$g$-factor anisotropy in a GaAs/Al${}_x$Ga${}_{1-x}$As quantum well probed by electron spin resonance

The anisotropy of electron $g$-factor is investigated for several GaAs/Al${}_x$Ga${}_{1-x}$As heterostructures using an electrically detected electron spin resonance technique at liquid helium temperature. For a modulation-doped 25-nm single quantum well with electron density $n=4\times {10}^{11}$ cm${}^{-2}$ we extracted an out-of-plane $g$-factor value of $\left|g_{\mathit{zz}}\right|=0.410$ and in-plane values of $\left|g_{\mathit{yy}}\right|=0.359$ and $\left|g_{\mathit{xx}}\right|=0.289$. In addition, linear in magnetic field corrections to the $g$-factor components were also extracted and strong anisotropy in their values was established.

Figure 1

Examples of ESR resonance lines measured in a single heterojunction with $n=1.35\times {10}^{11}\hspace{0.5em}{\mathrm{cm}}^{-2}$ near the filling factor $\nu =1$ (upper panel) and in a 25-nm quantum well with $n=4\times {10}^{11}\hspace{0.5em}{\mathrm{cm}}^{-2}$ near $\nu =3$ (lower panel). The exact filling factor and microwave frequency values are shown for each line; the magnetic field is perpendicular to the 2DEG plane.

Figure 2

Dependences of ESR frequency on the magnetic field for four different values of angle $\theta$ between the magnetic field and the normal to the 2DEG plane. The experimental error is much smaller than the symbol size (the latter is about three times larger than the ESR linewidth and the microwave frequency is known to nine digits.)

Figure 3

Magnetic field dependence of the $g$ factor in a single heterojunction with $n=1.35\times {10}^{11}\hspace{0.5em}{\mathrm{cm}}^{-2}$ (upper panel) and in a 25-nm quantum well with $n=3.6\times {10}^{11}\hspace{0.5em}{\mathrm{cm}}^{-2}$ (lower panel).

Figure 4

Dependences of the $g$ factor on the magnetic field for four different values of the tilt angle $\theta$ between the magnetic field and the normal to the 2DEG plane. The values for the $g$ factors shown are obtained by linear extrapolations of experimental data to zero magnetic field (lines).

Figure 5

Squared $g$-factor values obtained by linear extrapolation to zero magnetic field vs $\cos {}^2\theta$. Open circles and solid squares correspond to in-plane magnetic field directed along $y$ and $x$ axes, respectively.

Figure 6

$g$-factor dependence on the magnetic field measured on the sample with two mesas (electron density is $n=3.6\times {10}^{11}\hspace{0.5em}{\mathrm{cm}}^{-2}$). Solid and open symbols are for mesas $A$ and $B$, respectively. Squares are the results for $B\Vert z$, whereas the rest of symbols are obtained for $\theta ={58}^{°}$ (triangles and circles correspond to the cases of the in-plane magnetic field $B_{\mathit{xy}}$ parallel to the $x$ and $y$ axes).