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The in-plane spin splitting of conduction-band electron has been investigated in an asymmetric (001) GaAs/Al  x  Ga 1- x  As quantum well by time-resolved Kerr rotation technique under a transverse magnetic field. The distinctive anisotropy of the spin splitting was observed while the temperature is below approximately 200 K. This anisotropy emerges from the combined effect of Dresselhaus spin-orbit coupling plus asymmetric potential gradients. We also exploit the temperature dependence of spin-splitting energy. Both the anisotropy of spin splitting and the in-plane effective  g -factor decrease with increasing temperature.   PACS:  78.47.jm, 71.70.Ej, 75.75.+a, 72.25.Fe,

Anisotropic in-plane spin splitting in an asymmetric (001) GaAs/AlGaAs quantum well