges of iodine in LiIO₃ compare favorably with the experiments. Received: 20 October 1997 / Revised: 18 February 1998 / Accepted: 31 March 1998     

Transmission X-ray microscopy using X-ray magnetic circular dichroism

X-ray magnetic circular dichroism (X-MCD) was used as a large, element-specific and quantitative magnetic contrast mechanism in the soft X-ray microscopes at BESSY I (Berlin) and the ALS (Berkeley). The present state and potential of magnetic transmission X-ray microscopy (MTXM) is outlined. The possibility to record images in varying magnetic fields and the high spatial resolution down to 25 nm were used to image out-of-plane magnetized (4 ?Fe / 4 ?Gd)×75 systems. Magnetic domains could be studied in arrays of circular and square dots with lateral dimensions down to 180 nm. Hysteresis loops of individual dots were deduced using the direct proportionality of the X-MCD contrast to the sample magnetization. Images of a 3 nmCr / 50 nmFe / 6 nmCr film demonstrate for the first time that MTXM is also able to observe in-plane magnetized domains. In the future the possible applications of MTXM will be extended with regard to the strength of the external field, the available energy range and the sample conditions by building a dedicated transmission X-ray microscope for magnetic imaging at BESSY II. Received: 22 May 2001 / Accepted: 4 July 2001 / Published online: 5 October 2001     

X-ray magnetic circular dichroism involving valence states

Accepted: 6 March 1997     

Numerical simulation of the spectrum of X-ray natural circular dichroism in the CsCuCl3 crystal

The possibility of observing x-ray natural circular dichroism (XNCD) in enantiomorphous CsCuCl₃ crystals has been considered. The spectra of XNCD in CsCuCl₃ have been numerically simulated for the K, L1, L2, and L3 x-ray absorption edges of copper, cesium, and chlorine using FDMNES and LMTO programs. It has been shown that the largest value of dichroism signal can be expected near the copper and chlorine L1 edges.     

Magnetic circular dichroism in soft X-ray resonant inelastic scattering

We discuss the application of resonant inelastic X-ray scattering to the study of magnetic systems in the soft X-ray range. To this end we distinguish two broad areas. In the first the layout of the experiment is such that the absorption magnetic circular dichroism (MCD) is not zero. In the second the magnetisation is perpendicular to the incident helical beam so that the absorption MCD is zero. In the first area we summarise published results on Fe-Co alloys and we present new data on Mn impurities in Ni together with calculations. In the second area we summarise published results on Ni in Ni-ferrite with final 3s shell excitation and we present new results on Co-metal and Co in Co-ferrite measured with a new approach. This is based on the incident energy dependence of the integral of the Raman spectrum in inner shell excitation (integrated resonant Raman scattering). The potentialities and the limitations of the above methods are critically presented. Received: 23 May 2001 / Accepted: 4 July 2001 / Published online: 5 October 2001     

Soft X-ray magnetic circular dichroism of Cr-doped GaN

Soft X-ray magnetic circular dichroism (XMCD) have been measured for the Ga_0.97Cr_0.03N film grown by NH₃-assisted molecular beam epitaxy. Temperature dependence of the XMCD intensity was well described by the Curie–Weiss law. Although the sample showed ferromagnetic behavior at least up to room temperature, the ferromagnetic component could not be detected by the XMCD measurement.     

X-ray magnetic circular dichroism imaging with hard X-rays

X-ray polarization-contrast images resulting from X-ray magnetic circular dichroism (XMCD) in the hard X-ray region have been successfully recorded for the first time. The apparatus used consisted of an X-ray polarizer, double X-ray phase retarders, and a high-spatial-resolution X-ray charge-coupled-device detector. The sample used was a hexagonal-close-packed cobalt polycrystal foil having a thickness of about 4 microns. The X-ray polarization-contrast image resulting from XMCD was observed at a photon energy of 10 eV above the cobalt K-absorption edge (7709 eV). The observed contrast in the image was reversed by inversion of the magnetic field. Furthermore, the contrast was reversed again at a photon energy of 32 eV above the cobalt K-absorption edge.     

Resonant inelastic X-ray scattering and its magnetic circular dichroism

Magnetic circular dichroism in resonant inelastic X-ray scattering (MCD-RIXS) of ferromagnetic systems is discussed for the longitudinal geometry (LG), where the directions of incident X-ray and magnetization are parallel, and the transverse geometry (TG), where they are perpendicular. MCD-RIXS in LG is represented by two successive real processes, X-ray absorption and X-ray emission, while MCD-RIXS in TG is given by the interference process. We describe an application of MCD-RIXS in LG to the detection of Ce 4f² contribution in Ce, L₃ absorption edge of CeFe₂, and theoretical and experimental studies of MCD-RIXS in TG for Gd and Sm systems.     

