  The electric-field-induced resonant spin polarization of a two-dimensional
hole gas described by Luttinger Hamiltonian with structural inversion asymmetry
and Zeeman splitting in a perpendicular magnetic field was studied. The spin
polarization arising from splitting between the light and the heavy hole bands
shows a resonant peak at a certain magnetic field. Especially, the competition
between the Luttinger term and the structural inversion asymmetry leads to a
rich resonant peaks structure, and the required magnetic field for the
resonance may be effectively reduced by enlarging the effective width of the
quantum well. Furthermore, the Zeeman splitting tends to move the resonant spin
polarization to a relative high magnetic field and destroy these rich resonant
spin phenomena. Finally, both the height and the weight of the resonant peak
increase as the temperature decreases. It is believed that such resonant spin
phenomena can be verified in the sample of a two-dimensional hole gas, and it
may provide an efficient way to control spin polarization by an external
electric field.
