The transition between paramagnetism and ferromagnetism is the paradigm for a continuous phase transition at finite temperature. When such a transition is tuned to zero temperature in clean materials, the growth of low-energy zero-point fluctuations potentially drives an array of phenomena, including the formation of novel states such as nonconventional superconductivity. Experimentally, the growth of the fluctuations, however, is curtailed and the transition becomes discontinuous as its temperature is reduced. This is understood to arise from non-analytic corrections to the free energy that always occur 1 . In a recent theory 2,3 , changes of the excitation spectrum are self-consistently considered alongside the ground state. This analysis reveals that a transition to a new state may be an alternative outcome. As the excitation spectrum (the 'disorder') is pivotal to promoting the new 'order' this mechanism is referred to as 'order by disorder'. Here, we report the discovery of modulated order in PrPtAl, consistent with complex spirals, at the boundary between paramagnetism and ferromagnetism, giving the first clear experimental realization of such a state.In our theoretical model, deformations of the Fermi surface in the modulated state enlarge the phase space available for low-energy particle-hole fluctuations and this self-consistently lowers the free energy relative to a uniform ferromagnetic state. Although previous theory predicting spiral formation 4,5 based on this mechanism has considered isotropic magnets, easy-plane systems are better candidate materials, as a hard magnetic axis provides a natural orientation for the spiral wavevector and suppresses 'unwanted' moment fluctuations along the spiral direction. The anisotropy can be introduced with local moments 6 , although the theoretical description close to a ferromagnetic quantum critical point 7 has only recently been extended to include the coupling of these moments to the conduction electrons 8 . Here we describe our findings for PrPtAl. This material is close to being an easy-plane ferromagnet, but has an additional magnetic anisotropy between the two easy axes in the plane. The electronic levels of the praseodymium 4f 2 Pr 3+ ions are split in the crystal environment (PrPtAl has an orthorhombic TiNiSn structure) into nine non-magnetic singlet states. Inelastic neutron studies 9 reveal clear crystal field excitations between these. Choosing a system with only singlets simplifies the theory considerably, avoiding Kondo lattice physics, while still introducing magnetic anisotropy.As there are no preformed moments, ferromagnetic order is achieved by mixing singlets via an inter-site exchange interaction 10 , a process referred to as induced-moment magnetism. Our theoretical approach to analysing the magnetic interactions that bring about magnetic order in PrPtAl differs from the standard treatment 11 by keeping the full frequency dependence of the fermion-mediated Ruderman-Kittel-Kasuya-Yosida (RKKY) interaction. This is the key element for a descr...

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