X-ray circular dichroism under reflection from antiferromagnetically coupled multilayers

The fluorescence yield under the Bragg reflection of right and left circular polarized radiation with a wavelength in the vicinity of the FeL _{2, 3} absorption edges from the periodic multilayer [Fe(1.5 nm)/V(1.5 nm)]₁₀ that is characterized by the antiferromagnetic interlayer exchange coupling has been theoretically analyzed in L-MOKE geometry. It has been shown that the largest polarization asymmetry of reflectivity takes place at the ??magnetic?? Bragg reflection, which appears due to the doubling of the magnetic period. The expected occurrence of the dichronic signal in the fluorescence yield by its selective excitation in the layers with the same magnetization direction was confirmed, but the effect is suppressed by the specific behaviour of the standing waves in the strongly absorbing multilayers where the standing wave antinodes are situated in layers with low absorption.     

Magnetic circular dichroism in X-ray absorption: theoretical description and applications

A fully relativistic theory for magnetic X-ray dichroism is presented that is based on the Dirac equation for spin-polarised systems and relativistic multiple-scattering theory. This scheme allows one to treat not only translation-invariant solids but can also be applied to disordered alloys and surfaces. An application of the theoretical formalism is presented for a variety of systems, i.e. pure elements, multilayer systems and trilayer systems. PACS  71.15.Rf; 11.80.-m; 87.64.Ni; 31.15.Ew     

X-ray circular magnetic dichroism in the presence of strong spin fluctuations

The use of X-ray magnetic circular dichroism (XMCD) spectra for determininghe t magnitude of atomic magnetic moments in compounds of rare-earth and transition elements is discussed. The standard sum rule approach often yields a magnitude of moments that is often smaller than values obtained from magnetic measurements. We attribute this to strong spin fluctuations in the surface layers in which XMCD signals form. A way of determining the values of local magnetic moments in the presence of strong fluctuations is proposed and tested.     

Relativistic multiple scattering theory of K-edge X-ray magnetic circular dichroism

We discuss the angular dependent K-edge X-ray magnetic circular dichroism (XMCD) spectra based on the non-relativistic Green’s function expansion of the relativistic 4×4 Green’s function developed by Gesztesy et al. [Ann. Inst. Henri Poincaré 40 (1984) 159]. For the core functions we use the Dirac equation solutions whereas the relativistic effects for photoelectrons are automatically taken into account in the Gesztesy expansion. Analyses of the angular anisotropy provides us useful information on local symmetry violation around X-ray absorbing atoms even though we include relativistic effects. We explicitly show three different types of the symmetry which give rise to the suppression of the sin β-dependence in XMCD spectra. We also present explicit formulas of XMCD for randomly oriented and spatially fixed systems. Discussion on Debye–Waller factors is given in the present theoretical framework. Some illustrative calculations are also shown to understand the relativistic effects on the XMCD. The results are given for the Gd L₁-edge and Fe K-edge XMCD.     

Element-specific magnetocrystalline anisotropy energy studied by transverse magnetic circular X-ray dichroism

The magnetocrystalline anisotropy energy in 3d transition metal systems is related to the spin-subband orbital moments and the magnetic dipole operator which accounts for the spin-flip excitations. Magnetic circular X-ray dichroism measurements in a transverse geometry, where the light helicity is perpendicular to the magnetization direction, make it feasible to determine the easy-axis of magnetization.     

Sum rules for X-ray magnetic circular dichroism spectra in strongly correlated ferromagnets

It is proven that the sum rules for X-ray magnetic dichroism (XMCD) spectra that are used to separate spin and orbital contributions to the magnetic moment are formally correct for an arbitrary strength of electron-electron interactions. However, their practical application for strongly correlated systems can become complicated due to the spectral density weight spreading over a broad energy interval. Relevance of incoherent spectral density for the XMCD sum rules is illustrated by a simple model of a ferromagnet with orbital degrees of freedom.     

Imaging of magnetic domains with the X-ray microscope at BESSY using X-ray magnetic circular dichroism

X-ray Magnetic Circular Dichroism (X-MCD), i.e. the change of the absorption of circular polarized Xrays for reversed sample magnetization amounts at the L_{2, 3}-edges of 3d transition metals up to 50% percent. This can be used to obtain in energy-dispersive X-ray imaging techniques a considerable, element-specific magnetic contrast. On the other hand, with the transmission X-ray microscope (TXM) based on the zone-plate technique spatial resolutions of 30nm can be achieved. In this communication it is shown for the first time that the combination of the TXM with XMCD provides a huge contrast and is therefore a powerful new method to visualize in a quantitative and elementspecific manner magnetic domains. Using soft X-rays with a wavelength of 1:7nm corresponding to the energy of the Fe L₃-edge the variation of the shape and magnetization of domains in a magneto-optical GdFe layer system was studied with a lateral resolution of 60nm.