In-Plane Uniaxial Anisotropy

93 from the interplay between the direction of the Fe film magnetization and the space inver-sion asymmetry of the GaAs{110} surface. Moreover, a connection of the polar Kerr signal to an externally induced preferential magnetization direction caused by the prepa-ration technique, the sample holder, or the MOKE setup can be excluded by this experi-ment. The differences in the absolute value of the Kerr signal between the two non-equivalent GaAs{110} surfaces can be attributed to minimal differences in the thickness of the Fe film and will be addressed in section 7.5.

7.3 In-Plane Uniaxial Anisotropy

In this subsection, the in-plane magnetic properties of ultrathin Fe films on GaAs{110}

are investigated in greater detail. In order to learn more about the in-plane magnetic ani-sotropy of the metal-semiconductor interfaces, the samples are investigated by means of the in-plane rotatable magnetic field of the MOKE setup (see also section 2.2.2). Similar measurements were already presented in the two Bachelor’s theses of Rolf-Pissarczyk and Weikert [115, 146] which were supervised by the author of this PhD thesis.

Figure 7.7: In situ Kerr rotation signal measured in longitudinal geometry (𝛽𝛽= 90°) for a 3.2 ML thick Fe film on p-type GaAs(11�0) with an angle of incidence of 𝜃𝜃= 15°. The measurements have been conducted at a laser wavelength of 𝜆𝜆 ≈785 ^nm.

Here a Fe film of 3.2 ML nominal thickness on p-type GaAs(11�0) is investigated. In a first step, longitudinal MOKE measurements are conducted with the laser plane-of-incidence and external magnetic field oriented parallel to the <001> easy axis of the sam-ple. The corresponding Kerr signals are shown in Figure 7.7. At 𝛼𝛼₊=𝜗𝜗₊= 0° one finds a counterclockwise hysteresis curve with a Kerr signal of 𝜑𝜑⁺≈12 mdeg. For angles of 𝛼𝛼₋=𝜗𝜗₋= 180° one obtains a clockwise hysteresis curve with a Kerr signal of 𝜑𝜑⁻≈

−7.5 mdeg. From these values the longitudinal and polar Kerr component are calculated to 𝜑𝜑^𝐿𝐿≈2.25 mdeg and 𝜑𝜑^𝑃𝑃 ≈9.75 mdeg in accordance with equations (7.2) and (7.3).

As already mentioned above, these Kerr rotation values have to be treated with care

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cause they assume a canted film magnetization. However, this assumption is not justified for the ultrathin Fe films as will be discussed in section 7.6.

In a next step, the sample is investigated by applying the external magnetic field into different in-plane directions. The laser plane-of-incidence is set to a fixed in-plane angle of 𝜗𝜗= 90° corresponding to the [1�1�0] direction (perpendicular to the <001> easy axis).

Initially, the external magnetic field is set to 𝛼𝛼= 0° which corresponds to the [001] direc-tion, now perpendicular to the laser plane-of-incidence. This particular setup is also known as the transverse MOKE geometry as has been illustrated in Figure 2.1 in sec-tion 2.2.1. A Kerr rotasec-tion from any magnetizasec-tion component perpendicular (transverse) to the plane-of-incidence cannot be detected in the transverse MOKE setup. In other words: this particular experimental arrangement should filter out the Kerr signal from the in-plane magnetization along the <001> easy axis. The measured Kerr rotation for this configuration is shown in the upper left panel in Figure 7.8. Indeed, a Kerr rotation of 𝜑𝜑 ≈9.5 mdeg is detected. This value is in very good agreement with the polar Kerr com-ponent of 𝜑𝜑^𝑃𝑃≈9.75 mdeg obtained from the longitudinal measurement in Figure 7.7.

Furthermore, the counterclockwise sense of the transverse MOKE measurement matches the proposed sense of the polar component in the corresponding hysteresis curve from Figure 7.7. Therefore, one can say that the transverse MOKE measurement solely detects the polar Kerr rotation component from the sample. Rotating the in-plane angle of the magnetic field to 𝛼𝛼= 180° (corresponding to the [001�] direction) and keeping the laser plane-of-incidence at 𝜗𝜗= 90° yields a hysteresis curve of the same height but with a reversed (now clockwise) sense (see right upper panel in Figure 7.8). This is the behavior one would expect because a rotation of 𝛼𝛼 by 180° means that positive and negative 𝐵𝐵�⃗_ext are simply interchanged.

