Session M18 - Reflectometry and Magnetic Circular Dichroism.
MIXED session, Thursday morning, March 20
Room 2205, Conv. Center

[M18.01] Unique Phasing of X-Ray Reflectivity Data from Organic Overlayers on Solid Substrates via Interferometry and Holography

The incorporation of a mulilayer reference structure within a solid substrate, manufactured to designed specifications, greatly facilitates the investigation of the profile structure of organic overlayers subsequently deposited onto the substrate by allowing a unique interferometric phasing of x-ray reflectivity data. Furthermore, when the features of the reference structure are sufficiently sharp and appropriately positioned, the phase information itself is recorded in the data and can be recovered unambiguously by off-axis Fourier holography. An investigation of the interaction between an octadecyltrichlorosilane (OTS) self-assembled monolayer (SAM) on silicon and a cadmium arachidate (CdA) bilayer deposited on the SAM's surface by Langmuir-Blodgett techniques illustrates the application of these principles.

[M18.02] Exact Determination of the Phase in Neutron Reflectometry

Information about the scattering length density and corresponding composition depth profile normal to a flat material surface can be inferred from measurements of the specular neutron reflectivity as a function of glancing angle of incidence. Because intensities are measured, the phase of the reflected wave ordinarily is lost and, consequently, direct inversion is not possible, forcing a reliance on fitting schemes. Although phase information can be retrieved in conventional crystal structure determinations by the technique of isomorphic substitution, such a method requires that the scattering be accurately described within the Born approximation, which assumes that the incident wave is not appreciably distorted by its interaction with the sample. Such is not the case for reflectivity measurements in the vicinity of the critical angle. However, given the complex reflection amplitude a direct inversion can, in fact, be performed to extract the scattering density profile using the solution of the one-dimensional inverse scattering problem developed by Gel'fand, Levitan, and Marchenko. An exact determination of the phase in neutron reflectometry is indeed possible in principle by employing three known reference layers.(C.F. Majkrzak and N.F. Berk, Phys. Rev. B52, 10827(1995).) Practical applications of the method to problems in materials physics will be discussed, including actual measurements if data are available.

[M18.03] Inverting Specular Reflectivity from Symmetric Films

Specular reflectivities from real, symmetric, compactly supported potentials of known thickness can be exactly inverted in principle.(N.F. Berk and C.F. Majkrzak, J.\ Phys.\ Soc.\ Japan, in press.) For such potentials, the phase of the complex reflection coefficient is equal to the phase of the transmission coefficient, plus a part depending only on the thickness, and thus can be retrieved from a single measurment of reflectivity using an unambiguous logarithmic dispersion relation for the transmission, which is determined by the reflectivity. The method is general, to the extent that symmetric potentials can be formed by abutting two identical specimens of a film of interest. The resulting reflection coefficient can be inverted using the Gel'fand-Levitan-Marchenko integral equation, for which we show a simple solution method.

[M18.04] Determination of discontinuities of potentials from reflectivity data

Let V(x) denote a potential in the one dimensional Schrödinger equation \psi''+(k^2-V(x))\psi=0 for which V(x)=0 for x<0 and (2) V(x) is piecewise continuous with adequate decay as x\to+\infty. We are interested in the problem of determining V given the reflectivity r(k)=|R(k)|, where R is the usual left hand reflection coefficient. For very special classes of potentials it is known that r determines V uniquely. Here we show that under much more general (although still restrictive) assumptions, the location and magnitude of discontinuities of V can be determined from r. The nature of the restrictions is related to the behavior of R(k) for k in the upper half of the complex plane.

[M18.05] Specular Magnetic Reflectivity Measurements of UO_2

There is considerable interest in the application of X-ray scattering to the study of the magnetic structure near a surface. In our earlier work we reported the observation of magnetic truncation rods for an (001) surface of UO_2(G.M. Watson, D. Gibbs, G.H. Lander, B.D. Gaulin, L.E. Berman, Hj. Matzke, and W. Ellis, Phys. Rev. Lett. 77, 751 ('96).). We also found an enhanced magnetic disorder near the surface when the sample temperature was raised towards the bulk Neel temperature (T_N). In order to further characterize this disorder we have performed specular magnetic x-ray scattering measurements as a function of temperature utilizing a polarization analyzer to remove the specular charge scattering. These results indicate that the width of the magnetic interface diverges as the temperature approaches T_N.

