Anharmonic collective oscillations and gap generation from thermal fluctuations in isotropic classical spin systems

Spin waves are the fundamental excitations in magnetically ordered spin systems and are ubiquitously observed in magnetic materials. However, the standard understanding of spin waves as collective spin oscillations in an effective harmonic potential does not consider the possibility of soft modes, such as those due to an effective potential. In this work, we show that such quartic potentials arise under very general conditions in a broad class of isotropic spin systems without a fine-tuning of the interaction parameters. Considering models with spin-spiral ground states in two and three spatial dimensions, we numerically demonstrate that quartic amplitude spin oscillations produce a fluctuation-induced spin-wave gap which with temperature according to a characteristic power-law. In conjunction with a phenomenological theory, the present work provides a general theoretical framework for describing soft spin modes. This framework generalizes earlier treatments of soft-spin dynamics and gap generation in order-by-disorder systems arising from accidental classical ground-state degeneracies, and highlights the important role of finite-size effects relevant to numerical studies. Our predictions of a temperature-dependent gap in spiral spin systems could be tested in inelastic neutron scattering experiments, providing direct spectroscopic evidence for thermal effects arising from soft spin modes in magnetic materials.