Exchange-Mediated Anisotropy of (Ga,Mn)As Valence-Band Probed by Resonant Tunneling Spectroscopy

We report on experiments and theory of resonant tunneling anisotropic magnetoresistance (TAMR) in $\mathrm{AlAs}/\mathrm{GaAs}/\mathrm{AlAs}$ quantum wells (QW) contacted by a (Ga,Mn)As ferromagnetic electrode. Such resonance effects manifest themselves by bias-dependent oscillations of the TAMR signal correlated to the successive positions of heavy (HH) and light (LH) quantized hole energy levels in GaAs QW. We have modeled the experimental data by calculating the spin-dependent resonant tunneling transmission in the frame of the $6\times 6$ valence-band $k·p$ theory. The calculations emphasize the opposite contributions of the (Ga,Mn)As HH and LH subbands near the $\Gamma$ point, unraveling the anatomy of the diluted magnetic semiconductor valence band.

Figure 1

$dI/dV\mathrm{\text{−}}V$ acquired on the 6-nm GaAs QW exhibiting the successive HH and LH resonances. The positive bias corresponds to holes injected from (Ga,Mn)As into GaAs:Be. The opposite holds for negative bias. (Inset) Linear relationship of slope $s$ linking the measured resonant bias to the corresponding quantized energy level. VBO is the valence-band offset between GaAs and GaMnAs.

Figure 2

(a) TAMR-$V$ signal (dash-dotted red line) and $dI/dV\mathrm{\text{−}}V$ (dashed line) acquired on the 6-nm GaAs QW. The left axis displays the measured TAMR; the right one takes into account the up-renormalization (see text). Inset of a) TAMR-$T$ acquired at 2.75 V (LH2 peak) and $M\mathrm{\text{−}}T$. (b) TAMR-$V$ calculated (straight red line) and transmission coefficient (unit not shown) calculated at an average energy ${ϵ}_h=-160\mathrm{meV}$ and for respective small $k_{\parallel }$ (dotted blue line) and intermediate $k_{\parallel }$ (dashed black line). (c) energy and band-resolved TAMR-$V$ calculated for ${ϵ}_h=-160\mathrm{meV}$.

Figure 3

Transmission coefficients (in log scale) mapped on the two-dimensional Fermi surfaces for $n=2$ LH and $n=4$ HH (Ga,Mn)As subbands. These are calculated for out-of-plane (left) and in-plane magnetization (right) at an elastic energy ${ϵ}_h=-160\mathrm{meV}$ and at three different biases of $V=0.59\mathrm{eV}$ on LH2 resonance (a)–(d), out of LH2 resonance at $V=0.68\mathrm{eV}$ (e),(f), and $V=0.71\mathrm{eV}$ for very large $k_{\parallel }$ (g),(h).