Experimental Setup

For the in situ MOKE investigation of ultrathin Fe films on GaAs{110} a homebuilt po-larization-modulated ellipsometer (PME) is used in this thesis. The ellipsometer is com-bined with a homebuilt ultrahigh vacuum chamber that contains the investigated sample and 4 coiled magnetic poles for external field application (see Figure 2.2). This in situ 4-magnetic-pole setup based on a similar setup presented by Qiu et al. [113] was developed in the Master’s thesis of A. Grimsel [114]. The 4 magnetic pole shoes, which are arranged in a plane parallel to the sample surface, consist of soft iron and are each coiled with a separate copper wire so that each pole can be addressed separately. This allows the appli-cation of an external magnetic field to the sample in any arbitrary direction. Due to the implementation of high-current power supplies in the framework of S. Weikert’s Bache-lor’s thesis [115] in-plane fields of up to 130 mT and out-of-plane fields (all 4 magnetic poles have the same sign) of about 18 mT can be achieved with this setup. More details on the in situ 4-magnetic-pole setup can be found in Refs. [114, 115].

The setup allows an in-plane rotation of the sample by 360°. The arrangement of the win-dows of the UHV chamber permits the two angles of incidence of 𝜃𝜃 = 15° and 𝜃𝜃= 67°

for the optical path (for definition see also Figure 7.2 in chapter 7).

2.2 Magneto-Optic Kerr Effect

27 Figure 2.2: The MOKE setup consisting of the optical path of the polarization-modulated ellipsometer with a photoelastic modulator (PEM) and the in situ 4-magnetic-pole setup (encircled by the dotted black line) with the 4 magnetic poles M1—M4. Adapted from Ref. [116].

The working principle of the polarization-modulated ellipsometer used in this experi-mental setup is described in the textbook by Azzam [106] and was introduced by Jasperson et al. [117, 118]. The optical path of the setup is illustrated in Figure 2.2 and starts with the laser. Most of the measurements in this thesis are conducted with a linearly polarized HeNe laser with a wavelength of 𝜆𝜆_HeNe= 632.8 nm.⁶ The laser light then pass-es through a linear polarizer (extinction ratio better than 1: 10⁴) set to an angle of 𝛼𝛼_𝑃𝑃= 45° (angles along the optical path are specified with respect to the horizontal 𝑥𝑥 axis as defined in Figure 2.2). Subsequently, the linearly polarized light propagates through a 𝜆𝜆/4 compensator (waveplate) set to an angle of 𝛼𝛼_𝜆𝜆/4= 0° so that the laser light is trans-formed into a circularly polarized wave. Afterwards, this wave propagates through the photoelastic modulator (PEM) [117] shifting the 𝑥𝑥 component alternating by ±𝜋𝜋/2 with respect to the 𝑦𝑦 component of the wave at a modulation frequency of 𝜔𝜔_𝑀𝑀= 2𝜋𝜋/𝑇𝑇= 50 kHz. This means that at 𝑡𝑡= 0 and at 𝑡𝑡=𝑇𝑇/2 the circularly wave passed through the PEM unaltered and at 𝑡𝑡=𝑇𝑇/4 and at 𝑡𝑡= 3𝑇𝑇/4 the light leaves the PEM with a linear polarization at an angle of 𝛼𝛼= 45° and 𝛼𝛼= 135°, respectively. This modulated light wave then impinges onto the sample and is reflected off its surface. Subsequently, the wave reaches the analyzer (extinction ratio better than 1: 10⁴) that solely lets pass the wave component in 𝑦𝑦 direction perpendicular to the plane of incidence. If the sample is

6 Also other laser wavelengths can be chosen. In that case the polarizers and compensators have to be select-ed accordingly.

