ARTICLE IN PRESS
Physica B 345 (2004) 189–192
Interference effects in the X-ray Kerr rotation spectrum at the Fe 2p edge S. Valenciaa,*, H.-Ch. Mertinsa, D. Abramsohna, A. Gauppa, W. Gudata, P.M. Oppeneerb b
a BESSY, Albert-Einstein Strasse 15, D-12489 Berlin, Germany Leibniz-Institute of Solid State and Materials Research, P.O. Box 270016, D-01171 Dresden, Germany
Abstract We present longitudinal magneto-optical Kerr rotation spectra across the 2p absorption edge of a Fe film on Si substrate measured by means of polarization analysis upon reflection of linearly polarized synchrotron radiation. Large Kerr rotation angles of up to 711 were detected, more than one order of magnitude larger than those observed in the visible range. An enhancement of the Kerr rotation is observed below the absorption edge due to interference effects. The spectra are successfully modelled using magneto-optical constants, which we determined independently. r 2003 Elsevier B.V. All rights reserved. PACS: 78.20.Ci; 78.20.Ls Keywords: Longitudinal Kerr effect; X-ray; Magneto-optics
1. Introduction Among the X-ray magneto-optical reflection and scattering spectroscopies [1–4] the longitudinal magneto-optical Kerr effect (L-MOKE) is a relatively new phenomenon [5,6]. It is a polarization state effect and thus it is observed quite distinctly from the intensity measurements. L-MOKE describes the rotation of the polarization plane of linearly polarized light when reflected by samples that have a magnetization component parallel or antiparallel to the propagation direction of the light. In addition, the state of the *Corresponding author. Tel.: +49-30-6392-4718; fax: +4930-6392-2989. E-mail addresses:
[email protected] (S. Valencia),
[email protected] (H.-Ch. Mertins).
polarization changes to elliptical. In contrast to simple reflectance measurements the polarization analysis reveals information not only on the intensity but additionally on the phase of the light [7,8]. In the visible energy range the MOKE technique is a widely exploited standard tool for the characterization of magnetism and for microscopy of magnetic domains. While the effect is small in the visible range [9], large Kerr rotations are expected for the soft X-ray range due to the resonant enhancement at the 2p edges of 3d-transition metals [1,3]. Thus, a transfer of the MOKE technique to the soft X-ray range opens up new avenues for the element-selective investigation and microscopy of magnetic materials. In this paper we present experimental L-MOKE spectra measured at the 2p edge of Fe.
0921-4526/$ - see front matter r 2003 Elsevier B.V. All rights reserved. doi:10.1016/j.physb.2003.11.051
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2. Theoretical background The Kerr effect is the reflection analog to the Faraday effect measured in transmission [7]. The incident linearly polarized light is decomposed in equal-amplitude left- and right-circularly polarized waves. The propagation of these waves is described by the magneto-optical constants n7= 1–(d17Dd)+i(b17Db) where the subscripts7refer to parallel/antiparallel orientation of photon helicity and magnetization in the sample [10]. The real and imaginary part (1d1) and b1 denote the non-magnetic dispersion and absorption, respectively, while Dd and Db account for the respective magnetic contributions. The magnetic dichroism is defined by the Voigt parameter Q, which adopts for L-MOKE the form Q= (n+n)/(n sin ft) with n=1/2(n++n) and the complex angle of refraction ft. This leads to the Kerr equations, expressed (for p-geometry) by the non-magnetic reflection coefficient rpp and the magnetization dependent coefficients rps [10] yKp þ ieKp ¼ rps =rpp E
in0 nQ cos fi tan ft ; ðn2 n20 Þ cos ðfi þ ft Þ ð1Þ
with n0 optical constant of the top layer (vacuum) and angle of incidence fi (measured to the surface normal). The reflected light is elliptically polarized, expressed by eKp, and the polarization plane is tilted over an angle yKp with respect to that of the incident light (Fig. 1). The rotation is due to unequal amplitudes of the circularly polarized
waves, while the ellipticity is due to unequal phases. For the calculation of a layered system one has to apply Eq. (1) for every individual interface. The Kerr rotation can be approximated in terms of the optical constants. For small angles of gracing incidence (90 XfiX70 ) and assuming ftBfi we find from Eq. (1) Ddðb1 b0 Þ Dbðd0 d1 Þ yK E ; ð2Þ ðd0 d1 Þ2 þ ðb1 b0 Þ2 where d0 and b0 account for the top layer (or vacuum).
3. Experiment The experiments (Fig. 1) were performed at the undulator beamline UE56-1-PGM-1 of BESSY [11] using the polarimeter chamber [12]. The spectral resolution at the 2p edges was about E/DE=2500, the degree of linear polarisation was PLin>0.99 [11] and the magnetic fields were oriented in the sample’s plane, parallel to the light direction (L-MOKE). The linear polarization of the reflected beam was analyzed by rotating a W/Si reflection multilayer (150 periods of 1.12 nm each, angle of incidence close to the Brewster angle) around the reflected beam by the azimuthal angle g (see Fig. 1), while the intensity was monitored by a GaAs:P diode. The polarization analysis data were evaluated by a procedure, described in detail in Ref. [7]. The sample was an amorphous magnetron sputter deposited Fe layer (30 nm) on a Si wafer, capped with 3 nm Al to prevent oxidation.
