  We demonstrate an all-optical single beam pulsed atomic magnetometer assisted
by laser mode-hopping in a distributed Bragg reflector (DBR) laser. We
implement a temporal sequence of the laser current; sinusoidal current
modulation including the laser mode-hop current for synchronous optical pumping
and the following constant current for paramagnetic Faraday rotation
measurements to probe the free induction decay (FID) of transverse $^{87}$Rb
spin polarization. Repetitive sudden frequency shifts of 20 GHz around the
pressure-broadened $^{87}$Rb spectra originating from laser mode-hopping
enables discontinuous optical pumping modulation with a large depth which
enhances transverse spin polarization. We achieve a sensitivity of 3.77
pT/Hz$^{1/2}$ in a magnetic field of 14 $\mu$T, limited by the performance of
the frequency counter. The Cramer-Rao lower bound (CRLB) of the sensitivity due
to the non-magnetic noise such as photon shot-noise is 191 fT/Hz$^{1/2}$. Our
approach based on laser mode-hopping can be applied to miniaturization of
all-optical atomic magnetometers with sub-pT/Hz$^{1/2}$ sensitivities.
