Experimental setup

The experimental setup is a PCSA-ellipsometer, similar to the one described in [Mue97]. A short review of the working principle is presented in appendix A.

Computer

Figure 3.2: Schematic view of the PCSA-ellipsometer, constructed in the course of this the-sis. The electronic components have a gray background, the optical part is shown with white background.

A schematic view of the optical (white background) and electronic (gray background) part of the setup is shown in Fig. 3.2. A helium-neon laser with a power of 2 mW and a wavelength of λ = 632.8 nm (Melles Griot) is used as a light source. No special power stabilization is required, because the use of the modulator technique and the zero-point correction before each measurement makes the signal independent of small variations of the light intensity. To improve the polarity of the laser light, a dichroic polarizer is introduced into the beam. The extinction coefficient of this polarizer is given by the manufacturer Melles Griot to be <3×10⁻⁶ for the wavelength in use. The polarization axis is set 90^◦ with respect to the incidence plane of the light on the sample (see appendix A).

After passing the polarizer the light is retarded by the λ/4-plate (Melles Griot), consisting of a birefringent mica-plate. Its thickness is chosen to obtain a difference in optical length for fast and slow axis of λ/4 with a tolerance of λ/20. Therefore, the phase difference is π/2. As described in section A, the fast axis is oriented at ≈45^◦ with respect to the linear polarization direction of the light and that is why the light leaves the retarder circularly polarized. By a slight variation of the retarder orientation, ellipticities caused by stresses of the polarizer during its mounting can be corrected.

Before hitting the sample, the light passes through the modulator. One way of modulating the polarization state of light is to use a Faraday cell [Rob63, Zei91] which is known to be very sen-sitive, but has the disadvantage of probably creating magnetic stray fields at the position of the sample. To avoid these stray fields, a photoelastic modulator (PEM-90, HINDS instruments) was used in the present setup. In this type of modulator a time-dependent birefringence is in-duced in a quartz crystal by a piezoelectric transducer. The modulator is run with a frequency of ν = 50 kHz and a retardation amplitude of π/2. In conclusion, the previously circularly

po-3.1 Magneto-optical Kerr effect

Figure 3.3: Modulation of the polarization state of the light during one period T. The linear polarity changes between a) 45^◦ and 135^◦ before and b) 45^◦ +φ_Kerr and 135^◦ +φ_Kerr after reflection from the sample surface.

larized light shows a modulated linear and circular polarization after having passed the modu-lator. The linear polarization is oriented at 45^◦ after T/4 or 135^◦ after 3T/4 (see Fig. 3.3 a)).

After being modulated, the light hits the specimen surface under an angle of about 50^◦ with respect to the surface normal. The sample is placed in a magnetic field, produced by water cooled Helmholtz coils, each having 600 windings and an average radius of 80 mm. Applying a maximum current of 23 A at 150 V, the field strength H_{M OKE} is about 1600 Oe. H_{M OKE} is controlled online by a Hall probe (DTM-133/LPT-230,Group3) in front of the surface with the measured field having an accuracy of better than 0.06% at room-temperature.

The sample holder is either a goniometer which can be adjusted manually with an accuracy of 0.1^◦, or a computer-controlled goniometer which performs the automatized measurement of complete in-plane anisotropy polar diagrams with a step size of≥0.2^◦. Nevertheless, the main limit of the accuracy is not due to the goniometer, but to the mounting of the sample. Con-sequently, the goniometer errors given above are negligible in comparison with the mounting error which is considered to be as large as 2^◦.

After being reflected from the magnetized sample surface, the light has changed its linear po-larization state for t=T/4 or 3T/4 to 45^◦+φ_Kerr or 135^◦+φ_Kerr direction. φ_Kerr is the Kerr rotation obtained from the magnetized surface as discussed in section 3.1.1. The situation of the polarization states before and after being reflected by the sample is shown in Figure 3.3.

The analyzer is a dichroic sheet like the polarizer, but mounted in a precision polarizer holder (Melles Griot), which can be adjusted manually or motor-driven with an accuracy of 5 arc-min. The analyzer was set before each measurement to get the highest signal/noise ratio.

Finally, a silicon photodiode detector (S1337-1010BR, Hamamatsu) is used for the detection of the light. Its sensitive area is 1×1 cm² to allow for an automatic 360^◦ polar diagram

Area 1

measurement of a sample without realignment of the setup dur-ing the measurement. The components of the MOKE setup are controlled by a computer via RS232-interface or a DA/AD input-output-card. Fig. 3.2 shows a diagram of all components and their signal connections. The controlling of the data recording is per-formed by the program MOKE, written in Visual C++ code in the course of this thesis. The data points of the hysteresis curves for several in-plane angles ϕ of the specimen’s 0^◦ axis with re-spect to the external magnetic fieldH_{M OKE}, are stored in separate files. After finishing all measurements on one sample, the satu-ration magnetization Ms, the relative remanence Mr/Ms, the co-ercive field H_c, and the normalized magnetization energy E_m/M_s are extracted from these files as a function of ϕ. This work and the creation of the final file, containing all information necessary for the polar plots of Hc, Mr/Ms and Em/Ms, is done by the pro-gram MOKE-AUSWERTUNG, also implemented in Visual C++.

The program extracts the saturation magnetization by averaging the 5 highest values of the MOKE-signal in the positive as well as the negative branch of the hysteresis loop. The error is the mean error of this average. The remanence point is derived from linear regression of all points measured for magnetic fields in the range between −2 Oe and +2 Oe. This assumption is sufficient, espe-cially for curves with at least 5 points in this interval. To obtain the coercive field H_c, the two points closest to the magnetization reversal are interpolated linearly. The error is the distance to the nearest measured point. The normalized magnetization energy is derived by integrating the area over the anhysteretic magnetization curve, as described by Brockmann et al. [Bro97]. The integration was done as presented in Fig. 3.4 by the equation

E_m

M_s = Area 1−Area 2 + Area 3

2 . (3.10)

As the error of the coercive field is up to 3 Oe for some measurements, also the error forE_m/M_s is large in these cases.

A comparison of the parameters derived by the computer program with values obtained by

”hand-made” analysis showed that all results are identical within the given errors.