Work at Brookhaven National Laboratory is supported by the U.S. DOE under contract No. DE-AC02-CH7600016.

[M18.06] X-ray Scattering From Discotic Liquid Crystalline Compounds at the Air-Water Interface

We present the first X-ray diffraction study of Langmuir films of discotic compounds at the air-water interface. Such films are the precursors to heavily studied Langmuir-Blodgett films; the disc-shaped molecules are expected to adopt a ``face-on'' (triangular) or ``edge-on'' (columnar) structure. The subjects of our study were discotic liquid crystalline compounds of two types: hexasubstituted azacrown derivatives and triphenylene derivatives with various lengths of side chains. The X-ray grazing incidence and reflection measurements were performed on Beamline X22 at the National Synchrotron Light Source, Brookhaven. The specular reflectivity data were analyzed using the two- and three-box models. The analysis of the azacrown derivative yielded a ``face-on'' monolayer arrangement, consistent with pressure-area isotherm measurements. Among measured triphenylene derivatives were compounds where all six side chains were equal (OC_5H_11) and two so called ``triangle'' compounds, where the 2,3 and 3,6 positions respectively were substituted to shorter (OC_2H_4OH) amphiphilic chains. Moreover, a 1:1 mixture of the 2,3 and 3,6 ``triangles'' was also measured. Analysis of the triphenylene compounds yielded dimensions consistent with the known structure of the molecues, but indicated that the tail conformations must be different from those previously assumed. All triphenylene derivatives showed one diffraction peak in grazing incidence, consistent with intercolumnar distances of 13-20ÅSurprisingly the mixture of ``triangle'' compounds yielded intercolumnar spacings shorter than of each individual ``triangle'' compound.

[M18.07] Diffuse x-ray reflectivity measurements of correlated roughness of a Mo/Si multilayer

Diffuse x-ray reflectivity intensities were measured to characterize the interface morphology of a Mo/Si multilayer. The longitudinal offspecular scans and transverse scans at several multilayer peaks and valleys have been carried out. The parameters related to the interface morphology were obtained by fitting the measured intensities within the distorted wave Born approoximation. The intermixing widths at the interfaces were seperated from the total interfacial widths by analyzing the offspecular scan intensities.

[M18.08] Glancing Angle XAFS Studies of Cu Thermal Vibration at the Cu/Al_2O_3 Interface

Many properties of a material are not due to single-crystal properties, but rather the structure and behavior of internal interfaces. Unlike a free surface, there are few ways to non-destructively probe the buried interfaces. A considerable amount of research suggests that solids "pre-melt" at the surface. Less clear is the role of the solid-solid interface in melting. To further address this, XAFS measurements have been performed at the Cu K-edge in glancing-incidence mode to probe the structure of the Cu at the interface of two solids. By depositing an overlayer of Al_2O_3 on the more dense Cu layer one can control the penetration depth of the x-rays into the Cu layer with fine control of the incidence angle. From a comparison of the Cu XAFS at various x-ray polarization orientations, incidence angles and temperatures, interface structural parameters are obtained. By paying particular attention to the vibrational anisotropy revealed in the XAFS Debye-Waller ! factor, one can characterize atomic motion and the possibility of pre-melting processes. In previous work(R. A. Mayanovic and B.A. Bunker, Physics Letters A202 225-229 (1995)) nearest-neighbor data were obtained and analyzed to show a significant enhancement of vibrations perpendicular to the interface. Here, the results of newly-obtained data and more extensive analysis are presented.

[M18.09] Temperature Dependence of X-ray Magnetic Circular Dichroism at the L_3 Edge of REFe_2 Compounds

The temperature dependence (T=10-300K) of circular magnetic x-ray dichroism at the rare earth L_3 edge of REFe_2 compounds (RE=Ho-Lu) has been studied. The magnetization of the rare earth 4f and 5d states has been separately determined by measuring the magnitude of the quadrupolar and dipolar features in the dichroic spectra. The 5d moment is found to scale with the RE 4f moment in all compounds except Lu, in which it scales with the Fe moment. An explanation of this and other observed features will be discussed. \vfill \footnoterule

^*Work at the Advanced Photon Source is supported by USDOE-BES under contract No. W-31-109-ENG-38. Ames Laboratory is operated for USDOE by Iowa State Univ. under contract No. W-7405-ENG-82.

