  The formation of new phases close to itinerant electron quantum critical
points has been observed experimentally in many compounds. We present a unified
analytical model that explains the emergence of new types of order around
itinerant ferromagnetic quantum critical points. The central idea of our
analysis is that certain Fermi-surface deformations associated with the onset
of the competing order enhance the phase-space available for low-energy quantum
fluctuations and so self-consistently lower the free energy. We demonstrate
that this quantum order-by-disorder mechanism leads to instabilities towards
the formation of spiral and d-wave spin nematic phases close to itinerant
ferromagnetic quantum critical points in three spatial dimensions.
