In recent years , more and more gamma-ray bursts with late rebrightenings in multi-band afterglows unveil the late-time activities of the central engines .
GRB 100814A is a special one among the well-sampled events , with complex temporal and spectral evolution .
The single power-law shallow decay index of the optical light curve observed by GROND between 640 s and 10 ks is \alpha _ { opt } = 0.57 \pm 0.02 , which apparently conflicts with the simple external shock model expectation .
Especially , there is a remarkable rebrightening in the optical to near infrared bands at late time , challenging the external shock model with synchrotron emission coming from the interaction of the blast wave with the surrounding interstellar medium .
In this paper , we invoke a magnetar with spin evolution to explain the complex multi-band afterglow emission of GRB 100814A .
The initial shallow decay phase in optical bands and the plateau in X-ray can be explained as due to energy injection from a spin-down magnetar .
At late time , with the falling of materials from the fall-back disk onto the central object of the burster , angular momentum of the accreted materials is transferred to the magnetar , which leads to a spin-up process .
As a result , the magnetic dipole radiation luminosity will increase , resulting in the significant rebrightening of the optical afterglow .
It is shown that the observed multi-band afterglow emission can be well reproduced by the model .