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Abstract

The frustrated rare-earth pyrochlore Yb2Ti2O7 is remarkable among magnetic materials: despite a ferromagnetically ordered ground state it exhibits a broad, nearly gapless, continuum of excitations. This broad continuum connects smoothly to the sharp one-magnon excitations expected, and indeed observed, at high magnetic fields, raising the question: how does this picture of sharp magnons break down as the field is lowered? In this paper, we consider the effects of magnon interactions in Yb2Ti2O7, showing that their inclusion greatly extends the reach of spin-wave theory. First, we show that magnon interactions shift the phase boundary between the (splayed) ferromagnet (SFM) and the antiferromagnetic Gamma(5) phase so that Yb2Ti2O7 lies very close to it. Next, we show how the high-field limit connects to lower fields; this includes corrections to the critical fields for the [111] and [1 (1) over bar0] directions, bringing them closer to the observed experimental values, as well as accounting for the departures from linear spin-wave theory that appear in [001] applied fields below 3T [Thompson et al., Phys. Rev. Lett. 119, 057203 (2017)]. Turning to low fields, though the extent of the experimentally observed broadening is not quite reproduced, we find a rough correspondence between nonlinear spin-wave theory and inelastic neutron scattering data on both a single-crystal sample as well as on a powder sample [Pecanha-Antonio et al., Phys. Rev. 13 96, 214415 (2017)]. We conclude with an outlook on implications for future experimental and theoretical work on Yb2Ti2O7 and related materials, highlighting the importance of proximity to the splayed ferromagnet-Fs phase boundary and its potential role in intrinsic or extrinsic explanations of the low-field physics of Yb2Ti2O7.