  We present results of the first dedicated observation of the young X-ray
pulsar SXP 1062 in the broad X-ray energy band obtained during its 2019
outburst with the NuSTAR and XMM-Newton observatories. The analysis of the
pulse-phase averaged and phase-resolved spectra in the energy band from 0.5 to
70 keV did not reveal any evidence for the presence of a cyclotron line. The
spin period of the pulsar was found to have decreased to 979.48+/-0.06 s
implying a ~10% reduction compared to the last measured period during the
monitoring campaign conducted about five years ago, and is puzzling considering
that the system apparently did not show major outbursts ever since. The switch
of the pulsar to the spin-up regime supports the common assumption that torques
acting on the accreting neutron star are nearly balanced and thus SXP 1062
likely also spins with a period close to the equilibrium value for this system.
The current monitoring of the source revealed also a sharp drop of its soft
X-ray flux right after the outburst, which is in drastic contrast to the
behaviour during the previous outburst when the pulsar remained observable for
years with only a minor flux decrease after the end of the outburst. This
unexpected off state of the source lasted for at most 20 days after which SXP
1062 returned to the level observed during previous campaigns. We discuss this
and other findings in context of the modern models of accretion onto strongly
magnetized neutron stars.
