Dai Zhao

MAGNETIC LINEAR DICHROISM EFFECTS IN REFLECTION SPECTROSCOPY : A CASE STUDY AT THE FE M2,3 EDGE

Magneto-optical measurements are strongly dependent on the polarization of the radiation as well as the interaction geometry of the light with respect to the relative orientation and direction of the magnetization M. We performed magnetic circular dichroism (MCD) and magnetic linear dichroism (MLD) measurements around the Fe M2,3 transition by measuring the difference between the reflected intensities of right and left circular polarized light (MCD) and the difference between the reflected intensities for opposite magnetization directions (MLD). From the angular variations of the MCD measurements we extracted the dielectric tensor e(ω) which was then used as an input parameter to calculate the magneto-optical response of Fe in reflection MLD spectra. The experimental data around the M2,3 edge show good agreement with model calculations.

Step-induced magnetic-hysteresis anisotropy in ferromagnetic thin films

We investigate the quasistatic magnetic hysteresis of ferromagnetic thin films grown on a vicinal substrate, using Monte Carlo simulations within a two-dimensional XY model. Intrinsic in-plane anisotropy is assigned to surface sites according to their local symmetry. The simulated hysteresis loops show a strong anisotropy: the coercive field is the largest when the external field is along the step direction and vanishes when the external field is perpendicular to the step direction. In general, the coercivity increases with increasing step density, but displays a more complex dependence on film thickness. The simulations also suggest that the mechanism for the magnetization reversal is coherent rotation. These results are in good agreement with experiments.

M2,3 magnetic circular dichroism (MCD) measurements of Fe, Co and Ni using a newly developed quadruple reflection phase shifter

We report magnetic circular dichroism (MCD) experiments around the M 2,3 edges of Fe, Co and Ni films using a quadruple reflection polarizer. The quadruple reflector converts linearly polarized synchrotron radiation into left (LCP) and right (RCP) circularly polarized light. The MCD effect decreases strongly from peak to peak variations of ∼18% for Fe towards ∼ 4% for Ni. The data also show strong variations as a function of reflection angle. From the angular measurements of the MCD-effect we determined the frequency dependence of the off-diagonal element e xy = e 1 xy + i e 2 xy of the dielectric tensor of Fe around the M 2,3 transition.

Dielectric tensor formulation of magnetic dichroism sum rules

A formalism is developed to interpret the magnetic circular dichroism (MCD) sum rules in terms of the complex dielectric tensor e(ω). Utilizing classical Maxwell–Fresnel theory, the formalism is applied to the reflection spectra of Fe at the M2,3 transition to calculate the orbital moments 〈Lz〉. The analysis shows that due to the energy dependence of the unpolarized normalization integral and the absence of a well-defined cut-off energy across the transition edge, large errors can be introduced. Uncertainties in 〈Lz〉 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 unambiguously decompose MCD spectra into orbital and spin components should be practiced with great caution.

Strong Non-Linear MCD-Effects Due to Partially Circular Polarized Light Sources

Most soft x-ray magnetic dichroism studies are carried out with light of mixed polarization. The effect of incomplete circular polarization is usually taken care off by linearly extrapolating the data to P circ =l. Using a classical model which includes the polarization factor we show that the MCD-effect, which is the normalized quantity 2(I + -I - )/(I + +I - ), is highly non-linear with regard to cire . With a specially designed quadruple reflection phase shifter we measured the MCD effect with P cire circ ∼1. MCD spectra of Fe around the M 2,3 transition verify our model calculations of the polarization dependence. The data indicate that the observed non-linear response of the MCD-effect to P circ can generally introduce large errors in the quantitative analysis of MCD data where spin z > and orbital Z > moments are extracted by means of sum rules.

Magnetic circular versus linear dichroism effects: A case study at the Fe M2,3 edge (abstract)

Magneto-optical measurements are strongly dependent on the polarization of the radiation as well as the interaction geometry of the light with respect to the relative orientation and direction of the magnetization M. In an effort to identify the different angular and spectral contributions and to select the preferred experimental setup for magneto-optical measurements, we performed magnetic circular dichroism (MCD) and magnetic linear dichroism (MLD) measurements around the Fe M2,3 transition. The MCD experiments were performed by measuring the difference between the reflected intensities of left and right circularly polarized soft x-ray radiation. While for the MCD experiments, the magnetization was kept constant, it was modulated between M+ and M− for the MLD spectra. We used a quadruple reflection polarizer that was tuned to act as a λ/4 phase shifter for the MCD measurements and as a linear polarizer for the MLD experiments. The experiments confirm our model calculations for longitudinal and polar MCD...

STRONG ANGULAR EFFECTS IN REFLECTION MCD MEASUREMENTS OF M2,3 TRANSITIONS UTILIZING A NEWLY DEVELOPED QUADRUPLE REFLECTION POLARIZER

Abstract We report the first magnetic circular dichroism (MCD) experiments of Fe using a quadruple reflection polarizer. The polarizer operates as a λ 4 phase shifter converting linearly polarized bending magnet radiation into left and right handed circularly polarized light. Strong angular variations of the MCD effect were observed in Fe films at the M 2,3 transition. From the angular MCD measurements we extracted the energy dependence of the off-diagonal elements e xy of the dielectric tensor responsible for the MCD effect.

Magnetization on vicinal ferromagnetic surfaces

Using Ising model Monte Carlo simulations, we show a strong dependence of surface magnetization on surface miscut angle. For ferromagnetic surfaces, when surface spin exchange coupling is larger than that of the bulk, the surface magnetic ordering temperature decreases, toward the bulk Curie temperature, with increasing miscut angle; when surface spin exchange coupling is smaller than that of the bulk, a crossover behavior occurs: at low temperature, the surface magnetization decreases with increasing miscut angle; at high temperature, the reverse is true.

Alteration of MCD Spectra Due to thin film Interference Effects

MCD spectra at the M2 ,3 edge of thin Fe films exhibit thickness-dependent variations in line shape as well as in the absolute MCD-effect. Our data indicate that more information is contained in the MCD spectra than simply the evolution of a magnetic moment and ferromagnetic order. We developed a model to predict line shape modulations as a function of film thickness and angle of light incidence. Using the Fresnel-Maxwell formalism we calculate interference effects between left and right circularly polarized light reflected from the vacuum-film-substrate interfaces which are verified by our MCD measurements. Since the observed interference effects are a function of the excitation wavelength, our results can be directly scaled to show the significance of these effects in the more commonly used L2, 3 region of 3d ferromagnets. Our data point out that one might be ill advised to rely on L2 ,3 MCD experiments to try to extract the formation of magnetic moments in films of several 10s of A in thickness.

Determination of the energy dependence of the off‐diagonal terms of the dielectric tensor by means of M2,3 reflection MCD measurements (abstract)

We present the first magnetic circular dichroism (MCD) measurements around the M edges of 3d metals utilizing SRCs recently developed quadruple reflection polarizer system. The reflection polarizer converts linearly polarized light by means of the phase shift between s‐ and p‐reflections into either left or right circular polarized radiation. The concept of the phase shifter has been tested at a bending magnet beam line at the Aladdin storage ring using the M2,3 absorptions of magnetically ordered thin films of Fe, Co and Ni. The normalized MCD signal e.g., (IR−IL)/0.5*(IR+IL) is on the order of several % from peak to peak and scales linearly with the magnetic moments. The shape of the reflection MCD signals has a very pronounced angular dependence with a maximum around a reflection angle of θ=60°–65°. The main trends in the angular dependence of the reflection MCD signal can be verified by model calculations. The model also allows us to extract the energy dependence of the off‐diagonal terms in the diele...