[M18.10] Determination of magnetic moment directions using x-ray resonant exchange scattering

We present determinations of the magnetic structures of NdNi_2B_2C and SmNi_2B_2C by means of x-ray resonant exchange scattering (XRES) . The integrated intensity of a number of magnetic reflections was measured as a function of the Bragg angle and compared to model calculations for various magnetic structures. The two compounds were found to have the same magnetic modulation wave-vector but different moment directions. A resonant feature observed below the Sm L_3-absorption edge, similar to unexplained effects found in other light rare earth compounds, is identified as quadrupolar XRES and is used to refine the details of the moment direction.

[M18.11] Angle- and Temperature- Dependent Magnetic Circular Dichroism in Core Photoelectron Emission from Gd(0001)

We report on angle- and temperature-resolved magnetic circular dichroism (MCD) in photoemission from Gd 4f, 4d and 5p core-levels of thick (100 ML) magnetized Gd films. The MCD measurements were performed by changing the direction of the magnetization axis relative to the incident light, with the light helicity being kept constant, and the MCD asymmetries being calculated as a difference between spectra obtained with the two magnetizations. Our results agree very well with the published data of van der Laan et al. (P.R.B 53, R5998 (1996)). However, our energy resolution is significantly better, showing excellent agreement with atomic multiplet theory. We have also measured the dependence of the MCD asymmetry as a function of the angle between the exciting light and the magnetization axis. These data suggest a combined influence of both free-atom and photoelectron diffraction effects, and permit assessing the best geometries for use in studying purely magnetic phenomena. In addition, we have investigated the variation of the MCD asymmetry with substrate temperature. Work supported by ONR (Contracts N00014-94-1-0162), DOE, BES, Mat. Sci. Div. (Contract DE-AC03-76SF00098), CNPq (Brazil), and by the DFG (Germany).

[M18.12] Strong Non-linear MCD-effects due to Partially Circular Polarized Light Sources

Most MCD studies in the soft x-ray range are carried out with light of mixed polarization, where the effect of incomplete circular polarization is usually taken care of by linearly extrapolating the data to P_circ=100 %. We developed a simple model which includes the polarization factor in the MCD line shape. Calculations show that the MCD-signal, which is a relative measurement of the difference between reflection intensities obtained with opposite light helicity or opposite magnetization directions, is indeed proportional to P_circ, whereas the absolute MCD-effect ,which is the normalized quantity 2(I^+-I^-)/(I^++I^-) turns out to be highly non-linear with regard to P_circ. MCD experiments with a specially designed quadruple reflection phase shifter which allows us to take data with variable P_circ as well as P_circ \sim 1. Fe and Co M_2,3 MCD spectra verify the calculations. The data point out that the non-linear response of the MCD-effect to P_circ can generally introduce large errors in the quantitative analysis of MCD spectra where spin \langle S_z \rangle and orbital \langle L_z \rangle moments are extracted by means of sum rules.

[M18.13] A Classical Interpretation of Magnetic Dichroism Sum Rules in X-ray reflection Spectroscopy

A formalism is developed to interpret the magnetic circular dichroism (MCD) sum rules in terms of the complex dielectric tensor \varepsilon (ømega) Utilizing classical Maxwell-Fresnel theory, the formalism is applied to the reflection spectra at M_2,3 of 3d ferromagnets to calculate the orbital moments \langle L_z \rangle . The analysis shows that due to the energy dependence of the unpolarized normalization integral and the choice of a well defined cut-off energy across the transition edge, large errors can be introduced. Uncertainties in \langle L_z \rangle by more than 100 % are possible which makes a comparison with other literature values questionable . Due to the arbitrary energy cut-off, the application of the sum rules as a general tool to unambigiously decompose MCD spectra into orbital and spin components should be practiced with great caution.

Part M of program listing