28

magnetized, the linearly polarized waves will be rotated by the Kerr angle 𝜑𝜑_𝐾𝐾. This yields two slightly different amplitudes sin(45° +𝜑𝜑_𝐾𝐾) and sin(135° +𝜑𝜑_𝐾𝐾) passing through the analyzer for the two orthogonal linearly polarized light waves separated by 𝑡𝑡=𝑇𝑇/2.

Eventually, this leads to a 50 kHz modulation of the light intensity that is detected by the photodiode and fed into the lock-in amplifier where it is multiplied by the reference sig-nal of 𝜔𝜔_𝑀𝑀= 50 kHz from the PEM. The time-dependent product is integrated over a defined time which yields the output signal that is directly proportional to the Kerr rota-tion 𝜑𝜑_𝐾𝐾. A detailed derivation of the detected intensity 𝐼𝐼_𝐷𝐷 is given in [52, 116] and yields the proportionality

𝐼𝐼𝐷𝐷 ∝(𝛼𝛼_𝐴𝐴 − 𝜑𝜑𝐾𝐾)𝐽𝐽₁(𝛿𝛿_{𝑚𝑚𝑣𝑣𝑥𝑥}) sin(𝜔𝜔𝑀𝑀𝑡𝑡) +𝜂𝜂𝐾𝐾𝐽𝐽2(𝛿𝛿_{𝑚𝑚𝑣𝑣𝑥𝑥}) cos(2𝜔𝜔𝑀𝑀𝑡𝑡). ^(2.24) Here 𝛿𝛿_{𝑚𝑚𝑣𝑣𝑥𝑥} is the maximum phase shift the PEM is adjusted to, 𝛼𝛼_𝐴𝐴 presents the angle the analyzer is set to, and 𝐽𝐽₁(𝑥𝑥) and 𝐽𝐽₂(𝑥𝑥) represent the first and second Bessel func-tion [119], respectively. Expression (2.24) shows that if the reference frequency from the PEM, which is fed into the lock-in, is set to the first harmonic of 𝜔𝜔_𝑀𝑀, the output of the lock-in is proportional to the Kerr rotation. In this case one should choose 𝛿𝛿_{𝑚𝑚𝑣𝑣𝑥𝑥} =𝜋𝜋/2 because there the first Bessel function has a global maximum. Setting the reference fre-quency to the second harmonic of 𝜔𝜔_𝑀𝑀 leads to a proportionality of the lock-in output signal to the Kerr ellipticity 𝜂𝜂_𝐾𝐾. If one wants to measure the Kerr ellipticity the maximum phase shift of the PEM should be set to 𝛿𝛿_{𝑚𝑚𝑣𝑣𝑥𝑥}=𝜋𝜋 because there the second Bessel func-tion has a global maximum.

It can be shown [52] that for the experimental arrangement used in this thesis (analyzer solely lets pass the wave component perpendicular to the plane of incidence) the 50 kHz modulation of the light intensity at the detector ∆𝐼𝐼_𝐷𝐷 is given by

∆𝐼𝐼𝐷𝐷 ∝ 𝐸𝐸𝑠𝑠𝐸𝐸𝑝𝑝𝜑𝜑𝑝𝑝, (2.25) where 𝐸𝐸_𝑠𝑠 and 𝐸𝐸_𝑝𝑝 are the amplitudes of the electric fields of the s and p polarized light and 𝜑𝜑𝑝𝑝 is the Kerr rotation of the p polarized light. This means that the MOKE setup de-scribed in Figure 2.2 and used in this thesis is primarily sensitive to the Kerr rotation of the p polarized light 𝜑𝜑_𝑝𝑝. This information is of particular importance for the analysis of the experimental data in chapter 7 by means of the formalism presented in section 2.2.1.2.

In chapter 7, the experimental values for the Kerr rotation are given in units of mdeg.

These values are obtained by calibrating the lock-in in the following way: the analyzer is rotated around the zero position by ±2.5° in both directions. Then the calibration factor is obtained by dividing 5° by the corresponding detected voltage difference between the two positions of the analyzer.