Spin-polarized tunneling as a probe of the electronic properties of ${\mathrm{Ga}}_{1-x}{\mathrm{Mn}}_x\mathrm{As}$ heterostructures

We present magnetic and tunnel transport properties of $(\mathrm{Ga},\mathrm{Mn})\mathrm{As}∕(\mathrm{In},\mathrm{Ga})\mathrm{As}∕(\mathrm{Ga},\mathrm{Mn})\mathrm{As}$ structure before and after adequate annealing procedure. The conjugate increase of magnetization and tunnel magnetoresistance obtained after annealing is shown to be associated with the increase of both exchange energy ${\Delta }_{\mathit{exch}}$ and hole concentration by reduction of the Mn interstitial atom in the top magnetic electrode. Through a $6\times 6$ band $k\bullet p$ model, we established general phase diagrams of tunneling magnetoresistance (TMR) and tunneling anisotropic magnetoresistance (TAMR) vs (Ga,Mn)As Fermi energy $\left(E_F\right)$ and spin-splitting parameter $\left(B_G\right)$. This allows us to give a rough estimation of the exchange energy ${\Delta }_{\mathit{exch}}=6B_G\simeq -120\mathrm{meV}$ and hole concentration of the order of $p=1\times {10}^{20}{\mathrm{cm}}^{-3}$ for (Ga,Mn)As and beyond gives the general trend of TMR and TAMR vs the selected hole band involved in the tunneling transport.

Figure 1

(Color online) (a) Magnetization curve vs magnetic field at $10\mathrm{K}$ before and after annealing along [100] direction; (b) magnetization curve as a function of the temperature before and after annealing in a field of $500\mathrm{Oe}$.

Figure 2

(Color online) (a) Tunnel magnetoresistance measurements as a function of the magnetic field at $1\mathrm{mV}$ and $3\mathrm{K}$ for a $128\mu {\mathrm{m}}^2$ junction. (b) Tunnel magnetoresistance measurements as a function of resistance × area product at $3\mathrm{K}$ for four (un)annealed junctions. (c) Tunnel magnetoresistance at $1\mathrm{mV}$ as a function of the temperature before and after annealing. (d) Tunnel anisotropic magnetoresistance measurements as a function of the orientation of a $6\mathrm{kOe}$ saturating field at $1\mathrm{mV}$ and $3\mathrm{K}$ for a $128\mu {\mathrm{m}}^2$ junction. In the present case, 0° corresponds to an in-plane magnetization along [100] crystallographic direction and 90° to an out-of-plane magnetization along [001] crystallographic direction.

Figure 3

(Color online) Calculated resistance area $\left(\mathit{RA}\right)$ product of the trilayer structure as a function of the band offset $d_B$ between the ferromagnetic semiconductor and a $6\mathrm{nm}$ barrier of GaAs or (In,Ga)As. The physical parameters used for (Ga,Mn)As are $6B_G=-120\mathrm{meV}$ and $p=1.5\times {10}^{20}{\mathrm{cm}}^{-3}$. Insets: (bottom) $\mathit{RA}$ product as a function of the (In,Ga)As barrier width $d$ for a band offset $d_B=-0.7\mathrm{eV}$; (top) valence band profile of the heterojunctions.

Figure 4

(Color online) Tunnel magnetoresistance (a) and tunnel anisotropic magnetoresistance (b) vs Fermi energy and spin splitting for a $6\mathrm{nm}$ (In,Ga)As barrier and a band offset $d_B=-0.7\mathrm{eV}$. White lines represent the four bands at the center of the Brillouin zone. Gray lines indicate the Fermi energy for different hole concentrations.