Martingale at increasing stopping times is a martingale

Question

Let $Z_t $ be a martingale and

$$\sigma_u=inf\{t \geq0 : \langle Z,Z \rangle_t \geq u\}$$ Let $Y_u=Z_{\sigma_u}$.Then How do I show that $Y_u$ is a martingale.

I think we have to use the optional sampling theorem here but I am not sure how.Can anyone please help.