In several strongly correlated electron systems, the short range ordering of defects, charge and local lattice distortions are found to show complex inhomogeneous spatial distributions. There is growing evidence that such inhomogeneity plays a fundamental role in unique functionality of quantum complex materials. La 1.72 Sr 0.28 NiO 4 is a prototypical strongly correlated perovskite showing spin stripes order. In this work we present the spatial distribution of the spin order inhomogeneity by applying micro X-ray diffraction to La 1.72 Sr 0.28 NiO 4 , mapping the spin-density-wave order below the 120 K onset temperature. We find that the spin-density-wave order shows the formation of nanoscale puddles with large spatial fluctuations. The nano-puddle density changes on the microscopic scale forming a multiscale phase separation extending from nanoscale to micron scale with scale-free distribution. Indeed spin-density-wave striped puddles are disconnected by spatial regions with negligible spin-density-wave order. The present work highlights the complex spatial nanoscale phase separation of spin stripes in nickelate perovskites and opens new perspectives of local spin order control by strain.Condens. Matter 2019, 4, 77 2 of 10 the stripes phases have been the object of interest for decades [1][2][3], while in this last decade new scanning X-ray diffraction methods have been developed due to the ability to focus X-ray synchrotron radiation to micron and sub-micron spots. These methods have made it possible to obtain visualization of spatial topological inhomogeneity of charge density wave order in doped cuprate perovskites [4,5]. Short range generalized Wigner charge density waves have been found to be spatially inhomogeneous with the formation of "striped charge puddles" anti-correlated with competing puddles of "striped dopants rich clusters" [4][5][6]. These experimental results have opened a new era in the long-standing research of complexity in doped strongly correlated perovskites, since they have falsified popular stripes theories which for decades have assumed a homogeneous spatial distribution of spin stripes and charge-stripes. In this work we focus on the spin stripes phase in doped nickelate perovskites. In order to determine the role that the spatial distribution of ordered phases in cuprates plays for the superconductivity, it is instructive to study a non-superconducting reference system like the layered nickelates [7]. Keeping this idea in mind, we push forward the investigation of the spatial distribution of spin-density-wave stripes ordering (SDW-stripes) in La 2-x Sr x NiO 4 nickelates.It is well known that spin stripes appear in layered nickelates [7] in the doping interval 0.15 ≤ x ≤ 0.5 [7]. In the doping range 0.25 < x < 0.3 magnetic stripes and charge stripes can be easily investigated separately. In La 2-x Sr x NiO 4 the spin-order scattering exhibits peaks in the k-space for (1−ε; 0; l) with odd and even l, whereas charge-order scattering always peaks at (2ε; 0; l) with odd l, [7,8] where t...