Complex spin-density-wave ordering in La$_4$Ni$_{3}$O$_{10}$

The discovery of high-temperature superconductivity in layered nickelates under pressure has recently triggered enormous interest. Studies of these compounds have revealed a density-wave-like transition at ambient pressure, though its connection with superconductivity is still not well understood. Here, we report a detailed \msr\ study on single crystals of trilayer nickelate \LNO\ at ambient pressure. We have identified a spin-density-wave (SDW) transition at the temperature of $T_\mathrm{N} \sim$130 K, as well as a broad crossover around 70 - 100 K. Based on the temperature dependence of the muon precession amplitudes and magnetic susceptibility, we attribute this additional crossover either to a spin reorientation, or to an inhomogeneous SDW ordering.