Prediction of huge x-ray Faraday rotation at the GdN4,5threshold

Abstract

X-ray absorption spectra in a wide energy range around the 4d-4f excitation threshold of Gd were recorded by total electron yield from in-plane magnetized Gd metal films. Matching the experimental spectra to tabulated absorption data reveals unprecedented short light absorption lengths down to 3 nm. The associated real parts of the refractive index for circularly polarized light propagating parallel or antiparallel to the Gd magnetization, determined through the KramersKronig transformation, correspond to a magneto-optical Faraday rotation of 0.7• per atomic layer. This finding shall allow the study of magnetic structure and magnetization dynamics of lanthanide elements in nanosize systems and dilute alloys.PACS numbers: 78.20.Ls, 78.70.Dm Resonance enhancements of X-ray magnetic scattering cross sections at inner-shell absorption edges 1,2 have been used for years to investigate the magnetic structure of lanthanide 3 and actinide 4 systems in the hard X-ray regime (above 2 keV). The experimental demonstration of large changes in the specularly reflected X-ray intensity at the Fe L 2,3 edge 5 upon magnetization reversal initiated the ongoing search for magneto-optical (MO) effects in the soft X-ray regime, 6,7,8,9,10,11,12 as well as their application to element-specific studies of heteromagnetic systems. 13,14,15,16,17,18 Yet, in analyzing soft X-ray MO signals from thin films and multilayer systems with thicknesses comparable to the X-ray wavelength, previous investigations have shown 5,13,18 that a comparison with model calculations 19of the reflected specular intensity (based on the Fresnel equations) is needed in order to extract a layerresolved sample magnetization profile. Several experimental determinations of soft X-ray MO constants have been reported 8,9,10 for ferromagnetic transition metals in the region of the L 2,3 thresholds, but none so far for the lanthanide elements, despite their wide recognition as, e.g., constituents of exchange-spring magnets 20 and magnetic recording media 21 . Only recently has it been demonstrated that sizeable MO signals are obtained from lanthanide elements in the soft X-ray region at the N 4,5 thresholds. 22Here we show that calibrated N 4,5 absorption spectra from magnetized Gd metal, recorded with circularly polarized (CP) light in the energy interval from 110 to 200 eV, yield an X-ray absorption coefficient up to three times larger than expected. The magnetizationdependent absorption of CP light at the Gd N 4,5 giant resonance maximum, described by the imaginary part of the refraction index, is accompanied by a huge change in light propagation speed upon magnetization reversal, a dispersive effect described by the real part of the refraction index, implying a Faraday rotation (FR) of about 0.7• per atomic layer. Thus, even very small or diluted lanthanide systems are expected to show a measurable effect.The absorption experiments were performed at the high-resolution UE56 undulator beamline 23 of the Berliner Elektronenspeicherring für Synchrotronstrahlung (BES...

Bright circularly polarized soft X-ray high harmonics for X-ray magnetic circular dichroism

“…As can be seen from Fig. 4, the excellent agreement between the extracted MO absorption coefficients and previous work (41,44) shows that HHG can be successfully used for tabletop XMCD. The MO constants of Fe and Gd around the absorption edges show opposite signs.…”

“…The MO constants of Fe and Gd around the absorption edges show opposite signs. Because Δβ has the same sign for both elements (41,44), this indicates an antiferromagnetic alignment between Fe and Gd layers, as expected for these multilayers (47). Moreover, the XMCD results show that the small side peaks, which result from the imperfect circularity of the driving fields, also exhibit a high degree of circularity with the same circular polarization as their nearest main harmonic peak.…”

“…The refractive index is defined as n ± = 1 − ðδ ± ΔδÞ + iðβ ± ΔβÞ, where β and Δβ are the absorptive index and its magneto-optical (MO) correction, respectively (38)(39)(40). From I ± we obtain the XMCD asymmetry, defined as A XMCD = ðI + − I − Þ=ðI + + I − Þ = −tanhð2ωdΔβ=cÞ, from which the MO absorption coefficient Δβ = ℜð« xy =2= ffiffiffiffiffi ffi « xx p Þ is extracted and compared with previous synchrotron work ( [41][42][43][44][45][46], with « ij representing different components of the dielectric tensor. Note that the opposite sign of A XMCD for adjacent harmonics (Fig.…”

Stranski–Krastanov mechanism of growth and the effect of misfit sign on quantum dots nucleation

“…The calculations are performed with the (1+1)D model. [52] A sharp increase with decreasing absolute value of the misfit is observed only in the case of compressed overlayers, where N 12 clearly goes to infinity at some critical misfit f cr . It is woth to note that in tensile overlayers the increase is less sharp and the curve is displaced to larger absolute values of the misfit.…”

“…1 as a function of the film thickness measured in number of monolayers. [52] These dependences follow from the detailed consideration of the thickness variation of the film chemical potential [9]…”