Detector γ
φKp Ep Analyzer
φi M Sample
Fig. 1. Schematic set up for Kerr measurements on samples with magnetic moment M. The rotation yKp is detected by an azimuthal rotation of the analyzer and detector around the reflected beam.
4. Discussion The reflection spectrum and the magnetooptical Kerr rotation of p-polarized light across the Fe 2p edge are shown in Fig. 2. The reflectance is resonantly enhanced by two orders of magnitude at the 2p3/2 and 2p1/2 edges while it is low in between. Below the 2p3/2 edge, a minimum appears due to destructive interference of rays, reflected from the top surface and the interface between Fe and the substrate. This interference minimum disappears when changing the angle of incidence
ARTICLE IN PRESS S. Valencia et al. / Physica B 345 (2004) 189–192
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φi= 80o
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1x10-2
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0 -10 700
710
720
730
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Fig. 2. Top: reflectance across the Fe 2p absorption edge. Bottom: corresponding Kerr rotation yKp, experimental results and calculation.
by some degrees (not shown). Our X-ray Kerr rotation data (Fig. 2, bottom) are about 2 orders of magnitude larger, than those observed for Fe in the visible range [9] due to the strong spin–orbit coupling connected with the 2p–3d excitations. The shape of the Kerr rotation spectrum results from the interplay of three individual contributions: (i) The large rotation values yK of up to 12 that are found at the 2p3/2 and the 2p1/2 absorption edges are induced by the magnetic contributions Dd and Db of the optical constant [7] (see Eq. (2)). (ii) In between the 2p edges the Kerr rotation displays a broad maximum although the magnetic contributions Dd and Db are small [7,13]. In this range the Kerr effect is enlarged due to the vanishing optical contrast (n2–n20) between the magnetic sample and the top layer (see Eqs. (1) and (2)) which is close to zero in between the 2p edges. This is confirmed by considering the optical constants which have been determined through independent experiments by resonant magnetic Bragg scattering of circularly polarized light on a Fe/C multilayer [13]. In between the 2p edges we find, as expected, the experimentally determined optical constants b1, d1 of Fe to be close to the data b0, d0 of the Al cap layer taken from tabulated values [14]. Thus, the vanishing denominator (n2–n20) of Eq. (1) leads to an enhancement of the Kerr signal.
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(iii) Some structures in the Kerr spectra, e.g., the singularity at 706 eV, must be related to a third contribution. At this low energy no corresponding structure is found in the magneto-optical data, neither in Dd or Db nor in b1, d1. Even the denominator (n2–n20) cannot account for this singularity. From Eq. (1) an inverse proportionality between the Kerr data and the reflection coefficients rpp is deduced. Thus, strongly pronounced structures in the Kerr data are expected if the average reflectivity is reduced, e.g., by destructive interference on a layered system. This explanation is in accordance with the observation at the 2p3/2 edge where the small Kerr rotation is correlated to a large reflectance. For a quantitative modelling of the Kerr rotation and the reflectivity we have to take into account all the above mentioned contributions for the realistic layered structure. Therefore, we developed a computer code based on the formalism for magnetic multilayer systems, given by Zak et al. [15]. In Fig. 2 the calculations are shown, using the experimentally determined optical constants [13]. Based on this algorithm a systematic study of the influence of interference effects on the Kerr rotation and the reflectance is done by calculating the respective spectra for Fe layers with different thicknesses. The reflectance (Fig. 3(a)) of a bulk sample (d=500 nm) shows the 2p3/2 and 2p1/2 peaks without any substructure. With decreasing layer thickness, interference structures appear in the pre-edge region where the penetration depth of the light is large. Above the 2p3/2 edge the absorption is large and thus interference effects are negligible. The Kerr rotation is more affected by interference effects than the reflectance (Fig. 3(b)). The bulk sample is dominated by the magneto-optical constants at the edges and by the optical contrast at the reflecting interface in between the edges, as discussed in (i) and (ii). With decreasing layer thickness, strong rotation angles show up in the pre edge region exceeding that which result from the magnetooptical effect. In conclusion, we reported on the quantitative modelling of first X-ray Kerr rotation spectra which allows for the separation of atomically induced structures from interference effects.
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Reflectance
Acknowledgements
50
2x10
20 nm 20 nm
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φi= 79.5o
-25
500 nm
0 700 710 720 730
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700 710 720 730
(b)
Energy (eV)
Fig. 3. (a) Calculations of the reflectance for grazing incidence based on the independently determined optical constants. With decreasing layer thickness small interference structures show up in the pre-edge region, (b) calculations for the Kerr rotation show strong influence of interference effects. Spectra are vertically shifted with respect to the bulk sample (d=500 nm) as indicated.
We acknowledge the production of samples by O. Zaharko and H. Grimmer, PSI-Villigen, Switzerland and the BMBF for financing (05KS1IPB/8).
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Exploitation of the large Kerr effect allows for an element selective characterization of magnetic systems, similar to the widely used MOKE technique in the visible range.
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