  A millisecond pulsar (MSP) is an old neutron star (NS) that has accreted
material from its companion star, causing it to spin up, which is known as the
recycling scenario. During the mass transfer phase, the system manifests itself
as an X-ray binary. PSR J1402+13 is an MSP with a spin period of $5.89~{\rm
ms}$ and a spin period derivative of $\log\dot{P}_{\rm spin}=-16.32$. These
properties make it a notable object within the pulsar population, as MSPs
typically exhibit low spin period derivatives. In this paper, we aim to explain
how an MSP can posses high spin period derivative by binary evolution. By
utilizing the stellar evolution code \textsc{MESA}, we examine the effects of
irradiation on the companion star and the propeller effect on the NS during
binary evolution. We demonstrate that irradiation can modify the spin period
and mass of an MSP, resulting in a higher spin period derivative. These results
suggest that the irradiation effect may serve as a key factor in explaining
MSPs with high spin period derivatives.
