Unconventional density-wave state in Ruddlesden‒Popper nickelate La₄Ni₃O₁₀

The recent discovery of superconductivity in Ruddlesden‒Popper (RP) nickelates R_n+1Ni_nO_3n+1 (R = rare earth) under high pressure provides a new platform to understand the underlying physics of high-temperature superconductivity. Previous transport measurements suggest a notable correlation between pressure-induced high-temperature superconductivity and a density-wave (DW) state. Therefore, identifying the nature of the DW state is a prerequisite for decoding the superconducting mechanism in the new family of high-temperature superconductors. Here, we report a comprehensive investigation of the ambient-pressure DW transition in high-quality La₄Ni₃O₁₀ single crystals using ¹³⁹La (I = 7/2) nuclear magnetic resonance (NMR) and nuclear quadrupole resonance (NQR). Our findings reveal a two-stage evolution of the DW order. Below T* ≈ 150 K, a short-range charge order develops in the inner Ni-O layer, accompanied by a dramatic enhancement of spin fluctuations. This is followed by a DW transition at T_DW ≈ 133 K, establishing fully developed charge and spin orders across all Ni-O planes. The layer-dependent behaviour highlights that the mechanism of DW transitions in La₄Ni₃O₁₀ may involve both the interlayer coupling and the electronic structure disparities between the inner and outer layers. These findings provide a new framework for understanding the complex DW state in RP nickelates and their potential role in high-temperature superconductivity.