Valence-Band Structure of the Ferromagnetic Semiconductor GaMnAs Studied by Spin-Dependent Resonant Tunneling Spectroscopy

The valence-band structure and the Fermi level ($E_{\mathrm{F}}$) position of ferromagnetic-semiconductor GaMnAs are quantitatively investigated by electrically detecting the resonant tunneling levels of a GaMnAs quantum well (QW) in double-barrier heterostructures. The resonant level from the heavy-hole first state is clearly observed in the metallic GaMnAs QW, indicating that holes have a high coherency and that $E_{\mathrm{F}}$ exists in the band gap. Clear enhancement of tunnel magnetoresistance induced by resonant tunneling is demonstrated in these double-barrier heterostructures.

Figure 1

(a) Schematic cross sectional structures of RTD $A$ and $B$. (b) (c) The schematic band diagrams of our RTD structures assuming that $E_{\mathrm{F}}$ exists in IB and VB in GaMnAs, respectively. The black and blue lines are VB at the $\Gamma$ point ($E_V$) and quantum levels of VB, respectively. The red dash-dotted lines are $E_{\mathrm{F}}$. The green bands are IB in (b).

Figure 2

(a) $dI/dV\mathrm{\text{−}}V$ and (b) $d^{2}I/d{V}^2\mathrm{\text{−}}V$ characteristics of RTD $A$ and $B$ at 3 K. In both graphs, the blue and red (green and orange) curves correspond to RTD $A$ ($B$). The blue or green curve corresponds to the parallel magnetization (P). The red or orange curve corresponds to the antiparallel magnetization (AP). (c) and (d) show the temperature evolution of the bias dependence of TMR obtained in RTD $A$ and $B$, respectively.

Figure 3

(a) Thin black curves, thick blue lines, and red dash-dotted line are the $E_{\mathrm{V}}$ positions estimated in our RTD structures, $E_{\mathrm{V}}$ assumed in our calculation of the quantum levels, and $E_{\mathrm{F}}$, respectively. Here, the quantization, strain, and exchange splitting are neglected. (b) Experimentally obtained resonant-peak bias voltage $V_{\mathrm{R}}$ as a function of the calculated resonant level $E_{\mathrm{R}}$ with respect to $E_{\mathrm{F}}$ in RTD $B$ with various $E_{\mathrm{Diff}}$ when ${\Delta }_x$ is fixed at 5 meV.

Figure 4

(a) Calculated VB structures (black curves) of the GaAs:Be and the GaMnAs QW with the calculated sub-bands (colored curves) when the AlGaAs (middle figure) and AlMnAs (right figure) are used as the top tunnel barrier, where the best fitting parameters obtained in this study are used. (b)–(d) Schematic picture of the quantization of IB in the GaMnAs QW with the thickness $d$ of (b) 2.5 nm, (c) $\sim 20\mathrm{nm}$, and (d) infinity (i.e., bulk). The black, blue, and green lines are $E_{\mathrm{V}}$, quantum levels of VB, and the ones of the IB, respectively. The green bands are IB. Here, the exchange splitting and strain are neglected for simplicity.