The magnetic spectroscopes used in this study were XMCD and MOKE, the theory and the experimental set up for these techniques were outlined in chapter 2. The data treatment method used will be outlined here.
5.2.1 XMCD and ESHL
The requirements are for a sub-ML Co coverages that are buried under several ML of Au, the Co signal is thus attenuated by the capping layer due to the limited electron escape depth for the spectroscopies measured in total electron yield (TEY), this results in an inevitably
5.2. Magnetic spectroscopy and data analysis methods Magnetic behaviour
low signal. In the ideal low noise situations the Co signal can be high however this situation is not always realised in practice.
The treatment of the data was a challenge, as small variations in the XAS background could alter largely the values ofp (the integral of the XMCD over the L3 edge) andq (the
integral of the XMCD over the L3+2edges) extracted from the XMCD spectra. The values
ofp were taken from figure (figure 5.7b)≈785 eV but this varied with the monochromator calibration and the values of q were taken at the end of the spectra. Several variations of pre and/or post edge backgrounds were observed in the individual flux normalised XAS spectra and no common trend was observed in the background of the XAS. This resulted in variations in the XMCD spectra and the values of p and q extracted varied greatly.
The standard XMCD data analysis method was found to produce the most reliable results in the XMCD spectra, that is to scale the post edge jump of the flux normalised XAS to unity [106], and this process produced the most consistent values ofp andq (figure 5.7b) for all the data presented here. The difference spectra were obtained with this method. Using the sum rules as outlined in chapter 2, the orbital magnetic moment to spin magnetic moment ratio can be obtained.
The ESHL are obtained by measuring the observed dichroism as the applied magnetic field was varied [79].These hysteresis loops were collected in two equivalent ways during this study.
At beamline 6.3.1 in the ALS the circularly polarised radiation is selected by moving an aperture above or below the plane of the bend magnet emission to select different degrees of left or right circular polarisations. As this changes the entrance angle into the mono- chromator and thus the energy calibration, switching of the polarisation was not performed during the acquisition of ESHL here. Instead the TEY was collected at the peak of the L3 asymmetry as the magnetic field was cycled to positive saturation, then to negative
saturation and back again. Then the excitation energy was moved to the peak of the L2
asymmetry which shows the opposite dichroism to the L3, and the TEY was collected again
as the applied magnetic field was varied. The difference of these two TEY signals was taken to be in proportion to the measured magnetisation and hence produce the ESHL.
At I1011 at MAX-lab, an EPU is used instead of a bending magnet and the source point for the monochromator at I1011 beamline monochromator remains fixed and thus ideally the photon energy is fixed when switching from one circular polarisation to another. So for ESHL collected here the monochromator energy was selected for the peak dichroism of the L3 and fixed. Then between two successive cycles of the applied magnetic field the
polarisation was shifted instead of the monochromator energy. Again to obtain the ESHL loop the difference of the two cycles, which differ now in polarisation was taken.
5.2. Magnetic spectroscopy and data analysis methods Magnetic behaviour
The liner XAS (average of the two circular polarised spectra) was analysed to measure the post edge step edge jump, from all the XMCD collected and while it was found to be consistent with varying wire width or capping layer regions of the sample, but were not capable for compare different samples to each other.
5.2.2 MOKE
MOKE hysteresis loops were collected using the RAS system in TCD previously defined in chapter 2 as shown schematically in figure 2.16, with the inclusion of an electromag- net around the sample. While RAS could be performed without the presence of the first polarizer, it is necessary for MOKE experiments. Whereas RAS depends on the samples anisotropic reflectance for the RAS signal, MOKE is a rotation of the polarization of the light upon reflection. The first polarizer is necessary to make the incident polarisation fixed so then upon rotation the signal will be detected and will vary as the magnetisation of the sample varies.
