Evolution of in-plane magnetic anisotropy

In-plane uniaxial magnetic anisotropy in ultrathin films

Figure 3.11 shows magnetization curves for the 7-ML-thick Fe film (see Fig. 3.9, d_Fe = 7 MLs) at two different temperatures with the magnetic field applied parallel to the two major in-plane perpendicular directions, namely the [332] and [110] directions. The magnetization M is normalized to the saturation magnetization, M_s⁰ at T = 10 K. As can be seen, the 7 ML-Fe film exhibit a strong UMA with the easy axis along [332].

The hysteresis curve along this direction has a pure rectangular shape with a normalized remanence M_r/M_s ∼ 1. This indicates that the Fe layer is essentially single domain in nature or with a preferred domain orientation pointing along the easy axis as suggested for Fe/GaAs(001) [126]. An increase in the coercive field at 10 K is observed compared to 300 K. The magnetization curve along the[110]direction does not show any hysteresis and the coercive field vanishes. The magnetization curve is completely reversible indicating a

Figure 3.12: (a) Normalized magnetization curves along the major in-plane crystallo-graphic directions [332] and [110] for a GaAs(113)A sample with 4 MLs of Fe coverage.

(b) Magnetization curves along [332] for at different temperatures.

hard axis of magnetization. The reversibility of the magnetization curve is suggestive of a rotation process [105]. The in-plane anisotropy field is about 2.5 kOe at 10 K and 1.5 kOe at 300 K. It should be noted that the saturation magnetization for this sample at 300 K decreases to about 10 % of its value at 10 K. However, the saturation magnetization for T → 0 is close to the value of bulk Fe (1740 emu/cm³), indicating the absence of interfacial Fe-Ga-As compounds [115]. As an important observation, the UMA exhibits a hard axis along the [110] direction similar to the case of Fe/GaAs(001).

The first signature of a pronounced UMA was already observed at 4 MLs of Fe coverage.

As shown in Fig. 3.12(a), the magnetization curves measured at 10 K along[332]show an easy-axis behavior in contrast to the magnetization curves along [110]. In fact, the UMA persists up to the Curie temperature as shown in Fig. 3.12(b), which shows magnetization curves along [332] at different temperatures. However, the shape of the magnetization curves of this 4-ML-thick sample differs from that of the 7-ML-thick sample in Fig. 3.11.

First, the coercive field is larger at 10 K with a large switching width. Second, the magnetization curve along[332]deviates from the perfect rectangular shape. We attribute these features to the presence of islanding at 4 MLs of Fe coverage as evidenced from RHEED studies of Sec. 3.3.1.

Four-fold magnetic anisotropy in thick films

In Fig. 3.13, we present the normalized magnetization curves of a 100-nm-thick Fe film measured at RT with the magnetic field applied parallel to the four major in-plane crys-tallographic axes of the (113) surface, namely [332], [110], [031], and [301]. The [031]

and [301] directions lie at an angle of 42.1^◦ and 137.9^◦ relative to the [332] direction, respectively [see Fig. 3.13(b)]. Hysteresis loops taken along the [031] and [301]directions show a normalized remanence of about 1, characteristic of magnetization reversal along an easy axis. It should be mentioned that the measurement along these two directions has an experimental error of 1−5^◦, which arises from a possible misalignment of the sample

Figure 3.13: (a) Room temperature magnetization curves of Fe films on GaAs(113)A for d_Fe =714 MLs (100 nm) measured along the different in-plane crystallographic directions shown schematically in (b). The insets for the [332] and [110] directions show magnified portions of the magnetization curves in the low field region.

in the SQUID magnetometer. Thus, this sample exhibits a dominant in-plane four-fold anisotropy. Note that the in-plane h031i axes can be obtained from the intersection of the (113) plane with the {010} planes. Thus, the observation of easy axes along these in-plane h031idirections can be considered as analogous to the case of Fe on GaAs(001), where the in-plane h001i axes are the easy axes of magnetization. When the magnetic field is applied along the [332] and [110]directions, the normalized remanence reduces to about 0.7. Along the[110]direction, a magnetically intermediate direction of bulk Fe, the magnetization curve shows an abrupt transition at a very low field of about 2 Oe followed by a gradual increase to saturation at approximately 500 Oe. This saturating field of 500 Oe is close to the coercive field calculated from the coherent rotation model for bulk Fe [105]. The magnetization curves along [332] and [110] are equivalent to one another.

The saturation magnetization of this 100-nm-thick sample measured along the easy axes is close to the value of bulk Fe, i.e., 1740 emu/cm³. The RT coercive field along the easy axes is on the order of 7−10Oe. This reflects the high crystal quality of the Fe films.

It is important to note that the easy axis of magnetization in thick films (d_Fe≥70MLs) is found to be along the in-planeh031iaxes, which are not the easy axes of magnetization of bulk Fe. In fact, one of the easy axes of bulk Fe, namely the [001] direction lies out-of plane at an angle out-of 25.24^◦ to the surface normal and towards the [332] direction.

However, we found no evidence of a perpendicular easy axis for the magnetic field applied along a set of out-of-plane directions having different inclination angles, measured from the surface normal and towards the in-plane [332] direction. These observations indicate that the demagnetizing energy in this system is very large as a result of which the easy axis of magnetization lies in-plane. This is also confirmed by other techniques, including polar Kerr effect and the extraordinary Hall effect. Furthermore, for these thicker films,

Figure 3.14: Magnetization curves of a set of three samples of thicknesses 50 MLs, 70 MLs and 140 MLs along the four major in-plane directions. The curves are normalized to their saturation magnetization after correction for the diamagnetic contribution of the GaAs substrate.

we do not observe the expected six-fold magnetic anisotropy as mentioned before. This can be understood by taking into account the large demagnetization energy of the Fe films, and will be discussed in more detail in later sections.