Fyzikální ústav Akademie věd ČR

T. Jungwirth, Qian Niu, and A. H. MacDonald

We present a theory of the anomalous Hall effect in ferromagnetic (III, Mn)V semiconductors. Our theory relates the anomalous Hall conductance of a homogeneous ferromagnet to the Berry phase acquired by a quasiparticle wave function upon traversing closed paths on the spin-split Fermi surface. The quantitative agreement between our theory and experimental data in both (In, Mn)As and (Ga, Mn)As systems suggests that this disorder independent contribution to the anomalous Hall conductivity dominates in diluted magnetic semiconductors. The success of this model for (III, Mn)V materials is unprecedented in the longstanding effort to understand origins of the anomalous Hall effect in itinerant ferromagnets [1].

Full numerical simulations of σ_AH for GaAs host (top panel), InAs host (bottom panel), and AlAs host (inset) with hole densities p = 0.1 nm^-1 (dotted lines), p = 0.2 nm^-1 (dashed lines), and p = 0.35 nm^-1 (solid lines). The effective field h is responsible for splitting of the valence band due to the exchange interaction with the polarized Mn moments. Filled circles in the top and bottom panels represent measured Anomalous Hall Effect [2,3,4]. The saturation mean-field h values for the two points were estimated from nominal sample parameters [2,3,4]. Horizontal error bars correspond to the experimental uncertainty of the J_pd coupling constant. Experimental hole density in the (Ga, Mn)As sample is p = 0.35 nm^-1 ; for (In, Mn)As, p = 0.1 nm^-1 was determined indirectly from sample's transition temperature.

[1] T. Jungwirth, Qian Niu, and A. H. MacDonald: Phys. Rev. Lett. 88, 207208 (2002), doi:10.1103/PhysRevLett.88.207208

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[2] H. Ohno et al., Phys. Rev. Lett. 68, 2664 (1992).
[3] F. Matsukura et al., Phys. Rev. B 57, R2037 (1998).
[4] H. Ohno, J. Magn. Magn. Mater. 200, 110 (1999).