Fractal Magnetic Textures in Rare Earth Nickelates*

Correlated electron systems often manifest emergent quantum phenomena at the macroscale. Many emergent quantum electronic phases are inherently inhomogeneous due to the presence of competing degrees of freedom near phase boundaries. The macroscopic properties of quantum materials are largely dependent on the microscopic organizing principle of the electronic textures. One example is near a critical point, where electrons tend to organize into self-similar patterns that look the same at all length scales. The resulting fractal geometry is a hallmark of criticality.

In this talk, I will present our results on imaging the fractal magnetic texture in rare earth nickelates NdNiO₃. The measurement was carried out using resonant magnetic X-ray scattering nanoprobe with sub-100 nm spatial resolution that we commissioned at NSLS-II. Our measurements reveal a highly textured magnetic fabric, which is robust and nonvolatile upon thermal cycle across the transition temperature. The scale-free distribution of antiferromagnetic domains and its non-integral dimensionality point to a hitherto-unobserved magnetic fractal geometry in this system. These scale-invariant textures directly reflect the continuous nature of the magnetic transition and the proximity of this system to a critical point. The present study not only exposes the near-critical behavior in rare earth nickelates but also underscores the potential for X-ray scattering nanoprobes to image the multiscale signatures of criticality near a critical point.