Magnetically driven phonon instability enables the metal–insulator transition in h-FeS
Hexagonal iron sulfide exhibits a fascinating coexistence of metal–insulator, structural and magnetic transitions, reflecting an intimate interplay of its spin, phonon and charge degrees of freedom. Here, we show how a subtle competition of energetic and entropic free-energy components governs its thermodynamics and the sequence of phase transitions it undergoes upon cooling. By means of comprehensive neutron and X-ray scattering measurements, and supported by first-principles electronic structure simulations, we identify the critical role of the coupling between antiferromagnetic ordering and instabilities of anharmonic phonons in the metallic phase in driving the metal–insulator transition. The antiferromagnetic ordering enables the emergence of two zone-boundary soft phonons, whose coupling to a zone-centre mode drives the lattice distortion opening the electronic bandgap. Simultaneously, spin–lattice coupling opens a gap in the magnon spectrum that controls the entropy component of the metal–insulator transition free energy. Furthermore, these results reveal the importance of spin–phonon coupling to tune anharmonic effects, thus opening new avenues to design novel technologically important materials harbouring the metal–insulator transition and magnetoelectric behaviours.