Quantitative analysis of the angle dependence of planar Hall effect observed in ferromagnetic GaMnAs film

Abstract

The angle dependence of the planar Hall effect has been analyzed based on the magnetic free energy including the magnetic anisotropy and the Zeeman effects. The Zeeman effect dominated the magnetic anisotropy in high field and only a single energy minimum is shown in free energy over entire field angle, which leads to the coherent rotation of the magnetization in the form of a single domain state. When the field strength is reduced below 300Oe, multiple energy minima appear in the angle dependence of free energy due to the increase in the relative importance of magnetic anisotropy. In the low field region, reorientation of magnetization experiences abrupt transition between the free energy minima. The pinning fields obtained from the analysis showed systematic dependence on the strength of external field, which was used to rotate magnetization. We understood such pinning energy dependence in terms of the difference in the free energy density profile for the different field strengths.

Temperature-induced transition of magnetic anisotropy between in-plane and out-of-plane directions in GaMnAs film

“…For example, cubic anisotropy in the <100> directions, uniaxial anisotropy in the <110> directions, and another uniaxial anisotropy in the [100] direction have been detected in a GaMnAs film [10][11][12][13][14][15][16]. These anisotropies show dependence not only on the material parameters, as previously mentioned, but also on the temperature [17,18]. Many investigations have shown that the dominant magnetic anisotropy changes from cubic to uniaxial with increasing temperature [10,19].…”

“…However, the amplitude of the PHR decreases dramatically as the field strength is reduced to 500 Oe and below. This is due to the presence of areas with strong out-of-plane anisotropy and pinning field distributions even within the in-plane magnetic domains [18,21,24]. When a strong external field is applied along the film plane, total magnetization of the sample will align with the field and follow the direction of the field when it rotates.…”

Effect of pinning-field distribution on the process of magnetization reversal in Ga1−xMnxAs films

“…The difference between the two values arises from the presence of the uniaxal anisotropy term associated with the [110] direction, which reduces the energy barrier for the magnetization to cross that direction. 12 Therefore, a smaller average pinning field is needed for the reorientation of magnetization over the [110] direction than over the [110] direction, as can be seen in Fig. 3.…”

Coexistence of magnetic domains with in-plane and out-of-plane anisotropy in a single GaMnAs film

“…For example, in their ac susceptibility measurements on GaMnAs films, Hamaya et al [7] found a number of magnetic phases, which showed different magnetic anisotropies. Furthermore, variations of magnetic anisotropy within the film plane and along the film growth direction were found, respectively, by Kim et al [12] and by Son et al, [13] from their Hall effect measurements on GaMnAs films. Although these studies reported the fluctuation of magnetic anisotropies in the GaMnAs film, they were limited to cases in which the fluctuation occurred only between in-plane components of the anisotropy (i.e., between cubic anisotropy along the /1 0 0S direction and uniaxial anisotropy along the /1 1 0S directions) in the film plane.…”