As and Epitaxial-Growth MnSi Thin Films - OPUS Würzburg

16 2. Diluted Ferromagnetic Semiconductor (Ga, Mn)As
A way of visualizing these anisotropy terms was developed in [Papp 07a]. Sample resistance
polar plots (RPP) for different collections of anisotropies are shown in Figure 2.2.
In these plots, the innermost region (low-field) part is the most important for calculating
the anisotropy strengths. This lower field region would form of a square with corners
along the easy axis for a pure bixial anisotropy and the domain wall nucleation energy is
calculated from the length of the half diagonal ǫ/M.(Figure 2.2.a) Figure 2.2.b shows the
the model now including uniaxial terms, where the additional effects elongate the square
into a rectangle. The strength of the uniaxial anisotropy constant in the [¯110] direction
K¯110 (U h ) relative to the biaxial anisotropy constant K cryst can be obtained from the
angle δ (Figure 2.2.c).
With a uniaxial anisotropy term parallel to one of the biaxial easy axes (i.e. K [010]
u , U e ),
an asymmetry arises in the switching energy between the two biaxial easy axes. (e.g. the
energy required to switch towards the easier of the two biaxial easy axis is less than to
switch towards the second biaxial) [Goul 08] The ratio of K cryst : K 110 : K 010 is usually
of the order of 100 : 10 : 1. [Papp 07b] This ratio can easily be modified via changing
parameters such as hole concentration or temperature. [Sawi 04, Papp 07b]
2.2 Ultra-thin (Ga,Mn)As films
Because of increasing surface and finite-size effects, the behavior of ultra-thin films of
many materials differ significantly from the bulk. [Rush 07] observed a marked difference
of the AMR response between 5 and 25 nm (Ga,Mn)As layers showing an increased
crystalline contribution to the magnetic response, particularly a large uniaxial component
Fig. 2.3: Anisotropic magnetoresistance measurement for a device with Corbino geometry from
a 5 nm (Ga,Mn)As film with 5% nominal Mn concentration. The applied field is maintained at
saturation value and rotated along different angles. [Rush 07] used a phenomenological model
to fit the magnetic response and found unaxial crystalline terms dominating the measured magnetoresistance,
confirmed by this measurement. Reprinted from [Rush 07].