The spectroscopic RAS of a sample is shown in figure 5.1 with both positive and negative magnetic fields applied; there is a clear difference between the spectra with the different applied fields. The difference and summation of the two spectra are shown in figure 5.2. As can be seen the maximal difference in the spectra is seen at higher photon energies, however this is in the presence of quite high noise. The low noise and the relatively flat difference spectrum at 2 eV lead to MOKE loops being collected at this photon energy, and thus at an optical wavelength of ≈619 nm.
Figure 5.1: Spectroscopic RAS spectra of a sample with positive (black) and neg- ative (red) applied magnetic fields with of120mT.
Figure 5.2: Sum (black) and difference (red) of RAS spectra from figure 5.1. The strongest signal is not at 2 eV there is however the best signal to noise ratio.
5.2. Magnetic spectroscopy and data analysis methods Magnetic behaviour
To obtain temperature dependent MOKE loops, the sample was placed in a continuous flow cryostat. The cryostat was as Oxford Instruments Mircostat He with a tail, suitable for spectroscopic measurements and an Al body that could be placed between the poles of the electromagnet. It could be operated to liquid N2or liquid He temperatures with the sample
in a vacuum of ≈ 10−6mbar as supplied by a turbo molecular pump. Under applied field
the window of the cryostat exhibited a magnetic field dependent strain signal which varies with photon energy in approximately a square root behaviour. This magnetic dependent strain produced a background signal in the hysteresis loops, a similar background was also observed by others [107]. The presence of this background meant that the raw data obtained had to undergo a background subtraction to obtain usable MOKE loops that could then be fitted. The background was characterised by mounting a non-magnetic Si sample in the cryostat from which hysteresis loops were collected. This was obtained from several positions to ensure that the beam passed through different regions of the window. A representative example of the observed background is shown in figure 5.3. For each of the different window regions probed a third order polynomial was fitted to each arm of the observed backgrounds, the coefficients of the polynomial were observed to be the same within error, with the exception of the DC term. An average background was produced by averaging the terms of the coefficients and setting the constant term to be zero. This fitted background was used and subtracted from raw hysteresis data to give loops which were then fitted. For different maximum field strength (for example 50 mT) a similar strain field was observed,for all loops which underwent background subtraction the same background was used for all as the same saturating fields was used in all these loops. A similar procedure was carried out for a rotating field experiment only with a cosine instead of a polynomial. As in rotating field experiments the applied fields magnitude is constant and the angle at which is it applied is varied, which resulted in the observed cosine background as shown in figure 5.4.
5.2. Magnetic spectroscopy and data analysis methods Magnetic behaviour
Figure 5.3: The resultant fitted back- ground present on MOKE hysteresis loop, arising from the magnetic strain in the window of the cryostat at 2 eV.
Figure 5.4: The resultant fitted back- ground present on MOKE rotating field experiments, arising from the magnetic strain in the window of the cryostat at 2 eV.
5.2.3 Fitting hysteresis loops
The ideal ferromagnetic hysteresis loop is characterised as being center symmetric about the H=0, point with a clear saturation level of magnetisation in both the negative and positive branches and an open loop with a well-defined coercivity and stiffness or softness. This is best described by a sigmoidal function. The ESHL and MOKE loop data that were collected were fitted with a sigmoidal function of the form:
M±(H) =−Msat+
2Msat
1 +exp[−s(H∓Hc)]
(5.1) whereMsatis the saturation value of the magnetization,Hcis the coercivity of the hysteresis loop, sis the softness parameter andH is the applied field [21].
An alternative formulation is required to fit the rotating field loops where the magnitude of the applied field is constant but the direction that it is applied is varied. As the RAS MOKE system is only sensitive to the polar magnetism, a hysteresis loop is obtained with the easy axis information from a rotating field measurement which is obtained for a fit of the data.
M±(H) =−Msat(cos(θ)) + 2Msat(cos(θ))
1 +exp[−s(Hconstant(cos(x−θ))∓Hc)]
(5.2) where all the repeated symbols have the same meaning as above, but in addition θ is the angle the easy axis makes with the optical surface,Hconstant is the magnitude of the applied field and xis the angle between the applied field and the surface normal.