Quantum order-by-disorder driven phase reconstruction in the vicinity of ferromagnetic quantum critical points

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.