Pressure-enhanced splitting of density wave transitions in La$_3$Ni$_2$O$_{7-\delta}$

The observation of superconductivity in La$_3$Ni$_2$O$_{7-\delta}$ under pressure, following the suppression of a high-temperature density wave state, has attracted considerable attention. The nature of this density wave order was not clearly identified. Here, we probe the magnetic response of the zero-pressure phase of La$_3$Ni$_2$O$_{7-\delta}$ as hydrostatic pressure is applied and find that the apparent single density wave transition at zero applied pressure splits into two. The comparison of our muon-spin rotation and relaxation experiments with dipole-field numerical analysis reveals the magnetic structure's compatibility with a stripe-type arrangement of Ni moments, characterized by alternating lines of magnetic moments and nonmagnetic stripes at ambient pressure. When pressure is applied, the magnetic ordering temperature increases, while the unidentified density wave transition temperature falls. Our findings reveal that the ground state of the La$_3$Ni$_2$O$_{7-\delta}$ system is characterized by the coexistence of two distinct orders -- a magnetically ordered spin density wave and a lower-temperature ordering that is most likely a charge density wave -- with a notable pressure-enhanced separation between them.