  We describe the creation of a long-lived spin-orbit-coupled gas of quantum
degenerate atoms using the most magnetic fermionic element, dysprosium.
Spin-orbit-coupling arises from a synthetic gauge field created by the
adiabatic following of degenerate dressed states comprised of optically coupled
components of an atomic spin. Because of dysprosium's large electronic orbital
angular momentum and large magnetic moment, the lifetime of the gas is limited
not by spontaneous emission from the light-matter coupling, as for gases of
alkali-metal atoms, but by dipolar relaxation of the spin. This relaxation is
suppressed at large magnetic fields due to Fermi statistics. We observe
lifetimes up to 400 ms, which exceeds that of spin-orbit-coupled fermionic
alkali atoms by a factor of 10-100, and is close to the value obtained from a
theoretical model. Elastic dipolar interactions are also observed to influence
the Rabi evolution of the spin, revealing an interacting fermionic system. The
long lifetime of this weakly interacting spin-orbit-coupled degenerate Fermi
gas will facilitate the study of quantum many-body phenomena manifest at longer
timescales, with exciting implications for the exploration of exotic
topological quantum liquids.
