Scaling Theory of Magnetoresistance and Carrier Localization inGa1−xMnxAs

Abstract

We compare experimental resistivity data on Ga1−xMnxAs films with theoretical calculations using a scaling theory for strongly disordered ferromagnets. All characteristic features of the temperature dependence of the resistivity can be quantitatively understood through this approach as originating from the close vicinity of the metal-insulator transition. In particular, we find that the magnetic field induced changes in resistance cannot be explained within a mean-field treatment of the magnetic state, and that accounting for thermal fluctuations is crucial for a quantitative analysis. Similarly, while the non-interacting scaling theory is in reasonable agreement with the data, we find clear evidence in favor of interaction effects at low temperatures.

Scaling relations between anomalous Hall and longitudinal transport coefficients in metallic (Ga,Mn)As films

“…3(a) and 3(b) we first show ρ xx and ρ xy as function of temperature in the range 2 to 300 K for a typical metallic (Ga,Mn)As sample at several magnetic fields. As previously reported by several groups 35,36 , the temperature dependence of ρ xx shows a signature cusp at T C , which shifts to higher temperatures when a magnetic field is applied. From Fig.…”

“…4(a), the σ xx vs. temperature at field of 6 T is plotted as solid black square symbols. Based on a scaling theory for strongly disordered ferromagnets, the temperature variation of σ xx can be understood in terms of the microscopic conductance g 0 (m) of a small coherent cube of size ∼ ξ 0 and a length scale parameter ξ(T ) 36 , where m is the normalized magnetization, defined by…”

Localization and the anomalous Hall effect in a dirty metallic ferromagnet

“…As is well known, the temperature dependence of ρ xx shows a peak near T C and decreases to a minimum around T ∼ 8 − 15 K, showing a much weaker monotonic increase with decreasing temperature. The temperature dependence of ρ xx for T ≥ 4 K has recently been interpreted within a scaling analysis picture that takes into account the competition between localization and the onset of magnetic ordering [33]. However, the temperature dependence of ρ xy and σ xy has not been studied previously in great detail over a wide range of samples.…”

Visualizing Critical Correlations Near the Metal-Insulator Transition in Ga 1- x Mn x As

“…1C). All characteristic lengths, such as dopant separation or mean free path (~10 Å), are much shorter for Ga 1-x Mn x As in comparison to other semiconductors doped with shallow dopants (15). In addition to strong spatial variations, electronic states of Ga 1-x Mn x As are influenced by electron-electron interactions (Fig.…”

“…The nature of the electronic states underlying magnetism in these heavily doped semiconductors is still debated. It is often assumed that the carriers that mediate magnetism in Ga 1-x Mn x As are Bloch states associated with either the valence bands or extended states originating from an impurity band (11)(12)(13); however, the validity of these assumptions has been questioned (14,15).…”