As was described in section 2.2.2, the MOKE setup allows to rotate the in-plane magnetic field into any arbitrary direction. In the following, this feature is used to detect the Kerr signal for angles between 𝛼𝛼= 0° and 𝛼𝛼= 180°. The corresponding data are shown in Figure 7.8. The data show hysteresis loops with abrupt jumps for all measured directions.

Furthermore, the hysteresis widths (coercive fields) increase when approaching the [1�1�0]

direction. At 𝛼𝛼 ≈91° one does not observe any hysteresis at all but an even function of the polar Kerr component which will be discussed later in this section.

7.3 In-Plane Uniaxial Anisotropy

95 Figure 7.8: Measured Kerr signal for a 3.2 ML thick Fe film on p-GaAs(11�0) at a fixed rotation angle of the laser plane-of-incidence of 𝜗𝜗= 90° and for different in-plane mag-netic field directions with rotation angles 𝛼𝛼. The angle of incidence is set to 𝜃𝜃 = 15°. The measurements were conducted at a laser wavelength of 𝜆𝜆 ≈785 nm. For more details see continuous text.

Furthermore, another set of measurements is performed for the laser plane-of-incidence set to an in-plane angle of 𝜗𝜗= 270°. The resulting coercive fields (half hysteresis widths) for both geometries (𝜗𝜗= 90° and 𝜗𝜗= 270°) are plotted against the 𝐵𝐵�⃗_ext field rotation angle α in Figure 7.9. In the experiment the accuracy in adjusting the angles α and ϑ is in the range of ~1 deg. Therefore, the angles for which no switching (hysteresis) occurs can be identified as 𝛼𝛼= 90° and 𝛼𝛼= 270° corresponding to the <110> in-plane direction.

Moreover, the data suggest a 1/cos(α) dependence of the coercive field [115, 146] which is indicated by the black dashed lines in Figure 7.9. As illustrated in Figure 7.8, the

pro-96

jection of the external magnetic field in the 𝑥𝑥 direction (parallel to the <001> direction) is given by 𝐵𝐵_𝑥𝑥 = |𝐵𝐵�⃗_ext| ∙cos𝛼𝛼. Measurements where 𝐵𝐵�⃗_ext is applied along the <001> direc-tion (𝛼𝛼= 0° and 𝛼𝛼= 180°) exhibit a coercive field of 𝐵𝐵_𝑥𝑥^𝑠𝑠f≈0.45 mT. If the direction of 𝐵𝐵�⃗_ext is tilted out of the <001> direction, the measured coercive field grows by the factor of 1/ cos𝛼𝛼. Therefore, solely the component of the external magnetic field projected on the <001> in-plane easy axis (𝑥𝑥 direction) determines the switching behavior of the sam-ple. In other words: 𝐵𝐵_𝑥𝑥^𝑠𝑠f is the externally applied field along the <001> direction that is necessary to switch the magnetization of the sample.

Figure 7.9: Half hysteresis widths (coercive fields) for a 3.2 ML thick Fe film on p-GaAs(11�0) at a fixed rotation angle of the laser plane-of-incidence of (left) 𝜗𝜗= 90° and (right) 𝜗𝜗= 270° and for different in-plane magnetic field directions with a rotation angles 𝛼𝛼. The angle of incidence is set to 𝜃𝜃= 15°. The measurements are conducted at a laser wavelength of 𝜆𝜆 ≈785 nm. Positive and negative values denote counterclockwise and clockwise hysteresis curves, respectively. The data excellently describe a 1/cos(α) de-pendence (black dashed lines).

The Kerr rotation measured for external magnetic fields parallel or almost parallel to the in-plane <110> direction (see the three lower right panels in Figure 7.8) can be explained in the framework of an out-of-plane magnetization component. If the external field is applied exactly into the <110> in-plane direction (case 𝛼𝛼= 91° in Figure 7.8) there is no field component along the 𝑥𝑥 direction (or <001> direction) that is necessary to switch the in-plane magnetization component and the out-of-plane component coupled to it. Hence, no hysteresis is observed. The even function, which is observed instead, shows that the out-of-plane magnetization is continuously driven into the <110> direction. By applying an external field of sufficient strength of ~100 mT the polar component is zero and the magnetization is completely aligned along the <110> direction. The Kerr signal of

~5 mdeg of the even function accounts for half the polar component that is found for switching between two spin states (see upper panels in Figure 7.8). Furthermore, the dif-ference in the Kerr signal for an applied field of +100 mT and −100 mT can be