Lattice modulations in the double charge density wave system Er5Ir4Si10

Using total and resonant X-ray scattering combined with large-scale structural modeling, we investigate the lattice modulations in Er₅Ir₄Si₁₀, which hosts coexisting incommensurate and commensurate charge-density waves (CDWs). We find that long-range CDW order emerges from a precursor state characterized by local lattice distortions, as evidenced by pronounced diffuse scattering in the diffraction data. These distortions involve displacements of Er, Ir, and Si atoms from their room-temperature crystallographic positions that become increasingly correlated upon cooling, producing substantial changes in the local bonding network at low temperatures. Density-functional-theory calculations performed directly on the experimentally refined structural models reveal an extended soft/unstable phonon manifold on the q z =1/2 Brillouin-zone face in the precursor phase that includes the experimentally observed CDW modulation wave vector. Upon entering the CDW phase, the strongest phonon feature occurs at the corresponding physical wave vector, suggesting selection of the CDW modulation from this pre-existing soft manifold. The calculations also reveal a partial suppression of the electronic density of states at the Fermi level, consistent with earlier muon spin relaxation measurements. Our results identify correlated local lattice distortions and their associated phonon instabilities as important ingredients in the formation and evolution of CDW order in Er₅Ir₄Si₁₀ and support the broader view that precursor lattice distortions can play a significant role in the emergence of complex electronic phases in quantum materials.